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Properties

Label 2004.2.b
Level $2004$
Weight $2$
Character orbit 2004.b
Rep. character $\chi_{2004}(667,\cdot)$
Character field $\Q$
Dimension $168$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 2004 = 2^{2} \cdot 3 \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2004.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 668 \)
Character field: \(\Q\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2004, [\chi])\).

Total New Old
Modular forms 340 168 172
Cusp forms 332 168 164
Eisenstein series 8 0 8

Trace form

\( 168 q - 4 q^{4} + 4 q^{6} - 168 q^{9} + O(q^{10}) \) \( 168 q - 4 q^{4} + 4 q^{6} - 168 q^{9} - 8 q^{12} - 16 q^{14} - 20 q^{16} - 28 q^{22} - 4 q^{24} - 168 q^{25} - 4 q^{28} + 4 q^{36} + 8 q^{38} + 20 q^{42} + 12 q^{44} + 16 q^{48} - 152 q^{49} + 48 q^{50} - 4 q^{54} - 36 q^{56} + 12 q^{58} - 48 q^{61} + 4 q^{62} - 28 q^{64} - 16 q^{65} - 8 q^{66} + 40 q^{76} + 16 q^{77} + 168 q^{81} - 40 q^{84} + 32 q^{85} + 80 q^{88} + 16 q^{89} - 32 q^{94} + 24 q^{96} - 64 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2004, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2004, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2004, [\chi]) \cong \)