Properties

Label 1575.2.j
Level 1575
Weight 2
Character orbit j
Rep. character \(\chi_{1575}(226,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 120
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.j (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 7 \)
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 528 132 396
Cusp forms 432 120 312
Eisenstein series 96 12 84

Trace form

\( 120q - 54q^{4} - 12q^{8} + O(q^{10}) \) \( 120q - 54q^{4} - 12q^{8} + 10q^{11} - 4q^{13} - 12q^{14} - 42q^{16} - 12q^{17} + 6q^{19} - 16q^{22} + 10q^{23} - 2q^{28} - 20q^{31} + 22q^{32} + 48q^{34} + 14q^{37} + 22q^{38} - 16q^{41} + 16q^{43} + 64q^{44} - 6q^{47} + 2q^{49} + 44q^{52} - 20q^{53} + 6q^{56} - 2q^{58} + 30q^{59} - 6q^{61} + 36q^{62} - 16q^{67} - 8q^{68} - 8q^{71} + 22q^{73} - 24q^{74} - 76q^{76} + 64q^{77} - 22q^{82} + 24q^{83} + 6q^{86} + 76q^{88} - 16q^{89} + 32q^{91} - 76q^{92} - 54q^{94} + 8q^{97} - 10q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database