Properties

Label 288.2.f
Level 288
Weight 2
Character orbit f
Rep. character \(\chi_{288}(143,\cdot)\)
Character field \(\Q\)
Dimension 4
Newform subspaces 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: \(\Q\)
Newform subspaces: \( 1 \)
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 newform subspaces

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

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

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ 1
$3$ 1
$5$ \( ( 1 + 4 T^{2} + 25 T^{4} )^{2} \)
$7$ \( ( 1 - 4 T + 7 T^{2} )^{2}( 1 + 4 T + 7 T^{2} )^{2} \)
$11$ \( ( 1 - 6 T + 11 T^{2} )^{2}( 1 + 6 T + 11 T^{2} )^{2} \)
$13$ \( ( 1 - 14 T^{2} + 169 T^{4} )^{2} \)
$17$ \( ( 1 - 32 T^{2} + 289 T^{4} )^{2} \)
$19$ \( ( 1 - 4 T + 19 T^{2} )^{4} \)
$23$ \( ( 1 + 22 T^{2} + 529 T^{4} )^{2} \)
$29$ \( ( 1 + 52 T^{2} + 841 T^{4} )^{2} \)
$31$ \( ( 1 - 50 T^{2} + 961 T^{4} )^{2} \)
$37$ \( ( 1 - 37 T^{2} )^{4} \)
$41$ \( ( 1 - 80 T^{2} + 1681 T^{4} )^{2} \)
$43$ \( ( 1 + 8 T + 43 T^{2} )^{4} \)
$47$ \( ( 1 + 70 T^{2} + 2209 T^{4} )^{2} \)
$53$ \( ( 1 + 52 T^{2} + 2809 T^{4} )^{2} \)
$59$ \( ( 1 + 10 T^{2} + 3481 T^{4} )^{2} \)
$61$ \( ( 1 + 70 T^{2} + 3721 T^{4} )^{2} \)
$67$ \( ( 1 - 4 T + 67 T^{2} )^{4} \)
$71$ \( ( 1 - 74 T^{2} + 5041 T^{4} )^{2} \)
$73$ \( ( 1 + 4 T + 73 T^{2} )^{4} \)
$79$ \( ( 1 - 146 T^{2} + 6241 T^{4} )^{2} \)
$83$ \( ( 1 + 34 T^{2} + 6889 T^{4} )^{2} \)
$89$ \( ( 1 - 128 T^{2} + 7921 T^{4} )^{2} \)
$97$ \( ( 1 - 8 T + 97 T^{2} )^{4} \)
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