Space of modular forms of level 3330, weight 2, and Character 3330.fp

• Label: 3330.2.fp
• Level: $3330$
• Weight: $2$
• Character orbit: 3330.fp
• Rep. character: $\chi_{3330}(53,\cdot)$
• Character field: $\Q(\zeta_{36})$
• Dimension: $912$
• Sturm bound: $1368$

Defining parameters

Level:	\( N \)	\(=\)	\( 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3330.fp (of order \(36\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 555 \)
Character field:			\(\Q(\zeta_{36})\)
Sturm bound:			\(1368\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3330, [\chi])\).

	Total	New	Old
Modular forms	8400	912	7488
Cusp forms	8016	912	7104
Eisenstein series	384	0	384

Trace form

\( 912 q - 96 q^{25} + 96 q^{31} + 48 q^{37} - 24 q^{40} - 96 q^{55} + 12 q^{58} - 96 q^{61} + 96 q^{67} - 48 q^{70} + 24 q^{73} + 12 q^{85} + 48 q^{88} + 48 q^{91} + 96 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3330, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3330, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3330, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(555, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1110, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1665, [\chi])\)\(^{\oplus 2}\)