Properties

Label 1232.4.cj
Level $1232$
Weight $4$
Character orbit 1232.cj
Rep. character $\chi_{1232}(285,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $2288$
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.cj (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1232 \)
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 2320 0
Cusp forms 2288 2288 0
Eisenstein series 32 32 0

Trace form

\( 2288 q - 12 q^{3} - 24 q^{4} - 12 q^{5} + O(q^{10}) \) \( 2288 q - 12 q^{3} - 24 q^{4} - 12 q^{5} - 22 q^{11} - 12 q^{12} - 184 q^{14} - 32 q^{15} - 304 q^{16} - 748 q^{22} - 12 q^{26} - 24 q^{31} - 12 q^{33} - 528 q^{36} + 12 q^{37} - 12 q^{38} + 1380 q^{42} + 1018 q^{44} - 336 q^{45} - 24 q^{47} - 16 q^{49} - 756 q^{53} - 3252 q^{56} + 2216 q^{58} - 2076 q^{59} + 476 q^{60} - 5112 q^{64} - 4110 q^{66} + 2036 q^{67} - 3860 q^{70} - 1512 q^{75} + 682 q^{77} + 6960 q^{78} - 12 q^{80} + 87472 q^{81} + 84 q^{82} - 3480 q^{86} - 2166 q^{88} - 1712 q^{91} + 9664 q^{92} - 220 q^{93} - 4832 q^{99} + O(q^{100}) \)

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

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