Properties

Label 1575.2.cu
Level 1575
Weight 2
Character orbit cu
Rep. character \(\chi_{1575}(433,\cdot)\)
Character field \(\Q(\zeta_{20})\)
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.cu (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 175 \)
Character field: \(\Q(\zeta_{20})\)
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

\( 784q + 16q^{2} - 20q^{4} - 6q^{7} + 36q^{8} + O(q^{10}) \) \( 784q + 16q^{2} - 20q^{4} - 6q^{7} + 36q^{8} + 12q^{11} + 10q^{14} + 172q^{16} - 32q^{22} + 8q^{23} - 4q^{25} + 58q^{28} + 40q^{29} + 68q^{32} + 12q^{35} - 12q^{37} + 56q^{43} + 20q^{44} - 12q^{46} + 148q^{50} - 32q^{53} + 22q^{56} - 32q^{58} + 40q^{64} + 60q^{65} - 80q^{67} - 110q^{70} + 12q^{71} - 98q^{77} - 20q^{79} + 32q^{85} + 12q^{86} - 196q^{88} - 6q^{91} - 20q^{92} + 8q^{95} + 22q^{98} + O(q^{100}) \)

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