Space of modular forms of level 3380, weight 2, and Character 3380.db

• Label: 3380.2.db
• Level: $3380$
• Weight: $2$
• Character orbit: 3380.db
• Rep. character: $\chi_{3380}(59,\cdot)$
• Character field: $\Q(\zeta_{156})$
• Dimension: $26016$
• Sturm bound: $1092$

Defining parameters

Level:	\( N \)	\(=\)	\( 3380 = 2^{2} \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3380.db (of order \(156\) and degree \(48\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3380 \)
Character field:			\(\Q(\zeta_{156})\)
Sturm bound:			\(1092\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3380, [\chi])\).

	Total	New	Old
Modular forms	26400	26400	0
Cusp forms	26016	26016	0
Eisenstein series	384	384	0

Trace form

\( 26016 q - 92 q^{4} - 94 q^{5} - 104 q^{6} + 868 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3380, [\chi])\) into newform subspaces

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