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Properties

Label 2475.2.fb
Level $2475$
Weight $2$
Character orbit 2475.fb
Rep. character $\chi_{2475}(266,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $2848$
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.fb (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2475 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 2912 2912 0
Cusp forms 2848 2848 0
Eisenstein series 64 64 0

Trace form

\( 2848 q - 15 q^{2} - 5 q^{3} + 351 q^{4} - 6 q^{5} - 10 q^{7} + q^{9} + O(q^{10}) \) \( 2848 q - 15 q^{2} - 5 q^{3} + 351 q^{4} - 6 q^{5} - 10 q^{7} + q^{9} - 9 q^{11} - 34 q^{12} - 5 q^{13} - 18 q^{14} + 6 q^{15} + 341 q^{16} - 20 q^{18} - 20 q^{19} + 27 q^{20} - 11 q^{22} - 18 q^{23} - 40 q^{24} + 22 q^{27} - 60 q^{28} - 15 q^{29} - 10 q^{30} + 8 q^{31} + 48 q^{33} - 8 q^{34} + 20 q^{36} - 72 q^{37} + 21 q^{38} - 75 q^{39} + 20 q^{40} - 15 q^{41} + 40 q^{42} + 33 q^{45} - 27 q^{47} - 130 q^{48} - 338 q^{49} - 15 q^{50} - 50 q^{51} + 60 q^{54} - 18 q^{55} + 72 q^{56} + 60 q^{57} + 27 q^{58} - 24 q^{59} - 45 q^{60} - 5 q^{61} - 45 q^{63} - 648 q^{64} - 42 q^{66} + 3 q^{67} - 90 q^{68} - 40 q^{69} - 20 q^{70} - 105 q^{72} - 20 q^{73} - 60 q^{74} - 21 q^{75} + 15 q^{77} - 16 q^{78} + 45 q^{81} - 20 q^{82} - 5 q^{85} - 3 q^{86} + 160 q^{87} - 15 q^{88} + 130 q^{90} - 18 q^{91} - 195 q^{92} - 69 q^{93} + 30 q^{95} + 80 q^{96} - 22 q^{99} + O(q^{100}) \)

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.