Properties

Label 315.2.ce
Level 315
Weight 2
Character orbit ce
Rep. character \(\chi_{315}(53,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 64
Newform subspaces 1
Sturm bound 96
Trace bound 0

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Defining parameters

Level: \( N \) = \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 315.ce (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 105 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(96\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(315, [\chi])\).

Total New Old
Modular forms 224 64 160
Cusp forms 160 64 96
Eisenstein series 64 0 64

Trace form

\( 64q + 8q^{7} + O(q^{10}) \) \( 64q + 8q^{7} + 8q^{10} + 32q^{16} - 48q^{22} - 16q^{25} + 88q^{28} + 32q^{31} - 16q^{37} - 40q^{40} - 16q^{43} - 80q^{52} - 32q^{55} - 88q^{58} + 48q^{61} - 32q^{67} - 112q^{70} - 88q^{73} - 320q^{76} - 56q^{82} + 16q^{85} + 120q^{88} - 128q^{91} + 208q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(315, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
315.2.ce.a \(64\) \(2.515\) None \(0\) \(0\) \(0\) \(8\)

Decomposition of \(S_{2}^{\mathrm{old}}(315, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(315, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database