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Properties

Label 1232.4.do
Level $1232$
Weight $4$
Character orbit 1232.do
Rep. character $\chi_{1232}(51,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $9152$
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.do (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1232 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(768\)

Dimensions

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

Total New Old
Modular forms 9280 9280 0
Cusp forms 9152 9152 0
Eisenstein series 128 128 0

Trace form

\( 9152 q - 10 q^{2} - 6 q^{3} + 14 q^{4} - 6 q^{5} - 40 q^{6} - 40 q^{7} - 40 q^{8} + O(q^{10}) \) \( 9152 q - 10 q^{2} - 6 q^{3} + 14 q^{4} - 6 q^{5} - 40 q^{6} - 40 q^{7} - 40 q^{8} - 28 q^{11} - 16 q^{12} - 40 q^{13} - 188 q^{14} + 294 q^{16} - 20 q^{17} + 440 q^{18} - 10 q^{19} + 56 q^{20} - 2284 q^{22} - 688 q^{23} - 10 q^{24} - 6 q^{26} + 192 q^{27} - 20 q^{28} - 40 q^{29} - 10 q^{30} - 16 q^{33} - 20 q^{35} + 488 q^{36} - 30 q^{37} - 6 q^{38} - 20 q^{39} - 10 q^{40} - 1400 q^{42} + 1012 q^{44} + 876 q^{45} + 150 q^{46} + 56 q^{48} - 24 q^{49} - 40 q^{50} - 10 q^{51} - 10 q^{52} - 1134 q^{53} - 64 q^{55} - 4776 q^{56} - 2226 q^{58} - 694 q^{59} + 3902 q^{60} - 10 q^{61} - 40 q^{62} + 8096 q^{64} - 1344 q^{66} - 2056 q^{67} - 10 q^{68} + 300 q^{69} + 410 q^{70} + 400 q^{71} - 7660 q^{72} - 10 q^{74} - 290 q^{75} + 670 q^{77} + 7632 q^{78} + 4086 q^{80} - 87492 q^{81} + 26 q^{82} - 40 q^{83} + 12410 q^{84} - 40 q^{85} + 9268 q^{86} - 2172 q^{88} + 14540 q^{90} + 1796 q^{91} - 13468 q^{92} + 210 q^{93} + 10790 q^{94} - 10 q^{96} - 48 q^{97} - 4424 q^{99} + O(q^{100}) \)

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.