Error in modular form knowl

[jwj61]

From the feedback page:

In https://www.lmfdb.org/knowledge/show/cmf.decomposition.old.gamma1?timestamp=1544710775662027

The decomposition formula current reads "for $M$ dividing the level $N$... $ S_k^{\mathrm{old}}(\Gamma1(N)) \cong \bigoplus{M,t} \alpha_{M,t}\left(S_k^{\mathrm{new}}(\Gamma_1(M))\right). $". This inadvertently makes $S_k^{\mathrm{new}}(\Gamma_1(N))$ part of $S_k^{\mathrm{old}}(\Gamma_1(N))$ because $N$ divides $N$. The correct way to state this can be either

• "for proper divisor $M$ of level $N$ ,... $S_k^{\mathrm{old}}\cong$...", or
• "for $M$ dividing the level $N$,... $S_k\cong$..."

This error also shows up on all pages for Gamma1 modular form spaces. For example, at the bottom of https://www.lmfdb.org/ModularForm/GL2/Q/holomorphic/64/2/, the decomposition of $S_{2}^{\mathrm{old}}(\Gamma1(64))$ includes $S{2}^{\mathrm{new}}(\Gamma1(64))^{\oplus 1}$. It should be with either the left side corrected to $S{2}(\Gamma1(64))$, or removing $S{2}^{\mathrm{new}}(\Gamma_1(64))^{\oplus 1}$ from the right side.

In comparison, the decomposition of newform space (https://www.lmfdb.org/knowledge/show/cmf.decomposition.old.gamma0chi?timestamp=1544710745874729) and newfor space pages (https://www.lmfdb.org/ModularForm/GL2/Q/holomorphic/64/2/a/) don't have this problem.

[AndrewVSutherland]

I think the 2nd suggested fix is cleaner (it decomposes the entire cuspidal space into newspaces, rather than decomposing the oldspace). But we will then want to change the decomposition formulas on spaces with character to be consistent (as noted above, they currently decompose the oldspace correclty).