Properties

Label 288.2.f
Level 288
Weight 2
Character orbit f
Rep. character \(\chi_{288}(143,\cdot)\)
Character field \(\Q\)
Dimension 4
Newforms 1
Sturm bound 96
Trace bound 0

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Defining parameters

Level: \( N \) = \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 288.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 24 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(96\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 64 4 60
Cusp forms 32 4 28
Eisenstein series 32 0 32

Trace form

\( 4q + O(q^{10}) \) \( 4q + 16q^{19} + 4q^{25} - 32q^{43} - 20q^{49} + 16q^{67} - 16q^{73} - 48q^{91} + 32q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(288, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
288.2.f.a \(4\) \(2.300\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{5}-\beta _{3}q^{7}-2\beta _{1}q^{11}-\beta _{3}q^{13}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(288, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)