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Properties

Label 2475.2.gg
Level $2475$
Weight $2$
Character orbit 2475.gg
Rep. character $\chi_{2475}(13,\cdot)$
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.gg (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

\( 5696 q - 10 q^{2} - 14 q^{3} - 10 q^{4} - 6 q^{5} - 10 q^{7} - 30 q^{9} + O(q^{10}) \) \( 5696 q - 10 q^{2} - 14 q^{3} - 10 q^{4} - 6 q^{5} - 10 q^{7} - 30 q^{9} - 6 q^{11} - 24 q^{12} - 10 q^{13} - 20 q^{15} - 690 q^{16} - 40 q^{17} - 20 q^{18} - 40 q^{19} - 6 q^{20} - 12 q^{23} - 40 q^{24} - 12 q^{25} - 48 q^{26} + 4 q^{27} - 80 q^{28} - 10 q^{29} - 20 q^{30} - 2 q^{31} + 66 q^{33} - 20 q^{34} - 40 q^{35} - 72 q^{36} - 72 q^{37} - 22 q^{38} + 80 q^{39} - 10 q^{40} - 10 q^{41} - 44 q^{42} - 40 q^{44} - 44 q^{45} + 2 q^{47} + 16 q^{48} - 10 q^{50} - 40 q^{51} + 70 q^{52} + 96 q^{53} + 120 q^{54} - 52 q^{55} - 28 q^{56} - 100 q^{57} - 6 q^{58} + 8 q^{60} - 10 q^{61} - 40 q^{62} + 50 q^{63} + 40 q^{64} - 48 q^{66} - 10 q^{67} - 10 q^{68} - 20 q^{69} - 66 q^{70} + 52 q^{71} + 150 q^{72} - 40 q^{73} - 52 q^{75} + 20 q^{77} + 24 q^{78} + 100 q^{79} + 128 q^{80} + 26 q^{81} - 8 q^{82} + 90 q^{83} - 160 q^{84} - 10 q^{85} - 2 q^{86} - 160 q^{87} + 100 q^{88} + 20 q^{89} + 60 q^{90} - 8 q^{91} - 34 q^{92} + 122 q^{93} - 20 q^{94} + 40 q^{95} + 20 q^{96} - 12 q^{97} - 140 q^{98} + O(q^{100}) \)

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.