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Properties

Label 2475.2.dy
Level $2475$
Weight $2$
Character orbit 2475.dy
Rep. character $\chi_{2475}(41,\cdot)$
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.dy (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

\( 2848 q - 5 q^{3} - 1414 q^{4} - 6 q^{5} - 10 q^{7} + q^{9} + O(q^{10}) \) \( 2848 q - 5 q^{3} - 1414 q^{4} - 6 q^{5} - 10 q^{7} + q^{9} + 20 q^{10} - 9 q^{11} - 4 q^{12} - 5 q^{13} - 3 q^{14} + 6 q^{15} - 1394 q^{16} - 20 q^{18} - 3 q^{20} - 15 q^{21} + 29 q^{22} - 18 q^{23} + 10 q^{24} + 22 q^{27} + 20 q^{28} - 7 q^{31} + 3 q^{33} - 8 q^{34} - 20 q^{36} + 8 q^{37} - 54 q^{38} - 10 q^{39} - 50 q^{40} - 15 q^{41} + 20 q^{42} + 33 q^{45} + 20 q^{46} - 27 q^{47} + 5 q^{48} - 338 q^{49} + 105 q^{50} + 10 q^{51} + 25 q^{52} - 40 q^{54} - 18 q^{55} - 33 q^{56} + 60 q^{57} + 42 q^{58} - 9 q^{59} - 25 q^{60} - 5 q^{61} - 10 q^{63} + 2672 q^{64} + 90 q^{65} + 88 q^{66} + 3 q^{67} + 30 q^{68} - 10 q^{69} + 10 q^{70} - 145 q^{72} - 20 q^{73} - 26 q^{75} - 105 q^{77} + 14 q^{78} + 25 q^{79} + 5 q^{81} - 20 q^{82} + 135 q^{83} + 35 q^{84} - 5 q^{85} - 18 q^{86} + 30 q^{87} + 55 q^{88} + 52 q^{91} + 375 q^{92} + 61 q^{93} + 75 q^{94} + 60 q^{95} - 35 q^{96} - 10 q^{97} - 107 q^{99} + O(q^{100}) \)

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.