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Properties

Label 2475.2.fp
Level $2475$
Weight $2$
Character orbit 2475.fp
Rep. character $\chi_{2475}(47,\cdot)$
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.fp (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

\( 5696 q - 18 q^{2} - 10 q^{3} - 10 q^{4} - 18 q^{5} - 24 q^{6} - 6 q^{7} - 30 q^{9} + O(q^{10}) \) \( 5696 q - 18 q^{2} - 10 q^{3} - 10 q^{4} - 18 q^{5} - 24 q^{6} - 6 q^{7} - 30 q^{9} - 64 q^{10} - 18 q^{11} - 40 q^{12} - 6 q^{13} - 4 q^{15} - 690 q^{16} - 20 q^{18} - 40 q^{19} + 78 q^{20} - 24 q^{21} - 48 q^{23} + 40 q^{24} - 12 q^{25} - 28 q^{27} + 32 q^{28} - 30 q^{29} - 92 q^{30} - 2 q^{31} + 18 q^{33} - 20 q^{34} - 72 q^{36} + 24 q^{37} + 30 q^{38} + 80 q^{39} - 22 q^{40} - 6 q^{41} + 124 q^{42} - 16 q^{43} - 20 q^{45} - 48 q^{46} - 42 q^{47} + 96 q^{48} + 78 q^{50} - 24 q^{51} - 62 q^{52} - 160 q^{54} - 12 q^{55} - 36 q^{56} - 84 q^{57} + 42 q^{58} - 136 q^{60} - 2 q^{61} - 74 q^{63} + 40 q^{64} - 48 q^{65} - 48 q^{66} - 22 q^{67} + 30 q^{68} - 20 q^{69} + 54 q^{70} - 34 q^{72} - 24 q^{73} + 28 q^{75} - 64 q^{76} - 24 q^{77} - 104 q^{78} + 26 q^{81} - 8 q^{82} - 198 q^{83} - 6 q^{85} - 6 q^{86} + 52 q^{87} + 52 q^{88} + 176 q^{90} - 8 q^{91} + 114 q^{92} + 50 q^{93} + 72 q^{95} + 60 q^{96} - 12 q^{97} + O(q^{100}) \)

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.