Properties

Label 2475.2.ez
Level $2475$
Weight $2$
Character orbit 2475.ez
Rep. character $\chi_{2475}(101,\cdot)$
Character field $\Q(\zeta_{30})$
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.ez (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 99 \)
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 2976 1872 1104
Cusp forms 2784 1776 1008
Eisenstein series 192 96 96

Trace form

\( 1776 q + 15 q^{2} + 7 q^{3} + 219 q^{4} - 35 q^{6} + 5 q^{7} - 11 q^{9} + O(q^{10}) \) \( 1776 q + 15 q^{2} + 7 q^{3} + 219 q^{4} - 35 q^{6} + 5 q^{7} - 11 q^{9} - 39 q^{11} + 30 q^{12} + 5 q^{13} + 9 q^{14} + 191 q^{16} + 20 q^{18} - 10 q^{19} + 5 q^{22} + 6 q^{23} - 5 q^{24} + 31 q^{27} + 20 q^{28} + 60 q^{29} - 6 q^{31} - 14 q^{33} + 14 q^{34} - 37 q^{36} + 6 q^{37} - 57 q^{38} - 55 q^{39} - 45 q^{41} - 81 q^{42} - 40 q^{46} + 21 q^{47} + 70 q^{48} - 183 q^{49} + 15 q^{51} + 5 q^{52} - 186 q^{56} + 29 q^{58} + 159 q^{59} - 15 q^{61} + 35 q^{63} - 296 q^{64} + 81 q^{66} + 2 q^{67} + 210 q^{68} - 44 q^{69} - 125 q^{72} + 20 q^{73} + 15 q^{74} - 87 q^{77} + 128 q^{78} + 5 q^{79} + 41 q^{81} + 38 q^{82} - 30 q^{83} + 155 q^{84} - 120 q^{86} + 41 q^{88} - 100 q^{91} + 57 q^{92} + 20 q^{93} + 5 q^{94} + 105 q^{96} + 27 q^{97} + 47 q^{99} + O(q^{100}) \)

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

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