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Properties

Label 1575.2.cz
Level $1575$
Weight $2$
Character orbit 1575.cz
Rep. character $\chi_{1575}(164,\cdot)$
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.cz (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

\( 1888 q - 15 q^{3} - 470 q^{4} - 12 q^{5} + 12 q^{6} - 3 q^{9} + O(q^{10}) \) \( 1888 q - 15 q^{3} - 470 q^{4} - 12 q^{5} + 12 q^{6} - 3 q^{9} - 24 q^{10} - 9 q^{11} - 15 q^{12} - 9 q^{14} - 54 q^{15} - 446 q^{16} - 18 q^{19} + 6 q^{20} + 9 q^{21} - 10 q^{22} - 15 q^{23} + 18 q^{24} + 4 q^{25} + 12 q^{26} - 18 q^{29} - 38 q^{30} - 15 q^{33} + 12 q^{34} - 75 q^{35} - 40 q^{36} - 10 q^{37} - 15 q^{38} + 17 q^{39} + 15 q^{40} + 20 q^{42} + 60 q^{44} + 84 q^{45} + 2 q^{46} - 30 q^{47} + 30 q^{48} - 8 q^{49} - 60 q^{50} + 28 q^{51} - 15 q^{52} + 3 q^{54} - 60 q^{56} + 5 q^{58} - 18 q^{59} - 10 q^{60} - 180 q^{62} + 35 q^{63} - 436 q^{64} + 9 q^{66} - 10 q^{67} + 45 q^{69} + 20 q^{70} + 75 q^{72} - 30 q^{73} - 87 q^{75} + 48 q^{76} + 105 q^{77} + 10 q^{78} + 18 q^{79} - 216 q^{80} + 49 q^{81} - 116 q^{84} - 3 q^{85} + 51 q^{86} - 15 q^{87} + 5 q^{88} + 45 q^{89} + 162 q^{90} + 30 q^{91} - 210 q^{92} + 87 q^{96} + 30 q^{98} - 66 q^{99} + O(q^{100}) \)

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.