Space of modular forms of level 1140, weight 2, and Character 1140.bc

• Label: 1140.2.bc
• Level: $1140$
• Weight: $2$
• Character orbit: 1140.bc
• Rep. character: $\chi_{1140}(31,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $160$
• Sturm bound: $480$

Defining parameters

Level:	\( N \)	\(=\)	\( 1140 = 2^{2} \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1140.bc (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 76 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1140, [\chi])\).

	Total	New	Old
Modular forms	496	160	336
Cusp forms	464	160	304
Eisenstein series	32	0	32

Trace form

160 * q - 2 * q^4 + 2 * q^6 - 80 * q^9 + 6 * q^10 - 24 * q^13 - 2 * q^16 - 24 * q^21 - 4 * q^24 - 80 * q^25 - 40 * q^26 - 40 * q^28 + 60 * q^32 + 66 * q^34 - 2 * q^36 - 60 * q^38 - 24 * q^41 + 20 * q^44 + 48 * q^48 - 128 * q^49 - 12 * q^52 + 48 * q^53 + 2 * q^54 - 24 * q^57 + 88 * q^58 - 6 * q^60 - 8 * q^61 + 72 * q^62 + 64 * q^64 + 8 * q^66 - 104 * q^68 - 36 * q^70 + 24 * q^73 - 80 * q^74 + 60 * q^76 + 32 * q^77 - 60 * q^78 - 16 * q^80 - 80 * q^81 + 44 * q^82 + 16 * q^85 - 84 * q^86 + 72 * q^89 - 6 * q^90 + 24 * q^92 + 8 * q^93 + 36 * q^96 + 48 * q^97 + 24 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(1140, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1140, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1140, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(380, [\chi])\)\(^{\oplus 2}\)