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

• Label: 3330.2.dt
• Level: $3330$
• Weight: $2$
• Character orbit: 3330.dt
• Rep. character: $\chi_{3330}(29,\cdot)$
• Character field: $\Q(\zeta_{12})$
• 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.dt (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1665 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(1368\)

Dimensions

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

	Total	New	Old
Modular forms	2768	912	1856
Cusp forms	2704	912	1792
Eisenstein series	64	0	64

Trace form

\( 912 q + 16 q^{9} + O(q^{10}) \)

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

\( S_{2}^{\mathrm{old}}(3330, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1665, [\chi])\)\(^{\oplus 2}\)