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Properties

Label 832.4.cp
Level $832$
Weight $4$
Character orbit 832.cp
Rep. character $\chi_{832}(29,\cdot)$
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.cp (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

\( 5344 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 32 q^{5} - 8 q^{6} - 8 q^{7} - 32 q^{8} - 8 q^{9} + O(q^{10}) \) \( 5344 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 32 q^{5} - 8 q^{6} - 8 q^{7} - 32 q^{8} - 8 q^{9} - 8 q^{10} - 8 q^{11} - 32 q^{12} - 16 q^{13} - 32 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{17} - 32 q^{18} - 8 q^{19} - 8 q^{20} - 32 q^{21} - 8 q^{22} - 8 q^{23} - 8 q^{24} - 32 q^{25} - 96 q^{26} - 32 q^{27} - 768 q^{28} - 8 q^{29} - 8 q^{30} - 1248 q^{32} + 1968 q^{34} - 8 q^{35} - 8 q^{36} - 8 q^{37} - 912 q^{38} - 16 q^{39} - 3312 q^{40} - 8 q^{41} - 8 q^{42} - 8 q^{43} - 32 q^{44} - 8 q^{45} - 8 q^{46} - 32 q^{47} - 8 q^{48} - 8 q^{49} - 8 q^{50} - 32 q^{51} + 3296 q^{52} - 32 q^{53} - 8 q^{54} - 584 q^{55} - 8 q^{56} - 32 q^{57} - 4760 q^{58} - 2760 q^{59} - 9824 q^{60} - 8 q^{61} - 2872 q^{62} - 16 q^{63} - 32 q^{64} - 32 q^{65} - 160 q^{66} - 8 q^{67} - 2072 q^{68} - 8 q^{69} + 8032 q^{70} + 888 q^{71} - 656 q^{72} - 32 q^{73} - 8 q^{74} - 4424 q^{75} - 8 q^{76} - 32 q^{77} + 1976 q^{78} - 32 q^{79} - 18568 q^{80} - 8 q^{81} - 13928 q^{82} - 32 q^{83} - 8 q^{84} - 8 q^{85} - 2112 q^{86} - 8 q^{87} - 3128 q^{88} - 8 q^{89} + 18688 q^{90} - 16 q^{91} - 32 q^{92} + 208 q^{93} - 8 q^{94} - 32 q^{96} - 8 q^{98} - 464 q^{99} + O(q^{100}) \)

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.