Properties

Label 2475.2.cy
Level $2475$
Weight $2$
Character orbit 2475.cy
Rep. character $\chi_{2475}(301,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $1776$
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.cy (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 99 \)
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 2976 1872 1104
Cusp forms 2784 1776 1008
Eisenstein series 192 96 96

Trace form

\( 1776 q + q^{2} + 5 q^{3} + 219 q^{4} - 11 q^{6} + 3 q^{7} + 32 q^{8} + 13 q^{9} + O(q^{10}) \) \( 1776 q + q^{2} + 5 q^{3} + 219 q^{4} - 11 q^{6} + 3 q^{7} + 32 q^{8} + 13 q^{9} - 13 q^{11} + 22 q^{12} + 3 q^{13} - 21 q^{14} + 191 q^{16} + 16 q^{17} - 4 q^{18} + 30 q^{19} - 28 q^{21} + 11 q^{22} + 6 q^{23} + 93 q^{24} + 28 q^{26} + 23 q^{27} + 36 q^{28} + 14 q^{29} - 12 q^{31} + 64 q^{32} + 22 q^{33} + 26 q^{34} - 13 q^{36} + 18 q^{37} + 29 q^{38} + 29 q^{39} + 39 q^{41} + 21 q^{42} + 14 q^{43} - 2 q^{44} - 48 q^{46} - 13 q^{47} - 130 q^{48} + 189 q^{49} + 17 q^{51} + 15 q^{52} + 16 q^{53} - 188 q^{54} - 38 q^{56} - 78 q^{57} - 7 q^{58} - 27 q^{59} - 9 q^{61} + 50 q^{62} + 53 q^{63} - 296 q^{64} - 31 q^{66} + 26 q^{67} - 66 q^{68} + 16 q^{69} + 14 q^{71} - 77 q^{72} - 24 q^{73} - 65 q^{74} + 26 q^{76} + 47 q^{77} + 64 q^{78} + 3 q^{79} - 87 q^{81} + 38 q^{82} - 44 q^{83} + 225 q^{84} - 104 q^{86} - 140 q^{87} - 37 q^{88} - 184 q^{89} - 44 q^{91} - 81 q^{92} - 62 q^{93} + 3 q^{94} + 153 q^{96} - 27 q^{97} - 120 q^{98} + 187 q^{99} + O(q^{100}) \)

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

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

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

\( S_{2}^{\mathrm{old}}(2475, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(495, [\chi])\)\(^{\oplus 2}\)