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Properties

Label 2475.2.ef
Level $2475$
Weight $2$
Character orbit 2475.ef
Rep. character $\chi_{2475}(4,\cdot)$
Character field $\Q(\zeta_{30})$
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.ef (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2475 \)
Character field: \(\Q(\zeta_{30})\)
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

\( 2848 q - 5 q^{2} - 10 q^{3} - 353 q^{4} - 4 q^{5} + 6 q^{6} - 40 q^{8} - 4 q^{9} + O(q^{10}) \) \( 2848 q - 5 q^{2} - 10 q^{3} - 353 q^{4} - 4 q^{5} + 6 q^{6} - 40 q^{8} - 4 q^{9} - 24 q^{10} - 3 q^{11} - 30 q^{12} - 5 q^{13} - 5 q^{14} - q^{15} + 345 q^{16} - 20 q^{17} - 4 q^{19} + 21 q^{20} - 5 q^{22} - 10 q^{23} - 24 q^{24} - 8 q^{26} - 10 q^{27} - 25 q^{29} - 52 q^{30} - 12 q^{31} - 35 q^{33} - 4 q^{34} - 22 q^{35} + 4 q^{36} - 20 q^{37} - 15 q^{38} - 15 q^{39} + 3 q^{40} - 134 q^{41} + 20 q^{44} - 45 q^{45} + 12 q^{46} - 5 q^{47} - 338 q^{49} - 19 q^{50} - 6 q^{51} + 5 q^{52} - 120 q^{53} - 16 q^{54} - 38 q^{55} - 24 q^{56} - 25 q^{58} + q^{59} + 81 q^{60} - q^{61} + 170 q^{62} + 656 q^{64} - 62 q^{66} + 5 q^{67} - 20 q^{68} + 50 q^{69} + 6 q^{70} - 44 q^{71} - 44 q^{74} - 9 q^{75} + 16 q^{76} + 65 q^{77} + 40 q^{78} - 25 q^{79} - 384 q^{80} - 20 q^{81} + 20 q^{82} - 5 q^{83} - 25 q^{84} - 13 q^{85} - 5 q^{86} - 20 q^{87} - 15 q^{88} - 54 q^{89} - 156 q^{90} + 32 q^{91} - 85 q^{92} + 45 q^{93} + 27 q^{94} + 39 q^{95} - 60 q^{96} - 20 q^{97} + 30 q^{98} - 10 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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