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Properties

Label 2475.2.cx
Level $2475$
Weight $2$
Character orbit 2475.cx
Rep. character $\chi_{2475}(421,\cdot)$
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.cx (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

\( 2848 q - q^{2} + q^{3} + 351 q^{4} - 2 q^{5} - 6 q^{7} + q^{9} + O(q^{10}) \) \( 2848 q - q^{2} + q^{3} + 351 q^{4} - 2 q^{5} - 6 q^{7} + q^{9} - 40 q^{10} - 3 q^{11} - 10 q^{12} - q^{13} - 22 q^{14} - 14 q^{15} + 341 q^{16} - 24 q^{17} - 20 q^{18} - 4 q^{19} - 31 q^{20} - 24 q^{21} - 11 q^{22} - 10 q^{23} + 8 q^{24} - 40 q^{26} - 26 q^{27} - 12 q^{28} - 25 q^{29} + 30 q^{30} - 10 q^{31} - 16 q^{32} + 66 q^{33} - 8 q^{34} - 52 q^{35} + 20 q^{36} + 24 q^{37} - 9 q^{38} - 9 q^{39} - 18 q^{40} - 33 q^{41} + 88 q^{42} - 16 q^{43} - 16 q^{44} - 39 q^{45} - 40 q^{46} + 7 q^{47} - 50 q^{48} + 326 q^{49} + 25 q^{50} - 18 q^{51} + 50 q^{52} + 16 q^{53} - 32 q^{54} - 14 q^{55} + 28 q^{56} + 60 q^{57} - 21 q^{58} - 4 q^{59} - 39 q^{60} - q^{61} - 160 q^{62} - 15 q^{63} - 648 q^{64} - 16 q^{65} + 46 q^{66} - 15 q^{67} - 26 q^{68} - 4 q^{69} - 2 q^{70} + 26 q^{71} + 73 q^{72} - 4 q^{73} - 48 q^{74} - 43 q^{75} - 16 q^{76} - 39 q^{77} - 24 q^{78} + 30 q^{79} + 148 q^{80} - 19 q^{81} - 20 q^{82} - 66 q^{83} + 66 q^{84} - 43 q^{85} + 3 q^{86} - 120 q^{87} - 63 q^{88} + 26 q^{89} + 26 q^{90} + 10 q^{91} + 15 q^{92} - 57 q^{93} - 30 q^{94} - 74 q^{95} + 116 q^{96} - 26 q^{98} - 10 q^{99} + O(q^{100}) \)

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.