Properties

Label 1575.2.ef
Level 1575
Weight 2
Character orbit ef
Rep. character \(\chi_{1575}(92,\cdot)\)
Character field \(\Q(\zeta_{60})\)
Dimension 2880
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.ef (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 225 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 3904 2880 1024
Cusp forms 3776 2880 896
Eisenstein series 128 0 128

Trace form

\( 2880q - 4q^{3} + O(q^{10}) \) \( 2880q - 4q^{3} + 16q^{12} - 16q^{15} - 360q^{16} + 64q^{18} + 48q^{20} + 24q^{23} - 48q^{25} + 32q^{27} + 20q^{30} + 60q^{32} + 16q^{33} + 24q^{37} - 72q^{38} + 40q^{39} - 160q^{42} - 40q^{45} - 12q^{47} + 156q^{48} + 260q^{54} + 24q^{55} + 4q^{57} - 60q^{59} - 188q^{60} + 32q^{63} + 72q^{65} + 12q^{67} - 216q^{72} + 108q^{75} - 272q^{78} + 40q^{81} + 96q^{82} - 120q^{83} + 48q^{85} - 216q^{87} + 48q^{88} - 252q^{90} - 156q^{92} + 24q^{93} + 240q^{94} - 120q^{95} + 60q^{97} + O(q^{100}) \)

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