Properties

Label 1575.2.i
Level 1575
Weight 2
Character orbit i
Rep. character \(\chi_{1575}(526,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 228
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.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 504 228 276
Cusp forms 456 228 228
Eisenstein series 48 0 48

Trace form

\( 228q - 2q^{2} - 114q^{4} - 8q^{6} - 8q^{9} + O(q^{10}) \) \( 228q - 2q^{2} - 114q^{4} - 8q^{6} - 8q^{9} + 8q^{11} + 32q^{12} + 4q^{14} - 114q^{16} - 12q^{17} - 26q^{18} - 12q^{19} + 2q^{21} + 6q^{22} - 12q^{23} + 48q^{24} + 56q^{26} - 12q^{27} + 22q^{29} - 6q^{31} - 12q^{32} + 24q^{33} + 18q^{34} - 2q^{36} + 12q^{37} + 18q^{38} - 20q^{39} + 6q^{41} - 20q^{42} + 6q^{43} - 100q^{44} - 24q^{46} - 30q^{47} - 14q^{48} - 114q^{49} + 50q^{51} + 18q^{52} + 56q^{53} - 20q^{54} + 12q^{56} + 46q^{57} + 18q^{58} + 52q^{59} + 24q^{62} + 168q^{64} - 130q^{66} + 92q^{68} - 28q^{69} - 84q^{71} + 28q^{72} - 36q^{73} + 4q^{74} + 30q^{76} - 8q^{77} + 8q^{78} - 6q^{79} - 92q^{81} - 96q^{82} - 10q^{83} - 30q^{84} - 8q^{86} + 4q^{87} + 42q^{88} + 100q^{89} + 12q^{91} - 86q^{92} - 30q^{93} + 42q^{94} + 68q^{96} + 36q^{97} + 4q^{98} - 52q^{99} + O(q^{100}) \)

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

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

Decomposition of \(S_{2}^{\mathrm{old}}(1575, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database