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Properties

Label 2475.2.es
Level $2475$
Weight $2$
Character orbit 2475.es
Rep. character $\chi_{2475}(194,\cdot)$
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.es (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

\( 2848 q - 15 q^{2} - 5 q^{3} - 353 q^{4} - 12 q^{5} + q^{9} + O(q^{10}) \) \( 2848 q - 15 q^{2} - 5 q^{3} - 353 q^{4} - 12 q^{5} + q^{9} - 9 q^{11} + 10 q^{12} - 5 q^{13} - 18 q^{14} - 10 q^{15} + 345 q^{16} - 20 q^{19} + 51 q^{20} - 5 q^{22} - 30 q^{23} - 40 q^{24} - 50 q^{27} - 20 q^{28} - 15 q^{29} - 10 q^{30} - 10 q^{31} - 50 q^{33} - 4 q^{34} + 4 q^{36} - 135 q^{38} - 45 q^{39} - 30 q^{40} - 15 q^{41} - 60 q^{42} - 13 q^{45} - 15 q^{47} - 30 q^{48} + 326 q^{49} - 15 q^{50} + 10 q^{51} - 90 q^{52} + 60 q^{54} + 6 q^{55} - 108 q^{56} + 15 q^{58} - 24 q^{59} + 21 q^{60} - 5 q^{61} - 45 q^{63} + 656 q^{64} + 66 q^{66} - 25 q^{67} + 60 q^{68} - 4 q^{69} - 46 q^{70} - 85 q^{72} - 20 q^{73} - 31 q^{75} - 135 q^{77} - 80 q^{78} - 19 q^{81} - 20 q^{82} + 270 q^{83} - 5 q^{85} - 3 q^{86} - 45 q^{88} - 70 q^{90} + 10 q^{91} + 45 q^{92} - 105 q^{93} - 210 q^{95} - 140 q^{96} - 22 q^{99} + O(q^{100}) \)

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.