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Properties

Label 1183.2.ba
Level $1183$
Weight $2$
Character orbit 1183.ba
Rep. character $\chi_{1183}(89,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $372$
Sturm bound $242$

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Defining parameters

Level: \( N \) \(=\) \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1183.ba (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(242\)

Dimensions

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

Total New Old
Modular forms 540 452 88
Cusp forms 428 372 56
Eisenstein series 112 80 32

Trace form

\( 372 q + 2 q^{2} + 6 q^{3} + 6 q^{5} + 12 q^{6} + 6 q^{7} + 4 q^{8} + 146 q^{9} + O(q^{10}) \) \( 372 q + 2 q^{2} + 6 q^{3} + 6 q^{5} + 12 q^{6} + 6 q^{7} + 4 q^{8} + 146 q^{9} + 6 q^{10} - 2 q^{11} + 8 q^{12} - 32 q^{14} - 10 q^{15} - 260 q^{16} + 12 q^{17} - 2 q^{18} - 14 q^{19} - 36 q^{20} + 6 q^{21} + 12 q^{22} + 18 q^{24} - 2 q^{28} + 16 q^{29} + 30 q^{30} + 4 q^{31} - 10 q^{32} + 12 q^{33} + 12 q^{34} + 32 q^{35} - 54 q^{36} + 10 q^{37} - 120 q^{40} + 18 q^{41} + 42 q^{42} - 48 q^{43} + 6 q^{44} + 6 q^{45} - 24 q^{46} + 6 q^{47} - 204 q^{48} + 50 q^{49} - 10 q^{50} + 12 q^{51} - 44 q^{53} + 30 q^{54} - 30 q^{55} - 54 q^{56} - 12 q^{57} + 46 q^{58} - 42 q^{59} - 10 q^{60} - 66 q^{61} - 36 q^{62} - 54 q^{63} - 198 q^{66} + 10 q^{67} + 42 q^{69} + 88 q^{70} + 42 q^{71} - 46 q^{72} - 40 q^{73} - 12 q^{74} + 40 q^{75} + 52 q^{76} - 24 q^{79} - 30 q^{80} + 14 q^{81} + 54 q^{82} - 66 q^{83} - 104 q^{84} + 54 q^{85} + 18 q^{86} + 6 q^{88} - 72 q^{90} + 132 q^{92} - 20 q^{93} + 6 q^{94} + 66 q^{96} + 62 q^{97} + 56 q^{98} + 36 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1183, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)