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Properties

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 $768$

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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

\( 3456 q + 20 q^{4} + O(q^{10}) \) \( 3456 q + 20 q^{4} - 20 q^{11} - 96 q^{12} + 210 q^{14} + 300 q^{16} + 450 q^{18} + 550 q^{22} - 656 q^{23} + 1148 q^{26} + 4080 q^{30} + 1000 q^{34} - 24 q^{37} + 2072 q^{38} - 282 q^{44} + 42336 q^{49} + 9360 q^{52} - 1128 q^{53} - 576 q^{55} - 196 q^{56} - 2220 q^{58} + 1224 q^{60} + 476 q^{64} - 836 q^{66} - 2040 q^{67} - 15340 q^{68} + 504 q^{70} - 750 q^{72} - 9500 q^{74} - 6624 q^{75} - 952 q^{77} - 3304 q^{78} - 17200 q^{80} + 69984 q^{81} + 3920 q^{82} - 13400 q^{83} - 10 q^{86} + 19082 q^{88} + 25920 q^{90} + 14094 q^{92} - 18340 q^{94} + 3000 q^{96} + 8912 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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