Properties

Label 864.2.w
Level 864
Weight 2
Character orbit w
Rep. character \(\chi_{864}(107,\cdot)\)
Character field \(\Q(\zeta_{8})\)
Dimension 256
Newform subspaces 2
Sturm bound 288
Trace bound 10

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Defining parameters

Level: \( N \) = \( 864 = 2^{5} \cdot 3^{3} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 864.w (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 96 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 2 \)
Sturm bound: \(288\)
Trace bound: \(10\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(864, [\chi])\).

Total New Old
Modular forms 600 256 344
Cusp forms 552 256 296
Eisenstein series 48 0 48

Trace form

\( 256q + O(q^{10}) \) \( 256q - 8q^{10} + 64q^{16} - 16q^{22} + 32q^{40} + 32q^{46} + 56q^{52} + 32q^{55} + 32q^{58} - 32q^{61} + 48q^{64} - 128q^{67} + 48q^{70} - 64q^{76} + 32q^{79} - 40q^{82} - 40q^{88} + 48q^{91} - 72q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(864, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
864.2.w.a \(128\) \(6.899\) None \(0\) \(0\) \(0\) \(0\)
864.2.w.b \(128\) \(6.899\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(864, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(864, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database