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

• Label: 2912.2.fe
• Level: $2912$
• Weight: $2$
• Character orbit: 2912.fe
• Rep. character: $\chi_{2912}(145,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $432$
• Sturm bound: $896$

Defining parameters

Level:	\( N \)	\(=\)	\( 2912 = 2^{5} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2912.fe (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 728 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(896\)

Dimensions

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

	Total	New	Old
Modular forms	1856	464	1392
Cusp forms	1728	432	1296
Eisenstein series	128	32	96

Trace form

\( 432 q + 8 q^{7} - 196 q^{9} + 28 q^{15} - 24 q^{17} + 12 q^{31} - 12 q^{33} - 20 q^{39} + 12 q^{47} + 36 q^{49} + 4 q^{57} - 32 q^{63} - 4 q^{65} + 48 q^{71} - 12 q^{73} + 8 q^{79} - 136 q^{81} - 12 q^{89}+O(q^{100}) \)

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

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