Properties

Label 2475.2.cw
Level $2475$
Weight $2$
Character orbit 2475.cw
Rep. character $\chi_{2475}(196,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $2848$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 2475 = 3^{2} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2475.cw (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2475 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2475, [\chi])\).

Total New Old
Modular forms 2912 2912 0
Cusp forms 2848 2848 0
Eisenstein series 64 64 0

Trace form

\( 2848 q - q^{2} - 14 q^{3} + 351 q^{4} - 2 q^{5} - 6 q^{7} - 20 q^{8} - 14 q^{9} + O(q^{10}) \) \( 2848 q - q^{2} - 14 q^{3} + 351 q^{4} - 2 q^{5} - 6 q^{7} - 20 q^{8} - 14 q^{9} - 20 q^{10} - 3 q^{11} + 20 q^{12} - 6 q^{13} - 17 q^{14} - 9 q^{15} + 351 q^{16} - 4 q^{17} - 4 q^{19} - 11 q^{20} - 9 q^{21} - 11 q^{22} - 10 q^{23} - 42 q^{24} + 4 q^{27} - 52 q^{28} - 25 q^{29} - 50 q^{30} - 10 q^{31} - 16 q^{32} + 6 q^{33} - 8 q^{34} - 52 q^{35} + 10 q^{36} - 16 q^{37} + q^{38} - 54 q^{39} + 7 q^{40} - 33 q^{41} - 2 q^{42} - 16 q^{43} - 36 q^{44} + 11 q^{45} - 20 q^{46} - 38 q^{47} + 65 q^{48} + 326 q^{49} + 5 q^{50} - 18 q^{51} + 15 q^{52} - 164 q^{53} - 12 q^{54} - 24 q^{55} - 7 q^{56} - 41 q^{58} - 4 q^{59} + 36 q^{60} - 6 q^{61} + 10 q^{62} - 15 q^{63} - 688 q^{64} + 4 q^{65} + 76 q^{66} - 15 q^{67} - 6 q^{68} + 21 q^{69} - 2 q^{70} + 26 q^{71} - 102 q^{72} - 4 q^{73} - 48 q^{74} + 87 q^{75} - 16 q^{76} + q^{77} - 14 q^{78} + 5 q^{79} + 108 q^{80} - 54 q^{81} - 20 q^{82} - 11 q^{83} - 49 q^{84} + 7 q^{85} + 3 q^{86} + 70 q^{87} - 23 q^{88} - 24 q^{89} - 44 q^{90} + 10 q^{91} + 30 q^{92} + 13 q^{93} - 45 q^{94} + 71 q^{95} + 136 q^{96} + 5 q^{97} - 76 q^{98} + 75 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2475, [\chi])\) into newform subspaces

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