Properties

Label 3004.2.d
Level $3004$
Weight $2$
Character orbit 3004.d
Rep. character $\chi_{3004}(3003,\cdot)$
Character field $\Q$
Dimension $374$
Sturm bound $752$

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Defining parameters

Level: \( N \) \(=\) \( 3004 = 2^{2} \cdot 751 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3004.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3004 \)
Character field: \(\Q\)
Sturm bound: \(752\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3004, [\chi])\).

Total New Old
Modular forms 378 378 0
Cusp forms 374 374 0
Eisenstein series 4 4 0

Trace form

\( 374 q - 4 q^{2} - 8 q^{4} - 4 q^{5} + 2 q^{8} + 366 q^{9} + O(q^{10}) \) \( 374 q - 4 q^{2} - 8 q^{4} - 4 q^{5} + 2 q^{8} + 366 q^{9} - 16 q^{10} - 12 q^{13} - 32 q^{16} - 22 q^{18} - 2 q^{20} - 8 q^{21} + 370 q^{25} - 18 q^{26} + 16 q^{32} - 24 q^{33} - 62 q^{36} + 20 q^{37} - 2 q^{38} + 22 q^{40} + 16 q^{42} - 60 q^{45} - 28 q^{46} + 342 q^{49} - 14 q^{50} + 2 q^{52} - 44 q^{53} + 20 q^{61} - 62 q^{64} - 40 q^{65} - 8 q^{66} - 60 q^{72} + 10 q^{74} + 36 q^{76} + 24 q^{80} + 358 q^{81} - 2 q^{84} + 56 q^{86} + 4 q^{89} - 66 q^{90} - 36 q^{92} + 32 q^{93} + 30 q^{94} - 28 q^{97} + 56 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3004, [\chi])\) into newform subspaces

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