Properties

Label 1575.2.bx
Level 1575
Weight 2
Character orbit bx
Rep. character \(\chi_{1575}(64,\cdot)\)
Character field \(\Q(\zeta_{10})\)
Dimension 296
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.bx (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 992 296 696
Cusp forms 928 296 632
Eisenstein series 64 0 64

Trace form

\( 296q + 72q^{4} + 10q^{5} + O(q^{10}) \) \( 296q + 72q^{4} + 10q^{5} + 8q^{10} - 8q^{11} + 4q^{14} - 44q^{16} - 12q^{19} - 70q^{22} + 10q^{23} + 40q^{25} + 12q^{26} + 22q^{29} + 12q^{31} - 12q^{34} + 2q^{35} - 10q^{37} + 70q^{38} + 126q^{40} + 4q^{41} + 62q^{44} + 20q^{46} + 90q^{47} - 296q^{49} - 94q^{50} - 20q^{53} + 6q^{55} - 12q^{56} + 130q^{58} - 18q^{59} + 20q^{61} + 50q^{62} + 36q^{64} - 98q^{65} - 70q^{67} - 8q^{70} - 24q^{71} - 40q^{73} - 44q^{74} - 12q^{76} - 20q^{77} - 48q^{79} - 80q^{80} - 30q^{83} - 52q^{85} - 100q^{86} - 140q^{88} - 2q^{89} + 8q^{91} + 120q^{92} - 54q^{95} - 30q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database