Space of modular forms of level 3808, weight 2, and Character 3808.cv

• Label: 3808.2.cv
• Level: $3808$
• Weight: $2$
• Character orbit: 3808.cv
• Rep. character: $\chi_{3808}(477,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $1536$
• Sturm bound: $1152$

Defining parameters

Level:	\( N \)	\(=\)	\( 3808 = 2^{5} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3808.cv (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 32 \)
Character field:			\(\Q(\zeta_{8})\)
Sturm bound:			\(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3808, [\chi])\).

	Total	New	Old
Modular forms	2320	1536	784
Cusp forms	2288	1536	752
Eisenstein series	32	0	32

Trace form

1536 * q + 64 * q^12 + 40 * q^16 + 40 * q^18 + 56 * q^22 + 16 * q^23 - 80 * q^26 + 96 * q^27 - 40 * q^30 + 8 * q^36 + 112 * q^38 + 96 * q^39 - 80 * q^40 + 16 * q^43 - 8 * q^44 + 32 * q^53 - 128 * q^55 - 56 * q^56 - 144 * q^58 + 16 * q^60 + 48 * q^62 - 80 * q^63 + 128 * q^66 - 80 * q^67 - 96 * q^70 - 144 * q^72 - 56 * q^74 - 128 * q^75 + 128 * q^76 + 32 * q^77 - 48 * q^78 - 128 * q^80 + 128 * q^86 + 224 * q^87 - 160 * q^88 + 8 * q^92 + 256 * q^95 + 128 * q^96 + 256 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(3808, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3808, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3808, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(544, [\chi])\)\(^{\oplus 2}\)