Space of modular forms of level 3960, weight 2, and Character 3960.g

• Label: 3960.2.g
• Level: $3960$
• Weight: $2$
• Character orbit: 3960.g
• Rep. character: $\chi_{3960}(1099,\cdot)$
• Character field: $\Q$
• Dimension: $356$
• Sturm bound: $1728$

Defining parameters

Level:	\( N \)	\(=\)	\( 3960 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3960.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 440 \)
Character field:			\(\Q\)
Sturm bound:			\(1728\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3960, [\chi])\).

	Total	New	Old
Modular forms	880	364	516
Cusp forms	848	356	492
Eisenstein series	32	8	24

Trace form

\( 356 q - 4 q^{4} + 4 q^{11} - 16 q^{16} - 16 q^{20} - 4 q^{25} - 36 q^{26} - 16 q^{34} - 8 q^{44} - 340 q^{49} + 32 q^{56} + 24 q^{59} + 68 q^{64} + 28 q^{70} - 20 q^{80} + 20 q^{86} + 8 q^{89} + 64 q^{91}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3960, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3960, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3960, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(440, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1320, [\chi])\)\(^{\oplus 2}\)