Properties

Label 288.2.w
Level 288
Weight 2
Character orbit w
Rep. character \(\chi_{288}(35,\cdot)\)
Character field \(\Q(\zeta_{8})\)
Dimension 64
Newform subspaces 2
Sturm bound 96
Trace bound 2

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Defining parameters

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

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(288, [\chi])\).

Total New Old
Modular forms 208 64 144
Cusp forms 176 64 112
Eisenstein series 32 0 32

Trace form

\( 64q + O(q^{10}) \) \( 64q + 16q^{10} + 16q^{16} + 32q^{22} - 64q^{40} - 64q^{46} - 112q^{52} - 64q^{55} - 64q^{58} + 64q^{61} - 96q^{64} - 32q^{67} - 96q^{70} - 16q^{76} - 64q^{79} + 80q^{82} + 80q^{88} - 96q^{91} + 144q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(288, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
288.2.w.a \(32\) \(2.300\) None \(-4\) \(0\) \(0\) \(0\)
288.2.w.b \(32\) \(2.300\) None \(4\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(288, [\chi])\) into lower level spaces

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database