Space of modular forms of level 1232, weight 4, and Character 1232.cu

• Label: 1232.4.cu
• Level: $1232$
• Weight: $4$
• Character orbit: 1232.cu
• Rep. character: $\chi_{1232}(211,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $3456$
• Sturm bound: $768$

Defining parameters

Level:	\( N \)	\(=\)	\( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1232.cu (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 176 \)
Character field:			\(\Q(\zeta_{20})\)
Sturm bound:			\(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1232, [\chi])\).

	Total	New	Old
Modular forms	4640	3456	1184
Cusp forms	4576	3456	1120
Eisenstein series	64	0	64

Trace form

3456 * q + 20 * q^4 - 20 * q^11 - 96 * q^12 + 210 * q^14 + 300 * q^16 + 450 * q^18 + 550 * q^22 - 656 * q^23 + 1148 * q^26 + 4080 * q^30 + 1000 * q^34 - 24 * q^37 + 2072 * q^38 - 282 * q^44 + 42336 * q^49 + 9360 * q^52 - 1128 * q^53 - 576 * q^55 - 196 * q^56 - 2220 * q^58 + 1224 * q^60 + 476 * q^64 - 836 * q^66 - 2040 * q^67 - 15340 * q^68 + 504 * q^70 - 750 * q^72 - 9500 * q^74 - 6624 * q^75 - 952 * q^77 - 3304 * q^78 - 17200 * q^80 + 69984 * q^81 + 3920 * q^82 - 13400 * q^83 - 10 * q^86 + 19082 * q^88 + 25920 * q^90 + 14094 * q^92 - 18340 * q^94 + 3000 * q^96 + 8912 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(1232, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1232, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1232, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 2}\)