Properties

Label 1575.2.dk
Level 1575
Weight 2
Character orbit dk
Rep. character \(\chi_{1575}(109,\cdot)\)
Character field \(\Q(\zeta_{30})\)
Dimension 784
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.dk (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 175 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 1984 816 1168
Cusp forms 1856 784 1072
Eisenstein series 128 32 96

Trace form

\( 784q + 5q^{2} - 99q^{4} + 5q^{5} - 10q^{8} + O(q^{10}) \) \( 784q + 5q^{2} - 99q^{4} + 5q^{5} - 10q^{8} - 5q^{10} + 6q^{11} - 20q^{13} + 6q^{14} + 85q^{16} + 15q^{17} - 11q^{19} + 16q^{20} + 20q^{22} + 35q^{23} + 9q^{25} + 60q^{26} - 60q^{28} + 3q^{31} + 44q^{34} + 14q^{35} - 5q^{37} - 10q^{38} - 33q^{40} + 26q^{41} + 31q^{44} + 37q^{46} + 5q^{47} - 6q^{49} + 86q^{50} + 70q^{52} + 35q^{53} - 28q^{55} - 32q^{56} + 55q^{58} + 15q^{59} + 7q^{61} - 100q^{62} + 98q^{64} + 43q^{65} + 25q^{67} + 5q^{70} + 14q^{71} - 45q^{73} + 6q^{74} + 132q^{76} + 5q^{77} + q^{79} - 36q^{80} - 10q^{83} + 50q^{85} - 35q^{86} - 40q^{88} + 42q^{89} + 26q^{91} - 190q^{92} - 27q^{94} + 25q^{95} - 160q^{97} - 180q^{98} + O(q^{100}) \)

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

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database