Space of modular forms of level 2352, weight 4, and Character 2352.bt

• Label: 2352.4.bt
• Level: $2352$
• Weight: $4$
• Character orbit: 2352.bt
• Rep. character: $\chi_{2352}(19,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $1920$
• Sturm bound: $1792$

Defining parameters

Level:	\( N \)	\(=\)	\( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2352.bt (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 112 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(1792\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2352, [\chi])\).

	Total	New	Old
Modular forms	5440	1920	3520
Cusp forms	5312	1920	3392
Eisenstein series	128	0	128

Trace form

1920 * q - 40 * q^4 - 168 * q^8 + 36 * q^10 + 80 * q^11 - 120 * q^16 + 72 * q^18 + 1448 * q^22 - 1312 * q^23 + 1600 * q^29 - 32 * q^37 + 2340 * q^40 + 3232 * q^43 + 232 * q^44 + 700 * q^46 - 5656 * q^50 - 2160 * q^52 + 1504 * q^53 - 1252 * q^58 - 4128 * q^59 - 2448 * q^60 + 8792 * q^64 - 4104 * q^66 - 2664 * q^67 + 6060 * q^68 + 896 * q^71 + 1224 * q^72 + 476 * q^74 - 3816 * q^78 + 7524 * q^80 + 77760 * q^81 + 5220 * q^82 + 5592 * q^86 + 1300 * q^88 - 12696 * q^92 - 7020 * q^94 - 7740 * q^96 + 1440 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(2352, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(2352, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2352, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(784, [\chi])\)\(^{\oplus 2}\)