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Properties

Label 1503.2.g
Level $1503$
Weight $2$
Character orbit 1503.g
Rep. character $\chi_{1503}(500,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $332$
Sturm bound $336$

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Defining parameters

Level: \( N \) \(=\) \( 1503 = 3^{2} \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1503.g (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1503 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1503, [\chi])\).

Total New Old
Modular forms 340 340 0
Cusp forms 332 332 0
Eisenstein series 8 8 0

Trace form

\( 332 q - 6 q^{2} - 4 q^{3} + 162 q^{4} - 22 q^{6} - 2 q^{7} - 16 q^{9} + O(q^{10}) \) \( 332 q - 6 q^{2} - 4 q^{3} + 162 q^{4} - 22 q^{6} - 2 q^{7} - 16 q^{9} - 18 q^{11} - 14 q^{12} + 6 q^{14} - 158 q^{16} + 34 q^{18} - 8 q^{19} - 20 q^{21} - 10 q^{22} - 54 q^{24} - 160 q^{25} + 20 q^{27} - 42 q^{29} - 2 q^{31} + 114 q^{32} - 4 q^{33} + 42 q^{36} - 78 q^{38} - 23 q^{42} - 6 q^{47} - 10 q^{48} - 144 q^{49} + 72 q^{50} - 29 q^{54} + 60 q^{56} - 2 q^{57} + 8 q^{58} - 14 q^{61} - 292 q^{64} + 6 q^{65} + 70 q^{66} - 23 q^{72} + 28 q^{75} - 30 q^{76} - 108 q^{77} + 60 q^{84} + 2 q^{87} + 58 q^{88} + 20 q^{94} + 28 q^{96} - 2 q^{97} - 106 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1503, [\chi])\) into newform subspaces

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