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Properties

Label 2475.2.gj
Level $2475$
Weight $2$
Character orbit 2475.gj
Rep. character $\chi_{2475}(502,\cdot)$
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.gj (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

\( 5696 q - 10 q^{2} - 4 q^{3} - 6 q^{5} - 20 q^{6} - 10 q^{7} - 80 q^{8} - 10 q^{9} + O(q^{10}) \) \( 5696 q - 10 q^{2} - 4 q^{3} - 6 q^{5} - 20 q^{6} - 10 q^{7} - 80 q^{8} - 10 q^{9} - 6 q^{11} - 34 q^{12} - 10 q^{13} - 10 q^{14} - 20 q^{15} + 2740 q^{16} - 40 q^{17} - 20 q^{18} - 80 q^{19} - 46 q^{20} - 40 q^{22} - 12 q^{23} - 40 q^{24} - 12 q^{25} - 48 q^{26} - 76 q^{27} - 20 q^{29} - 20 q^{30} - 2 q^{31} + 80 q^{32} - 24 q^{33} - 20 q^{34} - 40 q^{35} - 12 q^{36} - 12 q^{37} - 42 q^{38} - 20 q^{39} + 30 q^{40} - 10 q^{41} - 64 q^{42} - 120 q^{44} - 94 q^{45} - 40 q^{46} + 2 q^{47} + 206 q^{48} + 70 q^{50} - 40 q^{51} - 90 q^{52} - 104 q^{53} + 120 q^{54} - 52 q^{55} - 28 q^{56} - 100 q^{57} - 6 q^{58} - 10 q^{59} - 192 q^{60} - 10 q^{61} - 40 q^{62} - 20 q^{63} + 12 q^{66} - 10 q^{67} + 30 q^{68} + 34 q^{70} - 48 q^{71} - 40 q^{72} - 40 q^{73} - 52 q^{75} + 20 q^{77} + 44 q^{78} - 70 q^{79} - 272 q^{80} + 26 q^{81} - 8 q^{82} - 10 q^{83} + 40 q^{84} - 10 q^{85} - 12 q^{86} + 30 q^{87} - 60 q^{88} - 80 q^{89} - 20 q^{90} - 8 q^{91} + 36 q^{92} - 108 q^{93} + 110 q^{94} - 60 q^{95} - 60 q^{96} - 12 q^{97} + 170 q^{99} + O(q^{100}) \)

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.