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Properties

Label 2475.2.cz
Level $2475$
Weight $2$
Character orbit 2475.cz
Rep. character $\chi_{2475}(16,\cdot)$
Character field $\Q(\zeta_{15})$
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.cz (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2475 \)
Character field: \(\Q(\zeta_{15})\)
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

\( 2848 q - q^{2} - 4 q^{3} + 351 q^{4} - 2 q^{5} - 10 q^{6} - 6 q^{7} - 4 q^{9} + O(q^{10}) \) \( 2848 q - q^{2} - 4 q^{3} + 351 q^{4} - 2 q^{5} - 10 q^{6} - 6 q^{7} - 4 q^{9} - 40 q^{10} - 3 q^{11} - 10 q^{12} - q^{13} + 3 q^{14} + 21 q^{15} + 341 q^{16} - 4 q^{17} - 20 q^{18} - 4 q^{19} + 29 q^{20} - 24 q^{21} - 11 q^{22} - 10 q^{23} + 8 q^{24} - 40 q^{26} + 14 q^{27} - 72 q^{28} - 25 q^{29} + 20 q^{30} - 16 q^{32} - 9 q^{33} - 8 q^{34} - 2 q^{35} - 40 q^{36} - 16 q^{37} + 21 q^{38} - 9 q^{39} + 7 q^{40} + 122 q^{41} - 152 q^{42} - 16 q^{43} + 4 q^{44} - 39 q^{45} - 20 q^{46} + 7 q^{47} + 70 q^{48} + 326 q^{49} - 35 q^{50} - 18 q^{51} - 35 q^{52} - 64 q^{53} - 32 q^{54} - 14 q^{55} + 28 q^{56} + 60 q^{57} + 39 q^{58} + q^{59} + 21 q^{60} - q^{61} + 50 q^{62} - 60 q^{63} - 648 q^{64} - 16 q^{65} + 26 q^{66} - 15 q^{67} - 26 q^{68} + 6 q^{69} - 52 q^{70} - 44 q^{71} - 192 q^{72} - 24 q^{73} - 48 q^{74} + 77 q^{75} - 16 q^{76} + 71 q^{77} - 24 q^{78} - 25 q^{79} - 72 q^{80} - 4 q^{81} - 20 q^{82} + 39 q^{83} - 59 q^{84} + 7 q^{85} + 3 q^{86} - 120 q^{87} - 33 q^{88} + 26 q^{89} - 104 q^{90} - 80 q^{91} - 75 q^{92} - 57 q^{93} - 5 q^{94} + 71 q^{95} - 24 q^{96} - 10 q^{97} - 26 q^{98} - 10 q^{99} + O(q^{100}) \)

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.