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Properties

Label 2475.2.ej
Level $2475$
Weight $2$
Character orbit 2475.ej
Rep. character $\chi_{2475}(229,\cdot)$
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.ej (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

\( 2848 q - 5 q^{2} - 353 q^{4} - 4 q^{5} - 4 q^{6} - 20 q^{8} - 14 q^{9} + O(q^{10}) \) \( 2848 q - 5 q^{2} - 353 q^{4} - 4 q^{5} - 4 q^{6} - 20 q^{8} - 14 q^{9} - 44 q^{10} - 3 q^{11} - 50 q^{12} + 15 q^{14} - 11 q^{15} + 335 q^{16} - 20 q^{17} + 20 q^{18} - 4 q^{19} - 19 q^{20} - 15 q^{21} - 5 q^{22} - 10 q^{23} + 26 q^{24} - 48 q^{26} - 20 q^{28} - 25 q^{29} + 18 q^{30} + 8 q^{31} - 50 q^{33} - 4 q^{34} + 28 q^{35} - 6 q^{36} - 20 q^{37} - 35 q^{38} - 90 q^{39} + 3 q^{40} + 31 q^{41} + 70 q^{42} - 20 q^{44} - 45 q^{45} + 12 q^{46} - 25 q^{48} - 338 q^{49} + 21 q^{50} - 6 q^{51} - 45 q^{52} - 20 q^{53} - 36 q^{54} + 72 q^{55} + 11 q^{56} + 60 q^{57} - 5 q^{58} - 4 q^{59} + 66 q^{60} - 6 q^{61} - 170 q^{62} + 25 q^{63} + 616 q^{64} - 20 q^{65} - 52 q^{66} + 5 q^{67} + 40 q^{68} + 35 q^{69} + 56 q^{70} + 26 q^{71} - 90 q^{72} - 20 q^{73} - 44 q^{74} - 59 q^{75} - 64 q^{76} - 5 q^{77} - 70 q^{78} + 5 q^{79} + 36 q^{80} + 10 q^{81} + 20 q^{82} - 55 q^{83} + 25 q^{84} - 13 q^{85} - 5 q^{86} - 20 q^{87} - 5 q^{88} - 104 q^{89} - 96 q^{90} - 18 q^{91} - 55 q^{93} - 53 q^{94} + 39 q^{95} - 240 q^{96} - 5 q^{97} - 60 q^{98} + 75 q^{99} + O(q^{100}) \)

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.