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Properties

Label 2012.2.b
Level $2012$
Weight $2$
Character orbit 2012.b
Rep. character $\chi_{2012}(2011,\cdot)$
Character field $\Q$
Dimension $250$
Sturm bound $504$

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Defining parameters

Level: \( N \) \(=\) \( 2012 = 2^{2} \cdot 503 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2012.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2012 \)
Character field: \(\Q\)
Sturm bound: \(504\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2012, [\chi])\).

Total New Old
Modular forms 254 254 0
Cusp forms 250 250 0
Eisenstein series 4 4 0

Trace form

\( 250 q - 2 q^{2} + 2 q^{4} + 6 q^{6} - 8 q^{8} - 250 q^{9} + O(q^{10}) \) \( 250 q - 2 q^{2} + 2 q^{4} + 6 q^{6} - 8 q^{8} - 250 q^{9} + 4 q^{12} - 4 q^{13} + 16 q^{14} + 2 q^{16} - 14 q^{18} - 10 q^{22} + 26 q^{24} - 246 q^{25} + 12 q^{26} + 14 q^{28} + 18 q^{32} + 8 q^{33} - 22 q^{42} - 28 q^{44} - 8 q^{46} + 10 q^{48} - 250 q^{49} - 34 q^{50} - 52 q^{52} - 40 q^{54} + 38 q^{56} - 36 q^{61} + 8 q^{64} + 70 q^{66} + 48 q^{69} - 82 q^{72} - 4 q^{73} - 16 q^{77} - 52 q^{78} + 282 q^{81} + 22 q^{84} - 40 q^{85} + 6 q^{86} - 20 q^{88} - 12 q^{92} - 60 q^{94} + 114 q^{96} - 4 q^{97} - 96 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2012, [\chi])\) into newform subspaces

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