Space of modular forms of level 3696, weight 2, and Character 3696.do

• Label: 3696.2.do
• Level: $3696$
• Weight: $2$
• Character orbit: 3696.do
• Rep. character: $\chi_{3696}(127,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $288$
• Sturm bound: $1536$

Defining parameters

Level:	\( N \)	\(=\)	\( 3696 = 2^{4} \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3696.do (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 44 \)
Character field:			\(\Q(\zeta_{10})\)
Sturm bound:			\(1536\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3696, [\chi])\).

	Total	New	Old
Modular forms	3168	288	2880
Cusp forms	2976	288	2688
Eisenstein series	192	0	192

Trace form

\( 288 q + 72 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3696, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3696, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3696, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(132, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(264, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(308, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(528, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(616, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(924, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1232, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1848, [\chi])\)\(^{\oplus 2}\)