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Properties

Label 832.4.ct
Level $832$
Weight $4$
Character orbit 832.ct
Rep. character $\chi_{832}(115,\cdot)$
Character field $\Q(\zeta_{48})$
Dimension $5344$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 832 = 2^{6} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 832.ct (of order \(48\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 832 \)
Character field: \(\Q(\zeta_{48})\)
Sturm bound: \(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(832, [\chi])\).

Total New Old
Modular forms 5408 5408 0
Cusp forms 5344 5344 0
Eisenstein series 64 64 0

Trace form

\( 5344 q - 16 q^{2} - 8 q^{3} - 24 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 8 q^{9} + O(q^{10}) \) \( 5344 q - 16 q^{2} - 8 q^{3} - 24 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 8 q^{9} - 24 q^{10} - 16 q^{11} + 192 q^{12} - 16 q^{13} - 32 q^{14} - 24 q^{15} - 8 q^{16} - 24 q^{17} - 16 q^{18} - 16 q^{19} + 144 q^{20} - 16 q^{21} - 8 q^{22} - 24 q^{23} - 16 q^{24} - 16 q^{26} - 32 q^{27} + 1504 q^{28} - 8 q^{29} - 152 q^{30} - 32 q^{31} + 1224 q^{32} - 1080 q^{34} - 8 q^{35} - 24 q^{36} - 16 q^{37} + 2384 q^{39} - 32 q^{40} - 16 q^{41} - 8 q^{42} - 24 q^{43} - 16 q^{44} - 232 q^{45} - 2896 q^{46} + 14656 q^{48} - 24 q^{49} + 4248 q^{50} - 3472 q^{52} - 32 q^{53} - 16 q^{54} - 584 q^{55} + 1976 q^{56} - 16 q^{57} + 2360 q^{58} - 2768 q^{59} - 5424 q^{60} - 8 q^{61} - 24 q^{62} - 32 q^{65} - 32 q^{66} - 16 q^{67} - 2072 q^{68} - 24 q^{69} - 3256 q^{70} - 464 q^{71} - 664 q^{72} - 16 q^{73} - 8 q^{74} + 976 q^{75} - 4304 q^{76} - 5080 q^{78} - 32 q^{79} + 9264 q^{80} - 8 q^{81} - 24 q^{82} - 16 q^{83} - 8984 q^{84} + 1984 q^{85} - 1344 q^{86} - 8 q^{87} - 24 q^{88} - 16 q^{89} - 3456 q^{90} - 16 q^{91} - 32 q^{92} + 200 q^{93} + 184 q^{94} - 48 q^{95} - 22688 q^{96} + 48 q^{98} + 21016 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(832, [\chi])\) into newform subspaces

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