Properties

Label 1575.2.db
Level $1575$
Weight $2$
Character orbit 1575.db
Rep. character $\chi_{1575}(4,\cdot)$
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.db (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

\( 1888 q + 5 q^{2} - 5 q^{3} - 229 q^{4} - 8 q^{5} - 16 q^{6} - 40 q^{8} - 3 q^{9} + O(q^{10}) \) \( 1888 q + 5 q^{2} - 5 q^{3} - 229 q^{4} - 8 q^{5} - 16 q^{6} - 40 q^{8} - 3 q^{9} - 12 q^{10} - 6 q^{11} - 5 q^{12} - 10 q^{13} - 15 q^{14} + 16 q^{15} + 231 q^{16} - 10 q^{17} - 6 q^{19} + 2 q^{20} + 18 q^{21} - 10 q^{22} - 10 q^{23} - 22 q^{24} - 8 q^{25} - 108 q^{26} - 50 q^{27} - 6 q^{29} + 29 q^{30} + 3 q^{31} + 20 q^{33} - 2 q^{34} - 19 q^{35} - 28 q^{36} - 10 q^{37} - 10 q^{38} + 31 q^{39} - 26 q^{40} + 26 q^{41} - 40 q^{42} + 14 q^{44} + 93 q^{45} - 14 q^{46} + 5 q^{47} - 30 q^{48} - 8 q^{49} - 44 q^{50} - 8 q^{51} + 30 q^{52} - 10 q^{53} + 5 q^{54} - 10 q^{55} + 10 q^{56} - 10 q^{58} - 45 q^{59} - 9 q^{60} + 3 q^{61} - 100 q^{62} - 95 q^{63} + 420 q^{64} + 13 q^{65} + 13 q^{66} + 5 q^{67} - 39 q^{69} + 24 q^{70} - 6 q^{71} - 45 q^{72} - 10 q^{73} - q^{75} - 32 q^{76} + 215 q^{77} + 10 q^{78} + 15 q^{79} - 98 q^{80} - 7 q^{81} - 80 q^{83} - 147 q^{84} - 3 q^{85} + 10 q^{86} - 5 q^{87} - 10 q^{88} - 39 q^{89} + 30 q^{90} - 54 q^{91} + 50 q^{92} + 19 q^{94} + 42 q^{95} - 29 q^{96} - 10 q^{97} - 30 q^{98} - 30 q^{99} + O(q^{100}) \)

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

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