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

• Label: 1248.2.ec
• Level: $1248$
• Weight: $2$
• Character orbit: 1248.ec
• Rep. character: $\chi_{1248}(61,\cdot)$
• Character field: $\Q(\zeta_{24})$
• Dimension: $896$
• Sturm bound: $448$

Defining parameters

Level:	\( N \)	\(=\)	\( 1248 = 2^{5} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1248.ec (of order \(24\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 416 \)
Character field:			\(\Q(\zeta_{24})\)
Sturm bound:			\(448\)

Dimensions

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

	Total	New	Old
Modular forms	1824	896	928
Cusp forms	1760	896	864
Eisenstein series	64	0	64

Trace form

896 * q - 32 * q^12 + 64 * q^14 - 32 * q^20 + 16 * q^22 + 80 * q^26 + 40 * q^28 + 40 * q^32 - 80 * q^34 - 80 * q^38 - 80 * q^40 + 64 * q^46 - 88 * q^52 - 32 * q^55 + 64 * q^59 - 96 * q^60 - 48 * q^62 - 48 * q^68 + 336 * q^70 - 128 * q^71 - 32 * q^75 + 128 * q^76 - 24 * q^78 - 80 * q^82 + 128 * q^86 + 40 * q^88 + 48 * q^91 - 288 * q^92 - 24 * q^94 + 80 * q^96

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

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