Space of modular forms of level 1240, weight 2, and Character 1240.bo

• Label: 1240.2.bo
• Level: $1240$
• Weight: $2$
• Character orbit: 1240.bo
• Rep. character: $\chi_{1240}(491,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $256$
• Sturm bound: $384$

Defining parameters

Level:	\( N \)	\(=\)	\( 1240 = 2^{3} \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1240.bo (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 248 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1240, [\chi])\).

	Total	New	Old
Modular forms	392	256	136
Cusp forms	376	256	120
Eisenstein series	16	0	16

Trace form

256 * q + 4 * q^4 - 12 * q^6 - 12 * q^8 + 128 * q^9 - 2 * q^10 - 8 * q^14 + 4 * q^16 + 6 * q^18 - 8 * q^19 - 4 * q^20 + 128 * q^25 + 20 * q^32 - 48 * q^34 + 14 * q^36 + 10 * q^38 - 16 * q^40 - 66 * q^42 - 42 * q^44 + 84 * q^48 + 160 * q^49 - 8 * q^51 + 84 * q^52 + 18 * q^56 - 48 * q^57 + 64 * q^59 - 38 * q^62 - 20 * q^64 + 4 * q^66 + 156 * q^68 - 8 * q^70 - 22 * q^72 - 48 * q^73 - 24 * q^74 - 50 * q^76 - 12 * q^78 - 128 * q^81 - 52 * q^82 - 6 * q^84 - 30 * q^86 + 42 * q^88 + 8 * q^90 - 80 * q^94 - 126 * q^96 - 32 * q^97 - 74 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(1240, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1240, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1240, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(248, [\chi])\)\(^{\oplus 2}\)