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Properties

Label 1116.2.z
Level $1116$
Weight $2$
Character orbit 1116.z
Rep. character $\chi_{1116}(367,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $376$
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.z (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1116 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(384\)

Dimensions

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

Total New Old
Modular forms 392 392 0
Cusp forms 376 376 0
Eisenstein series 16 16 0

Trace form

\( 376 q - 2 q^{2} - 2 q^{4} + 2 q^{5} - 12 q^{6} - 2 q^{8} - 2 q^{9} + O(q^{10}) \) \( 376 q - 2 q^{2} - 2 q^{4} + 2 q^{5} - 12 q^{6} - 2 q^{8} - 2 q^{9} - 12 q^{12} - 6 q^{13} - 10 q^{14} - 2 q^{16} - 12 q^{17} + 14 q^{20} - 6 q^{21} - 15 q^{22} + 6 q^{24} - 170 q^{25} - 6 q^{28} - 15 q^{30} - 12 q^{32} - 14 q^{33} - 9 q^{34} - 16 q^{36} - 12 q^{37} - q^{38} - 6 q^{40} + 2 q^{41} - 27 q^{42} - 18 q^{44} - 6 q^{45} + 39 q^{48} + 166 q^{49} + 66 q^{50} - 48 q^{53} - 34 q^{56} - 6 q^{57} + 27 q^{58} + 66 q^{60} - 21 q^{62} - 50 q^{64} - 6 q^{65} + 36 q^{66} - 28 q^{69} - 15 q^{70} + 3 q^{72} - 12 q^{73} - 93 q^{74} + 18 q^{76} - 84 q^{77} - 28 q^{78} - 57 q^{80} - 2 q^{81} - 18 q^{82} - 36 q^{84} + 30 q^{85} + 61 q^{90} - 12 q^{93} - 28 q^{94} - 60 q^{96} - 4 q^{97} + 19 q^{98} + O(q^{100}) \)

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.