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Properties

Label 3004.2.y
Level $3004$
Weight $2$
Character orbit 3004.y
Rep. character $\chi_{3004}(11,\cdot)$
Character field $\Q(\zeta_{150})$
Dimension $14960$
Sturm bound $752$

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Defining parameters

Level: \( N \) \(=\) \( 3004 = 2^{2} \cdot 751 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3004.y (of order \(150\) and degree \(40\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3004 \)
Character field: \(\Q(\zeta_{150})\)
Sturm bound: \(752\)

Dimensions

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

Total New Old
Modular forms 15120 15120 0
Cusp forms 14960 14960 0
Eisenstein series 160 160 0

Trace form

\( 14960 q - 20 q^{2} - 20 q^{4} - 80 q^{5} - 60 q^{6} - 80 q^{8} - 80 q^{9} + O(q^{10}) \) \( 14960 q - 20 q^{2} - 20 q^{4} - 80 q^{5} - 60 q^{6} - 80 q^{8} - 80 q^{9} - 80 q^{10} - 20 q^{12} - 240 q^{13} - 40 q^{14} + 20 q^{16} - 80 q^{17} - 40 q^{18} - 60 q^{20} - 80 q^{21} - 70 q^{22} - 50 q^{24} - 60 q^{25} + 30 q^{26} - 15 q^{28} - 80 q^{29} + 40 q^{30} + 20 q^{32} - 110 q^{33} - 35 q^{34} + 40 q^{36} - 80 q^{37} + 75 q^{38} + 15 q^{40} - 100 q^{41} - 90 q^{42} - 20 q^{44} + 40 q^{45} - 185 q^{46} - 50 q^{48} - 80 q^{49} - 40 q^{50} - 5 q^{52} - 60 q^{53} - 40 q^{54} + 380 q^{56} + 240 q^{57} - 10 q^{58} + 435 q^{60} - 90 q^{61} - 65 q^{62} - 320 q^{64} + 30 q^{66} - 40 q^{68} - 20 q^{69} - 515 q^{70} - 20 q^{72} - 120 q^{73} - 35 q^{74} + 20 q^{76} - 110 q^{77} + 90 q^{78} - 80 q^{80} - 80 q^{81} + 10 q^{82} - 40 q^{84} - 100 q^{85} + 205 q^{86} - 80 q^{88} - 120 q^{89} - 40 q^{90} + 340 q^{92} - 20 q^{93} - 40 q^{94} - 25 q^{96} - 40 q^{97} + 45 q^{98} + O(q^{100}) \)

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.