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Properties

Label 1575.2.dv
Level $1575$
Weight $2$
Character orbit 1575.dv
Rep. character $\chi_{1575}(59,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1888$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1575.dv (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1575 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1575, [\chi])\).

Total New Old
Modular forms 1952 1952 0
Cusp forms 1888 1888 0
Eisenstein series 64 64 0

Trace form

\( 1888 q - 15 q^{2} - 15 q^{3} + 235 q^{4} - 24 q^{5} - 12 q^{6} - 3 q^{9} + O(q^{10}) \) \( 1888 q - 15 q^{2} - 15 q^{3} + 235 q^{4} - 24 q^{5} - 12 q^{6} - 3 q^{9} - 24 q^{10} - 15 q^{12} - 9 q^{14} - 54 q^{15} + 223 q^{16} - 18 q^{19} - 6 q^{20} - 18 q^{21} - 10 q^{22} - 6 q^{24} - 8 q^{25} - 12 q^{26} - 18 q^{29} + 13 q^{30} - 9 q^{31} + 60 q^{33} - 12 q^{34} + 75 q^{35} - 40 q^{36} - 10 q^{37} - 30 q^{38} - 37 q^{39} + 20 q^{42} - 60 q^{44} - 3 q^{45} + 2 q^{46} - 15 q^{47} - 30 q^{48} - 8 q^{49} - 60 q^{50} - 8 q^{51} - 9 q^{54} - 72 q^{56} - 10 q^{58} - 9 q^{59} - 109 q^{60} - 9 q^{61} + 180 q^{62} + 5 q^{63} - 436 q^{64} - 69 q^{65} - 93 q^{66} + 5 q^{67} - 45 q^{69} - 40 q^{70} - 45 q^{72} - 30 q^{73} - 27 q^{75} - 48 q^{76} - 15 q^{77} + 10 q^{78} - 9 q^{79} + 216 q^{80} + q^{81} + 19 q^{84} - 3 q^{85} - 15 q^{87} - 10 q^{88} - 45 q^{89} - 162 q^{90} + 30 q^{91} - 210 q^{92} - 9 q^{94} + 78 q^{95} + 39 q^{96} - 30 q^{98} - 66 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1575, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.