Properties

Label 2475.2.em
Level $2475$
Weight $2$
Character orbit 2475.em
Rep. character $\chi_{2475}(239,\cdot)$
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.em (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

\( 2848 q - 15 q^{2} - 353 q^{4} - 12 q^{5} - 14 q^{9} + O(q^{10}) \) \( 2848 q - 15 q^{2} - 353 q^{4} - 12 q^{5} - 14 q^{9} + 20 q^{10} - 9 q^{11} - 10 q^{12} - 10 q^{13} - 3 q^{14} + 15 q^{15} + 335 q^{16} - 20 q^{19} - 9 q^{20} - 15 q^{21} - 5 q^{22} - 30 q^{23} - 10 q^{24} - 20 q^{28} - 15 q^{29} + 20 q^{30} - 10 q^{31} - 120 q^{32} - 20 q^{33} - 4 q^{34} - 6 q^{36} - 20 q^{37} + 75 q^{38} - 5 q^{40} - 15 q^{41} + 70 q^{42} - 63 q^{45} - 20 q^{46} - 25 q^{48} + 326 q^{49} - 15 q^{50} - 50 q^{51} + 35 q^{52} + 80 q^{54} - 104 q^{55} - 3 q^{56} - 5 q^{58} + 6 q^{59} - 4 q^{60} + 25 q^{63} + 616 q^{64} + 90 q^{65} + 36 q^{66} - 25 q^{67} - 60 q^{68} + 21 q^{69} - 46 q^{70} + 70 q^{72} - 20 q^{73} - 60 q^{74} - 61 q^{75} - 15 q^{77} + 30 q^{78} - 35 q^{79} - 54 q^{81} + 20 q^{82} - 165 q^{83} + 45 q^{84} - 5 q^{85} - 3 q^{86} - 5 q^{88} - 290 q^{90} + 10 q^{91} - 55 q^{93} + 15 q^{94} - 15 q^{95} - 5 q^{97} - 107 q^{99} + O(q^{100}) \)

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

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