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Properties

Label 1183.2.bg
Level $1183$
Weight $2$
Character orbit 1183.bg
Rep. character $\chi_{1183}(64,\cdot)$
Character field $\Q(\zeta_{26})$
Dimension $1080$
Sturm bound $242$

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Defining parameters

Level: \( N \) \(=\) \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1183.bg (of order \(26\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 169 \)
Character field: \(\Q(\zeta_{26})\)
Sturm bound: \(242\)

Dimensions

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

Total New Old
Modular forms 1464 1080 384
Cusp forms 1416 1080 336
Eisenstein series 48 0 48

Trace form

\( 1080 q + 88 q^{4} - 82 q^{9} + O(q^{10}) \) \( 1080 q + 88 q^{4} - 82 q^{9} - 8 q^{10} + 12 q^{12} - 8 q^{13} + 4 q^{14} - 52 q^{15} - 84 q^{16} + 8 q^{17} - 78 q^{18} - 68 q^{22} + 148 q^{23} + 156 q^{24} + 74 q^{25} - 12 q^{26} + 12 q^{27} + 16 q^{29} - 128 q^{30} - 104 q^{31} - 156 q^{32} - 130 q^{34} + 8 q^{35} + 80 q^{36} + 4 q^{38} + 60 q^{39} - 112 q^{40} + 4 q^{42} + 8 q^{43} + 130 q^{45} + 52 q^{47} - 70 q^{48} + 90 q^{49} - 138 q^{51} + 150 q^{52} + 26 q^{53} + 160 q^{55} - 12 q^{56} - 78 q^{57} - 52 q^{58} + 208 q^{60} - 28 q^{61} + 102 q^{62} + 64 q^{64} + 6 q^{65} - 420 q^{66} - 52 q^{67} - 8 q^{68} - 12 q^{69} - 338 q^{72} - 60 q^{75} - 208 q^{76} - 16 q^{77} + 244 q^{78} - 16 q^{79} - 42 q^{81} + 288 q^{82} - 260 q^{83} - 182 q^{85} - 160 q^{87} - 268 q^{88} - 36 q^{90} + 2 q^{91} + 56 q^{92} + 130 q^{93} - 84 q^{94} - 120 q^{95} + 338 q^{96} + O(q^{100}) \)

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

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