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Properties

Label 3004.2.be
Level $3004$
Weight $2$
Character orbit 3004.be
Rep. character $\chi_{3004}(3,\cdot)$
Character field $\Q(\zeta_{750})$
Dimension $74800$
Sturm bound $752$

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Defining parameters

Level: \( N \) \(=\) \( 3004 = 2^{2} \cdot 751 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3004.be (of order \(750\) and degree \(200\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3004 \)
Character field: \(\Q(\zeta_{750})\)
Sturm bound: \(752\)

Dimensions

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

Total New Old
Modular forms 75600 75600 0
Cusp forms 74800 74800 0
Eisenstein series 800 800 0

Trace form

\( 74800 q - 225 q^{2} - 225 q^{4} - 400 q^{5} - 200 q^{6} - 150 q^{8} - 400 q^{9} + O(q^{10}) \) \( 74800 q - 225 q^{2} - 225 q^{4} - 400 q^{5} - 200 q^{6} - 150 q^{8} - 400 q^{9} - 200 q^{10} - 200 q^{12} - 200 q^{13} - 200 q^{14} - 325 q^{16} - 400 q^{17} - 200 q^{18} - 200 q^{20} - 400 q^{21} - 300 q^{22} - 200 q^{24} - 400 q^{25} - 200 q^{26} - 200 q^{28} - 400 q^{29} - 200 q^{30} - 100 q^{32} - 400 q^{33} - 200 q^{34} - 200 q^{36} - 400 q^{37} - 200 q^{38} - 200 q^{40} - 400 q^{41} - 200 q^{42} - 200 q^{44} - 400 q^{45} - 200 q^{46} - 200 q^{48} - 400 q^{49} - 200 q^{50} - 200 q^{52} - 400 q^{53} - 200 q^{54} - 700 q^{56} - 700 q^{57} - 200 q^{58} - 800 q^{60} - 400 q^{61} - 200 q^{62} + 150 q^{64} - 400 q^{65} - 200 q^{66} - 200 q^{68} - 400 q^{69} + 200 q^{70} - 100 q^{72} - 600 q^{73} - 200 q^{74} - 225 q^{76} - 400 q^{77} - 175 q^{78} - 150 q^{80} - 400 q^{81} - 200 q^{82} - 200 q^{84} - 400 q^{85} - 375 q^{86} - 200 q^{88} - 400 q^{89} - 200 q^{90} - 675 q^{92} - 400 q^{93} - 200 q^{94} - 200 q^{96} - 400 q^{97} - 200 q^{98} + O(q^{100}) \)

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.