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Properties

Label 1116.2.cd
Level $1116$
Weight $2$
Character orbit 1116.cd
Rep. character $\chi_{1116}(479,\cdot)$
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.cd (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

\( 1504 q - 9 q^{2} - 3 q^{4} + 4 q^{6} + 45 q^{8} - 18 q^{9} + O(q^{10}) \) \( 1504 q - 9 q^{2} - 3 q^{4} + 4 q^{6} + 45 q^{8} - 18 q^{9} - 6 q^{10} - 12 q^{12} - 6 q^{13} - 12 q^{14} - 3 q^{16} - 11 q^{18} - 12 q^{20} - 42 q^{21} - 11 q^{22} - 6 q^{24} - 1392 q^{25} + 6 q^{26} - 14 q^{28} - 18 q^{29} - 4 q^{30} - 54 q^{32} - 6 q^{33} + 17 q^{34} - 16 q^{36} - 16 q^{37} - 15 q^{38} + 36 q^{40} - 30 q^{41} + 134 q^{42} + 87 q^{44} - 66 q^{45} - 38 q^{46} - 50 q^{48} + 322 q^{49} + 33 q^{50} + 11 q^{52} + 36 q^{53} + 51 q^{54} + 4 q^{57} - 76 q^{58} + 61 q^{60} - 16 q^{61} + 45 q^{62} - 63 q^{64} - 30 q^{65} - 190 q^{66} + 15 q^{68} + 42 q^{69} + 98 q^{70} - 12 q^{72} - 36 q^{73} + 15 q^{74} - 8 q^{76} + 30 q^{77} + 18 q^{78} + 60 q^{80} - 18 q^{81} + 2 q^{82} + 26 q^{84} + 54 q^{85} + 78 q^{86} - 4 q^{88} - 14 q^{90} - 24 q^{92} - 14 q^{93} + 2 q^{94} + 129 q^{96} - 6 q^{97} - 153 q^{98} + O(q^{100}) \)

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.