Space of modular forms of level 3864, weight 2, and Character 3864.dp

• Label: 3864.2.dp
• Level: $3864$
• Weight: $2$
• Character orbit: 3864.dp
• Rep. character: $\chi_{3864}(85,\cdot)$
• Character field: $\Q(\zeta_{22})$
• Dimension: $2880$
• Sturm bound: $1536$

Defining parameters

Level:	\( N \)	\(=\)	\( 3864 = 2^{3} \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3864.dp (of order \(22\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 184 \)
Character field:			\(\Q(\zeta_{22})\)
Sturm bound:			\(1536\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3864, [\chi])\).

	Total	New	Old
Modular forms	7760	2880	4880
Cusp forms	7600	2880	4720
Eisenstein series	160	0	160

Trace form

2880 * q - 4 * q^2 - 4 * q^4 - 8 * q^6 - 8 * q^7 - 4 * q^8 + 288 * q^9 + 8 * q^10 + 4 * q^14 + 16 * q^15 + 12 * q^16 + 4 * q^18 - 40 * q^20 - 40 * q^22 + 8 * q^23 + 8 * q^24 + 288 * q^25 + 40 * q^26 - 4 * q^28 - 32 * q^31 + 36 * q^32 - 44 * q^34 + 26 * q^36 + 76 * q^40 + 130 * q^44 - 176 * q^46 + 144 * q^48 - 288 * q^49 - 86 * q^50 + 32 * q^52 - 36 * q^54 + 28 * q^56 - 54 * q^58 + 36 * q^60 + 8 * q^62 + 8 * q^63 - 28 * q^64 - 32 * q^66 + 48 * q^68 - 16 * q^71 + 4 * q^72 - 66 * q^74 + 276 * q^76 + 96 * q^79 + 16 * q^80 - 288 * q^81 + 296 * q^82 + 400 * q^86 - 10 * q^88 - 8 * q^90 - 32 * q^92 + 104 * q^94 - 160 * q^95 - 48 * q^96 + 18 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(3864, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3864, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3864, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(184, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(552, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1288, [\chi])\)\(^{\oplus 2}\)