Space of modular forms of level 1248, weight 2, and Character 1248.ci

• Label: 1248.2.ci
• Level: $1248$
• Weight: $2$
• Character orbit: 1248.ci
• Rep. character: $\chi_{1248}(181,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $448$
• Sturm bound: $448$

Defining parameters

Level:	\( N \)	\(=\)	\( 1248 = 2^{5} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1248.ci (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 416 \)
Character field:			\(\Q(\zeta_{8})\)
Sturm bound:			\(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1248, [\chi])\).

	Total	New	Old
Modular forms	912	448	464
Cusp forms	880	448	432
Eisenstein series	32	0	32

Trace form

\( 448 q + 16 q^{12} - 64 q^{14} - 16 q^{22} - 40 q^{26} + 80 q^{38} - 80 q^{40} + 8 q^{52} + 32 q^{55} - 48 q^{62} + 48 q^{68} - 32 q^{75} - 24 q^{78} + 80 q^{82} - 80 q^{88} - 48 q^{91} + 144 q^{92} - 48 q^{94}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1248, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1248, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1248, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(416, [\chi])\)\(^{\oplus 2}\)