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

• Label: 3330.2.n
• Level: $3330$
• Weight: $2$
• Character orbit: 3330.n
• Rep. character: $\chi_{3330}(179,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $152$
• Sturm bound: $1368$

Defining parameters

Level:	\( N \)	\(=\)	\( 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3330.n (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 555 \)
Character field:			\(\Q(i)\)
Sturm bound:			\(1368\)

Dimensions

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

	Total	New	Old
Modular forms	1400	152	1248
Cusp forms	1336	152	1184
Eisenstein series	64	0	64

Trace form

\( 152 q - 152 q^{16} - 32 q^{19} - 48 q^{31} + 32 q^{34} - 64 q^{46} - 216 q^{49} - 32 q^{55} + 72 q^{61} + 32 q^{70} - 32 q^{76} - 48 q^{79} - 16 q^{91}+O(q^{100}) \)

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

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