Properties

Label 1575.2.q
Level 1575
Weight 2
Character orbit q
Rep. character \(\chi_{1575}(316,\cdot)\)
Character field \(\Q(\zeta_{5})\)
Dimension 304
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.q (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 992 304 688
Cusp forms 928 304 624
Eisenstein series 64 0 64

Trace form

\( 304q - 2q^{2} - 78q^{4} - 12q^{5} - 6q^{8} + O(q^{10}) \) \( 304q - 2q^{2} - 78q^{4} - 12q^{5} - 6q^{8} + 6q^{10} + 8q^{11} + 4q^{14} - 106q^{16} - 16q^{17} - 12q^{19} + 52q^{20} + 34q^{22} + 18q^{23} + 2q^{25} - 32q^{26} + 2q^{29} - 12q^{31} + 56q^{32} + 18q^{34} - 2q^{35} + 8q^{37} - 46q^{38} - 36q^{40} - 24q^{41} + 36q^{43} + 62q^{44} - 20q^{46} + 10q^{47} + 304q^{49} + 76q^{50} + 28q^{52} + 46q^{53} + 94q^{55} + 12q^{56} + 2q^{58} - 18q^{59} - 40q^{61} + 74q^{62} - 114q^{64} + 28q^{65} + 18q^{67} - 12q^{68} + 16q^{70} + 64q^{71} - 68q^{73} - 64q^{74} + 12q^{76} + 12q^{77} - 48q^{79} - 138q^{80} - 148q^{82} + 6q^{83} - 14q^{85} + 100q^{86} - 132q^{88} + 68q^{89} - 8q^{91} + 40q^{92} + 40q^{94} + 122q^{95} - 18q^{97} - 2q^{98} + O(q^{100}) \)

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