Properties

Label 1183.2.bb
Level $1183$
Weight $2$
Character orbit 1183.bb
Rep. character $\chi_{1183}(437,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $368$
Sturm bound $242$

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Defining parameters

Level: \( N \) \(=\) \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1183.bb (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 544 448 96
Cusp forms 432 368 64
Eisenstein series 112 80 32

Trace form

\( 368q + 2q^{2} + 12q^{3} + 6q^{5} + 6q^{7} + 16q^{8} + 144q^{9} + O(q^{10}) \) \( 368q + 2q^{2} + 12q^{3} + 6q^{5} + 6q^{7} + 16q^{8} + 144q^{9} + 10q^{11} - 80q^{14} + 44q^{15} + 116q^{16} + 4q^{18} - 12q^{19} + 26q^{21} + 12q^{24} + 6q^{28} - 32q^{29} - 24q^{31} - 4q^{32} - 48q^{33} - 52q^{35} + 8q^{37} + 60q^{40} + 12q^{42} + 42q^{44} + 24q^{45} - 12q^{46} - 30q^{47} - 88q^{50} - 20q^{53} - 78q^{54} - 40q^{57} - 26q^{58} + 54q^{59} - 16q^{60} + 84q^{61} - 24q^{63} - 144q^{66} - 16q^{67} + 84q^{68} - 50q^{70} + 36q^{71} - 22q^{72} - 66q^{73} - 12q^{74} + 12q^{79} - 138q^{80} - 8q^{81} + 58q^{84} + 84q^{85} - 42q^{86} - 192q^{87} + 60q^{89} - 72q^{92} - 6q^{93} + 84q^{94} + 42q^{96} + 86q^{98} + 24q^{99} + O(q^{100}) \)

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

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