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Properties

Label 1116.2.ci
Level $1116$
Weight $2$
Character orbit 1116.ci
Rep. character $\chi_{1116}(139,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1504$
Sturm bound $384$

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Defining parameters

Level: \( N \) \(=\) \( 1116 = 2^{2} \cdot 3^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1116.ci (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1116 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1116, [\chi])\).

Total New Old
Modular forms 1568 1568 0
Cusp forms 1504 1504 0
Eisenstein series 64 64 0

Trace form

\( 1504 q - 3 q^{2} - 3 q^{4} - 16 q^{5} - 30 q^{8} - 12 q^{9} + O(q^{10}) \) \( 1504 q - 3 q^{2} - 3 q^{4} - 16 q^{5} - 30 q^{8} - 12 q^{9} + 20 q^{12} - 10 q^{13} + 5 q^{14} - 3 q^{16} - 40 q^{17} - 4 q^{18} + 21 q^{20} - 20 q^{21} - 5 q^{22} - 10 q^{24} - 704 q^{25} + 4 q^{28} - 10 q^{29} - 28 q^{32} - 24 q^{33} - 5 q^{34} - 10 q^{36} - 7 q^{38} - 6 q^{40} - 6 q^{41} - 35 q^{42} + 90 q^{44} - 18 q^{45} - 80 q^{46} + 20 q^{48} - 170 q^{49} - 46 q^{50} - 5 q^{52} - 40 q^{53} - 65 q^{54} + 6 q^{56} + 40 q^{58} - 60 q^{60} - 20 q^{62} + 66 q^{64} + 90 q^{65} + 146 q^{66} - 96 q^{69} + 9 q^{70} - 48 q^{72} - 40 q^{73} + 5 q^{74} - 23 q^{76} - 10 q^{77} - 99 q^{78} + 198 q^{80} - 12 q^{81} - 56 q^{82} - 80 q^{84} - 60 q^{85} + 45 q^{86} - 40 q^{89} + 11 q^{90} + 34 q^{93} + 18 q^{94} - 95 q^{96} - 6 q^{97} + 100 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1116, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.