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

• Label: 1232.4.ci
• Level: $1232$
• Weight: $4$
• Character orbit: 1232.ci
• Rep. character: $\chi_{1232}(221,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $1920$
• Sturm bound: $768$

Defining parameters

Level:	\( N \)	\(=\)	\( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1232.ci (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 112 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(768\)

Dimensions

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

	Total	New	Old
Modular forms	2320	1920	400
Cusp forms	2288	1920	368
Eisenstein series	32	0	32

Trace form

1920 * q - 168 * q^8 + 12 * q^10 - 208 * q^14 - 140 * q^18 - 80 * q^20 - 1000 * q^24 + 380 * q^28 + 1160 * q^30 + 1488 * q^31 - 980 * q^32 - 576 * q^34 + 456 * q^35 - 880 * q^36 - 440 * q^38 + 984 * q^40 - 2560 * q^42 - 616 * q^44 - 700 * q^46 - 3760 * q^47 + 2032 * q^48 - 2856 * q^50 + 1400 * q^51 + 1548 * q^52 + 2580 * q^56 + 3388 * q^58 - 688 * q^59 + 3664 * q^60 + 1872 * q^62 - 3864 * q^64 - 1100 * q^66 - 1848 * q^67 - 2020 * q^68 + 5404 * q^70 - 3976 * q^72 - 3640 * q^74 - 6120 * q^76 + 11560 * q^78 + 2508 * q^80 + 77760 * q^81 + 3480 * q^82 - 4880 * q^83 + 4484 * q^84 + 3936 * q^86 + 9360 * q^90 + 848 * q^91 - 5544 * q^92 - 7728 * q^95 - 8068 * q^96 + 4244 * q^98

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

\( S_{4}^{\mathrm{old}}(1232, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)