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Properties

Label 2475.2.fr
Level $2475$
Weight $2$
Character orbit 2475.fr
Rep. character $\chi_{2475}(52,\cdot)$
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.fr (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

\( 5696 q - 10 q^{2} - 14 q^{3} - 10 q^{4} - 6 q^{5} - 20 q^{6} - 10 q^{7} - 40 q^{8} + O(q^{10}) \) \( 5696 q - 10 q^{2} - 14 q^{3} - 10 q^{4} - 6 q^{5} - 20 q^{6} - 10 q^{7} - 40 q^{8} - 6 q^{11} - 34 q^{12} - 10 q^{13} - 10 q^{14} - 20 q^{15} - 690 q^{16} - 40 q^{17} - 20 q^{18} - 40 q^{19} + 34 q^{20} - 12 q^{23} + 40 q^{24} - 12 q^{25} - 48 q^{26} + 4 q^{27} - 40 q^{28} - 10 q^{29} - 20 q^{30} - 2 q^{31} - 80 q^{32} - 24 q^{33} - 20 q^{34} - 40 q^{35} - 12 q^{36} - 12 q^{37} + 38 q^{38} - 240 q^{39} - 10 q^{40} - 10 q^{41} + 36 q^{42} - 40 q^{44} - 94 q^{45} - 40 q^{46} - 38 q^{47} - 104 q^{48} - 10 q^{50} - 40 q^{51} - 10 q^{52} - 104 q^{53} - 120 q^{54} + 48 q^{55} - 28 q^{56} - 100 q^{57} - 46 q^{58} + 38 q^{60} - 40 q^{62} - 90 q^{63} - 40 q^{64} - 48 q^{66} - 10 q^{67} + 30 q^{68} - 120 q^{69} - 66 q^{70} + 52 q^{71} + 140 q^{72} - 40 q^{73} - 52 q^{75} + 20 q^{77} + 44 q^{78} - 70 q^{79} + 208 q^{80} - 44 q^{81} - 48 q^{82} - 110 q^{83} + 40 q^{84} - 10 q^{85} - 2 q^{86} - 30 q^{87} + 20 q^{88} - 80 q^{89} - 220 q^{90} - 8 q^{91} - 74 q^{92} - 58 q^{93} - 10 q^{94} - 170 q^{95} - 12 q^{97} - 170 q^{99} + O(q^{100}) \)

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.