Properties

Label 1183.2.w
Level $1183$
Weight $2$
Character orbit 1183.w
Rep. character $\chi_{1183}(19,\cdot)$
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.w (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

\( 372q + 2q^{2} + 6q^{4} + 6q^{5} - 12q^{6} - 2q^{7} + 4q^{8} - 292q^{9} + O(q^{10}) \) \( 372q + 2q^{2} + 6q^{4} + 6q^{5} - 12q^{6} - 2q^{7} + 4q^{8} - 292q^{9} + 12q^{10} - 2q^{11} - 8q^{12} - 32q^{14} - 10q^{15} + 130q^{16} + 6q^{17} + 4q^{18} + 8q^{19} + 36q^{20} + 2q^{21} + 12q^{22} + 6q^{23} - 12q^{24} + 18q^{28} + 16q^{29} + 38q^{31} + 20q^{32} - 18q^{33} - 12q^{34} + 14q^{35} - 54q^{36} + 16q^{37} - 120q^{40} - 18q^{41} - 24q^{42} - 48q^{43} + 6q^{44} - 12q^{45} - 18q^{46} + 42q^{47} + 204q^{48} - 8q^{49} - 10q^{50} - 12q^{51} - 44q^{53} + 30q^{54} + 30q^{55} + 24q^{56} - 12q^{57} - 62q^{58} + 6q^{59} - 16q^{60} + 36q^{62} + 38q^{63} - 198q^{66} + 4q^{67} - 66q^{68} - 42q^{69} - 68q^{70} + 42q^{71} + 38q^{72} - 14q^{73} + 6q^{74} + 20q^{75} - 52q^{76} - 24q^{79} - 12q^{80} - 28q^{81} + 108q^{82} + 66q^{83} + 56q^{84} + 54q^{85} + 30q^{86} + 174q^{87} + 30q^{89} + 72q^{90} + 132q^{92} - 14q^{93} + 6q^{95} - 18q^{96} - 62q^{97} - 112q^{98} + 36q^{99} + O(q^{100}) \)

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

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