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Properties

Label 1116.2.bl
Level $1116$
Weight $2$
Character orbit 1116.bl
Rep. character $\chi_{1116}(191,\cdot)$
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.bl (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

\( 376 q - 6 q^{2} - 2 q^{4} - 6 q^{5} + 6 q^{6} - 2 q^{9} + O(q^{10}) \) \( 376 q - 6 q^{2} - 2 q^{4} - 6 q^{5} + 6 q^{6} - 2 q^{9} - 4 q^{10} - 4 q^{12} + 2 q^{13} - 2 q^{16} - 2 q^{18} - 14 q^{21} - 3 q^{22} - 4 q^{24} + 174 q^{25} + 6 q^{26} - 6 q^{28} - 12 q^{29} + 9 q^{30} + 24 q^{32} - 14 q^{33} + 11 q^{34} - 16 q^{36} - 4 q^{37} + 3 q^{38} + 8 q^{40} - 6 q^{41} - 55 q^{42} - 78 q^{44} + 2 q^{45} - 12 q^{46} + q^{48} + 166 q^{49} + 32 q^{52} + 36 q^{53} - 6 q^{54} - 108 q^{56} - 14 q^{57} - 19 q^{58} + 54 q^{60} - 4 q^{61} + 45 q^{62} - 2 q^{64} - 6 q^{65} - 30 q^{66} - 4 q^{69} - 3 q^{70} - 55 q^{72} - 4 q^{73} - 9 q^{74} - 6 q^{76} - 60 q^{77} + 32 q^{78} - 15 q^{80} - 2 q^{81} - 22 q^{82} - 80 q^{84} - 14 q^{85} - 18 q^{88} - 27 q^{90} - 6 q^{92} + 36 q^{93} - 12 q^{94} - 36 q^{96} - 4 q^{97} - 153 q^{98} + O(q^{100}) \)

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.