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Properties

Label 1183.2.bt
Level $1183$
Weight $2$
Character orbit 1183.bt
Rep. character $\chi_{1183}(36,\cdot)$
Character field $\Q(\zeta_{78})$
Dimension $2160$
Sturm bound $242$

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Defining parameters

Level: \( N \) \(=\) \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1183.bt (of order \(78\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 169 \)
Character field: \(\Q(\zeta_{78})\)
Sturm bound: \(242\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1183, [\chi])\).

Total New Old
Modular forms 2976 2160 816
Cusp forms 2880 2160 720
Eisenstein series 96 0 96

Trace form

\( 2160 q - 88 q^{4} + 18 q^{6} + 88 q^{9} + O(q^{10}) \) \( 2160 q - 88 q^{4} + 18 q^{6} + 88 q^{9} - 4 q^{10} - 6 q^{11} - 12 q^{12} - 4 q^{13} + 8 q^{14} + 46 q^{15} + 84 q^{16} + 4 q^{17} - 156 q^{18} + 12 q^{20} + 38 q^{22} - 142 q^{23} - 168 q^{24} + 184 q^{25} + 42 q^{26} - 12 q^{27} - 10 q^{29} - 364 q^{30} + 104 q^{31} + 120 q^{32} + 30 q^{33} + 130 q^{34} - 8 q^{35} - 74 q^{36} + 42 q^{37} - 4 q^{38} - 48 q^{39} + 112 q^{40} - 30 q^{41} - 4 q^{42} + 16 q^{43} - 130 q^{45} - 12 q^{46} - 286 q^{47} + 64 q^{48} - 90 q^{49} + 18 q^{50} + 78 q^{51} - 132 q^{52} + 22 q^{53} - 12 q^{54} - 166 q^{55} + 12 q^{56} + 78 q^{57} + 64 q^{58} - 18 q^{59} - 208 q^{60} - 14 q^{61} - 114 q^{62} - 12 q^{63} + 164 q^{64} - 60 q^{65} - 108 q^{66} + 76 q^{67} - 4 q^{68} + 12 q^{69} + 24 q^{71} + 278 q^{72} + 18 q^{74} - 30 q^{75} - 398 q^{76} - 8 q^{77} - 250 q^{78} + 76 q^{79} + 72 q^{80} + 66 q^{81} - 246 q^{82} - 520 q^{83} - 18 q^{84} + 230 q^{85} + 202 q^{87} - 458 q^{88} + 12 q^{89} - 120 q^{90} - 14 q^{91} + 16 q^{92} - 112 q^{93} + 60 q^{94} - 72 q^{95} - 338 q^{96} - 6 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1183, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1183, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1183, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 2}\)