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Properties

Label 2475.2.gk
Level $2475$
Weight $2$
Character orbit 2475.gk
Rep. character $\chi_{2475}(113,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $5696$
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.gk (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2475 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2475, [\chi])\).

Total New Old
Modular forms 5824 5824 0
Cusp forms 5696 5696 0
Eisenstein series 128 128 0

Trace form

\( 5696 q - 18 q^{2} - 20 q^{3} - 18 q^{5} - 4 q^{6} - 6 q^{7} - 10 q^{9} + O(q^{10}) \) \( 5696 q - 18 q^{2} - 20 q^{3} - 18 q^{5} - 4 q^{6} - 6 q^{7} - 10 q^{9} - 64 q^{10} - 18 q^{11} - 50 q^{12} - 6 q^{13} - 30 q^{14} - 4 q^{15} + 2740 q^{16} - 20 q^{18} - 42 q^{20} - 24 q^{21} - 40 q^{22} - 48 q^{23} - 40 q^{24} - 12 q^{25} + 52 q^{27} - 128 q^{28} + 8 q^{30} - 2 q^{31} - 120 q^{32} - 12 q^{33} - 20 q^{34} - 12 q^{36} - 36 q^{37} + 90 q^{38} - 20 q^{39} + 18 q^{40} - 6 q^{41} - 136 q^{42} - 16 q^{43} + 30 q^{45} - 8 q^{46} - 42 q^{47} - 114 q^{48} - 162 q^{50} - 24 q^{51} - 62 q^{52} + 80 q^{54} - 12 q^{55} - 36 q^{56} + 36 q^{57} + 42 q^{58} - 30 q^{59} - 96 q^{60} - 2 q^{61} - 4 q^{63} - 48 q^{65} + 12 q^{66} - 22 q^{67} - 90 q^{68} - 46 q^{70} + 36 q^{72} - 24 q^{73} + 28 q^{75} + 16 q^{76} - 24 q^{77} - 84 q^{78} - 70 q^{79} + 26 q^{81} - 8 q^{82} + 102 q^{83} - 80 q^{84} - 6 q^{85} - 36 q^{86} - 78 q^{87} - 108 q^{88} + 96 q^{90} - 8 q^{91} - 336 q^{92} - 60 q^{93} + 110 q^{94} + 72 q^{95} + 60 q^{96} - 12 q^{97} - 170 q^{99} + O(q^{100}) \)

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.