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Properties

Label 3004.2.r
Level $3004$
Weight $2$
Character orbit 3004.r
Rep. character $\chi_{3004}(195,\cdot)$
Character field $\Q(\zeta_{50})$
Dimension $7480$
Sturm bound $752$

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Defining parameters

Level: \( N \) \(=\) \( 3004 = 2^{2} \cdot 751 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3004.r (of order \(50\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3004 \)
Character field: \(\Q(\zeta_{50})\)
Sturm bound: \(752\)

Dimensions

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

Total New Old
Modular forms 7560 7560 0
Cusp forms 7480 7480 0
Eisenstein series 80 80 0

Trace form

\( 7480 q - 40 q^{2} - 40 q^{4} - 40 q^{5} - 30 q^{6} - 40 q^{8} - 40 q^{9} + O(q^{10}) \) \( 7480 q - 40 q^{2} - 40 q^{4} - 40 q^{5} - 30 q^{6} - 40 q^{8} - 40 q^{9} - 10 q^{10} - 40 q^{12} - 120 q^{13} - 20 q^{14} - 80 q^{16} - 40 q^{17} - 20 q^{18} - 40 q^{21} + 10 q^{22} - 10 q^{24} - 60 q^{25} - 15 q^{26} - 45 q^{28} - 40 q^{29} + 20 q^{30} - 80 q^{32} - 10 q^{33} - 25 q^{34} + 20 q^{36} - 100 q^{37} + 15 q^{38} - 75 q^{40} - 50 q^{41} - 120 q^{42} + 20 q^{44} + 20 q^{45} + 5 q^{46} - 25 q^{48} - 40 q^{49} - 20 q^{50} + 65 q^{52} - 30 q^{53} - 20 q^{54} + 160 q^{56} - 240 q^{57} - 65 q^{58} + 105 q^{60} - 30 q^{61} + 5 q^{62} - 160 q^{64} + 30 q^{66} - 20 q^{68} - 100 q^{69} - 25 q^{70} - 40 q^{72} - 25 q^{74} + 40 q^{76} - 10 q^{77} - 40 q^{80} - 40 q^{81} - 25 q^{82} - 20 q^{84} - 50 q^{85} - 160 q^{86} + 20 q^{88} - 60 q^{89} - 20 q^{90} - 400 q^{92} - 100 q^{93} - 20 q^{94} - 35 q^{96} - 20 q^{97} - 105 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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