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Properties

Label 1183.2.bk
Level $1183$
Weight $2$
Character orbit 1183.bk
Rep. character $\chi_{1183}(29,\cdot)$
Character field $\Q(\zeta_{39})$
Dimension $2208$
Sturm bound $242$

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Defining parameters

Level: \( N \) \(=\) \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1183.bk (of order \(39\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 169 \)
Character field: \(\Q(\zeta_{39})\)
Sturm bound: \(242\)

Dimensions

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

Total New Old
Modular forms 2976 2208 768
Cusp forms 2880 2208 672
Eisenstein series 96 0 96

Trace form

\( 2208 q + 2 q^{2} + 94 q^{4} + 8 q^{5} - 6 q^{6} + 94 q^{9} + O(q^{10}) \) \( 2208 q + 2 q^{2} + 94 q^{4} + 8 q^{5} - 6 q^{6} + 94 q^{9} - 6 q^{10} + 2 q^{11} + 12 q^{12} + 2 q^{13} - 8 q^{14} - 50 q^{15} + 98 q^{16} - 10 q^{17} + 120 q^{18} + 8 q^{19} + 10 q^{20} + 4 q^{21} - 58 q^{22} - 154 q^{23} - 184 q^{24} - 160 q^{25} + 12 q^{26} + 36 q^{27} - 4 q^{29} + 236 q^{30} - 100 q^{31} - 174 q^{32} - 22 q^{33} - 122 q^{34} + 8 q^{35} + 76 q^{36} - 16 q^{37} + 52 q^{38} - 64 q^{39} - 178 q^{40} - 16 q^{41} + 4 q^{42} - 24 q^{44} - 120 q^{45} + 20 q^{46} - 2 q^{47} - 120 q^{48} + 92 q^{49} + 46 q^{50} - 110 q^{51} - 208 q^{52} - 64 q^{53} - 282 q^{55} + 12 q^{56} - 58 q^{57} - 46 q^{58} + 10 q^{59} - 132 q^{60} - 24 q^{61} - 138 q^{62} - 4 q^{63} - 152 q^{64} - 10 q^{65} + 244 q^{66} - 72 q^{67} - 78 q^{68} - 12 q^{69} - 48 q^{70} - 8 q^{71} - 312 q^{72} + 16 q^{73} - 74 q^{74} - 30 q^{75} + 434 q^{76} - 8 q^{77} - 186 q^{78} + 12 q^{79} + 34 q^{80} + 96 q^{81} - 316 q^{82} + 508 q^{83} - 22 q^{84} - 210 q^{85} - 48 q^{86} - 226 q^{87} + 502 q^{88} - 228 q^{89} - 20 q^{90} - 2 q^{91} + 64 q^{92} - 112 q^{93} - 92 q^{94} + 112 q^{95} - 126 q^{96} + 26 q^{97} + 2 q^{98} - 76 q^{99} + O(q^{100}) \)

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

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