Properties

Label 1575.2.dl
Level 1575
Weight 2
Character orbit dl
Rep. character \(\chi_{1575}(236,\cdot)\)
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.dl (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

\( 1888q - 9q^{2} - 9q^{3} - 229q^{4} - 24q^{5} + 12q^{6} - 8q^{7} - 3q^{9} + O(q^{10}) \) \( 1888q - 9q^{2} - 9q^{3} - 229q^{4} - 24q^{5} + 12q^{6} - 8q^{7} - 3q^{9} - 24q^{10} - 9q^{12} - 9q^{14} + 16q^{15} + 231q^{16} + 18q^{17} + 16q^{18} - 18q^{19} + 6q^{20} + 6q^{21} - 14q^{22} - 42q^{24} - 8q^{25} + 12q^{26} - 36q^{27} - 28q^{28} - 18q^{29} + 17q^{30} - 9q^{31} - 108q^{32} - 54q^{33} + 12q^{34} - 75q^{35} + 32q^{36} - 6q^{37} - 18q^{38} - 13q^{39} + 2q^{42} - 16q^{43} - 36q^{44} - 3q^{45} - 14q^{46} - 9q^{47} - 60q^{48} - 8q^{49} - 36q^{50} - 8q^{51} - 9q^{54} + 54q^{56} - 72q^{57} - 14q^{58} - 9q^{59} - 31q^{60} - 9q^{61} + 132q^{62} + 49q^{63} + 420q^{64} - 27q^{65} + 3q^{66} + 3q^{67} - 624q^{68} - 81q^{69} + 72q^{70} + 57q^{72} - 18q^{73} + 3q^{75} - 57q^{77} + 4q^{78} - 9q^{79} - 240q^{80} - 7q^{81} - 60q^{82} - 3q^{84} - 13q^{85} + 9q^{87} - 54q^{88} - 45q^{89} + 18q^{90} - 54q^{91} + 78q^{92} + 26q^{93} - 9q^{94} - 42q^{95} - 57q^{96} - 18q^{98} - 66q^{99} + O(q^{100}) \)

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

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database