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Properties

Label 2004.2.c
Level $2004$
Weight $2$
Character orbit 2004.c
Rep. character $\chi_{2004}(335,\cdot)$
Character field $\Q$
Dimension $332$
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.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
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 340 332 8
Cusp forms 332 332 0
Eisenstein series 8 0 8

Trace form

\( 332 q - 4 q^{9} + O(q^{10}) \) \( 332 q - 4 q^{9} + 10 q^{12} - 8 q^{13} - 16 q^{16} + 10 q^{18} - 4 q^{22} - 10 q^{24} - 324 q^{25} + 28 q^{28} - 16 q^{33} - 12 q^{34} - 8 q^{37} - 21 q^{42} + 24 q^{45} + 32 q^{46} + 15 q^{48} - 316 q^{49} + 4 q^{52} - q^{54} + 8 q^{57} + 24 q^{58} - 24 q^{60} + 24 q^{61} - 12 q^{64} + 32 q^{66} - 24 q^{69} - 45 q^{72} - 8 q^{73} + 56 q^{76} - 38 q^{78} + 36 q^{81} - 48 q^{82} + 27 q^{84} - 24 q^{88} - 20 q^{90} - 24 q^{93} + 12 q^{94} + 14 q^{96} - 8 q^{97} + O(q^{100}) \)

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.