Space of modular forms of level 2912, weight 2, and Character 2912.db

• Label: 2912.2.db
• Level: $2912$
• Weight: $2$
• Character orbit: 2912.db
• Rep. character: $\chi_{2912}(815,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $216$
• Sturm bound: $896$

Defining parameters

Level:	\( N \)	\(=\)	\( 2912 = 2^{5} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2912.db (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 728 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(896\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2912, [\chi])\).

	Total	New	Old
Modular forms	928	232	696
Cusp forms	864	216	648
Eisenstein series	64	16	48

Trace form

\( 216 q + 6 q^{3} + 102 q^{9} - 2 q^{11} + 6 q^{19} - 96 q^{25} - 6 q^{33} - 18 q^{35} + 4 q^{43} + 6 q^{49} - 8 q^{51} - 36 q^{57} - 12 q^{65} - 2 q^{67} - 36 q^{73} - 80 q^{81} - 42 q^{91} + 40 q^{99}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2912, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2912, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2912, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(728, [\chi])\)\(^{\oplus 3}\)