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Properties

Label 2475.2.cv
Level $2475$
Weight $2$
Character orbit 2475.cv
Rep. character $\chi_{2475}(166,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $2400$
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.cv (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 225 \)
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 2400 512
Cusp forms 2848 2400 448
Eisenstein series 64 0 64

Trace form

\( 2400 q + 2 q^{3} + 300 q^{4} + 4 q^{5} + 2 q^{9} + O(q^{10}) \) \( 2400 q + 2 q^{3} + 300 q^{4} + 4 q^{5} + 2 q^{9} + 8 q^{11} - 12 q^{12} + 16 q^{14} + 72 q^{15} + 300 q^{16} + 24 q^{17} - 40 q^{18} - 18 q^{20} - 24 q^{21} - 12 q^{23} + 28 q^{24} + 12 q^{25} + 192 q^{26} - 10 q^{27} + 18 q^{30} - 6 q^{31} - 40 q^{32} - 4 q^{33} - 76 q^{36} + 12 q^{37} - 84 q^{38} - 24 q^{39} + 144 q^{42} - 40 q^{44} - 3 q^{45} + 22 q^{47} + 10 q^{48} - 1200 q^{49} + 6 q^{50} + 44 q^{51} + 40 q^{53} - 78 q^{54} + 6 q^{55} + 48 q^{56} + 44 q^{57} + 51 q^{59} + 22 q^{60} - 72 q^{62} - 32 q^{63} - 600 q^{64} - 118 q^{65} + 9 q^{67} + 296 q^{68} - 37 q^{69} - 128 q^{71} - 140 q^{72} - 28 q^{74} - 97 q^{75} + 200 q^{78} - 508 q^{80} + 154 q^{81} - 96 q^{82} - 84 q^{83} - 224 q^{84} + 24 q^{85} + 158 q^{87} - 136 q^{89} - 88 q^{90} + 48 q^{92} - 116 q^{93} - 28 q^{95} - 84 q^{96} + 42 q^{97} - 208 q^{98} + 10 q^{99} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(2475, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2475, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)