Space of modular forms of level 3680, weight 2, and Character 3680.m

• Label: 3680.2.m
• Level: $3680$
• Weight: $2$
• Character orbit: 3680.m
• Rep. character: $\chi_{3680}(3679,\cdot)$
• Character field: $\Q$
• Dimension: $144$
• Sturm bound: $1152$

Defining parameters

Level:	\( N \)	\(=\)	\( 3680 = 2^{5} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3680.m (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 460 \)
Character field:			\(\Q\)
Sturm bound:			\(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3680, [\chi])\).

	Total	New	Old
Modular forms	592	144	448
Cusp forms	560	144	416
Eisenstein series	32	0	32

Trace form

\( 144 q + 144 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3680, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3680, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3680, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(460, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(920, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1840, [\chi])\)\(^{\oplus 2}\)