Space of modular forms of level 3040, weight 2, and Character 3040.cl

• Label: 3040.2.cl
• Level: $3040$
• Weight: $2$
• Character orbit: 3040.cl
• Rep. character: $\chi_{3040}(381,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $1152$
• Sturm bound: $960$

Defining parameters

Level:	\( N \)	\(=\)	\( 3040 = 2^{5} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3040.cl (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 32 \)
Character field:			\(\Q(\zeta_{8})\)
Sturm bound:			\(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3040, [\chi])\).

	Total	New	Old
Modular forms	1936	1152	784
Cusp forms	1904	1152	752
Eisenstein series	32	0	32

Trace form

1152 * q + 32 * q^14 + 80 * q^16 + 80 * q^18 + 32 * q^20 - 16 * q^22 + 32 * q^23 - 80 * q^24 + 96 * q^27 + 48 * q^36 + 96 * q^39 - 80 * q^42 + 32 * q^43 - 16 * q^44 - 96 * q^52 + 64 * q^53 - 16 * q^56 - 144 * q^58 - 64 * q^59 - 160 * q^63 + 32 * q^66 - 160 * q^67 - 48 * q^68 - 64 * q^71 - 144 * q^72 - 16 * q^74 + 64 * q^77 - 144 * q^78 - 32 * q^80 + 160 * q^83 - 112 * q^84 - 208 * q^86 + 192 * q^91 + 16 * q^92 + 96 * q^94 + 64 * q^95 + 32 * q^96 + 64 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(3040, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3040, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3040, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(608, [\chi])\)\(^{\oplus 2}\)