Properties

Label 1575.2.ct
Level 1575
Weight 2
Character orbit ct
Rep. character \(\chi_{1575}(106,\cdot)\)
Character field \(\Q(\zeta_{15})\)
Dimension 1440
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.ct (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 225 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 1952 1440 512
Cusp forms 1888 1440 448
Eisenstein series 64 0 64

Trace form

\( 1440q + 4q^{3} + 180q^{4} + 8q^{5} + 4q^{9} + O(q^{10}) \) \( 1440q + 4q^{3} + 180q^{4} + 8q^{5} + 4q^{9} + 16q^{11} - 24q^{12} + 8q^{14} + 36q^{15} + 180q^{16} - 48q^{18} - 22q^{20} + 28q^{24} + 24q^{25} - 32q^{27} + 24q^{29} + 40q^{30} - 12q^{31} - 20q^{32} + 16q^{33} - 62q^{36} + 24q^{37} - 108q^{38} - 12q^{39} + 60q^{42} - 80q^{44} + 98q^{45} + 14q^{47} + 70q^{48} - 720q^{49} - 10q^{50} + 20q^{51} + 80q^{53} - 126q^{54} + 12q^{55} + 24q^{56} + 44q^{57} + 6q^{59} + 2q^{60} + 120q^{62} - 12q^{63} - 360q^{64} - 104q^{65} + 180q^{66} + 18q^{67} + 104q^{68} + 10q^{69} - 72q^{71} - 52q^{72} - 188q^{74} - 16q^{75} + 44q^{78} - 304q^{80} + 92q^{81} - 96q^{82} - 40q^{83} + 24q^{85} + 20q^{86} + 146q^{87} + 48q^{88} - 80q^{89} - 68q^{90} - 88q^{92} - 56q^{93} - 72q^{94} - 20q^{95} - 8q^{96} + 36q^{97} - 44q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database