Properties

Label 225.2.s
Level 225
Weight 2
Character orbit s
Rep. character \(\chi_{225}(8,\cdot)\)
Character field \(\Q(\zeta_{20})\)
Dimension 80
Newform subspaces 1
Sturm bound 60
Trace bound 0

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Defining parameters

Level: \( N \) = \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 225.s (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 75 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 1 \)
Sturm bound: \(60\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(225, [\chi])\).

Total New Old
Modular forms 272 80 192
Cusp forms 208 80 128
Eisenstein series 64 0 64

Trace form

\( 80q + 8q^{7} + O(q^{10}) \) \( 80q + 8q^{7} + 8q^{10} - 4q^{13} + 20q^{16} - 40q^{19} - 88q^{22} - 16q^{25} - 128q^{28} - 20q^{34} - 4q^{37} + 12q^{40} + 32q^{43} - 4q^{52} - 8q^{55} - 12q^{58} + 160q^{64} + 64q^{67} + 136q^{70} + 76q^{73} + 80q^{79} + 84q^{82} + 52q^{85} - 56q^{88} - 80q^{94} - 236q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(225, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
225.2.s.a \(80\) \(1.797\) None \(0\) \(0\) \(0\) \(8\)

Decomposition of \(S_{2}^{\mathrm{old}}(225, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(225, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database