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Properties

Label 288.2.c
Level 288
Weight 2
Character orbit c
Rep. character \(\chi_{288}(287,\cdot)\)
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.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 12 \)
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

\( 4q + O(q^{10}) \) \( 4q + 16q^{13} + 12q^{25} - 24q^{37} - 36q^{49} - 8q^{61} - 24q^{85} - 32q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.c.a \(4\) \(2.300\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{2}q^{5}+\zeta_{8}q^{7}+\zeta_{8}^{3}q^{11}+4q^{13}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(288, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ 1
$3$ 1
$5$ \( ( 1 - 8 T^{2} + 25 T^{4} )^{2} \)
$7$ \( ( 1 + 2 T^{2} + 49 T^{4} )^{2} \)
$11$ \( ( 1 - 10 T^{2} + 121 T^{4} )^{2} \)
$13$ \( ( 1 - 4 T + 13 T^{2} )^{4} \)
$17$ \( ( 1 - 16 T^{2} + 289 T^{4} )^{2} \)
$19$ \( ( 1 - 19 T^{2} )^{4} \)
$23$ \( ( 1 + 14 T^{2} + 529 T^{4} )^{2} \)
$29$ \( ( 1 - 56 T^{2} + 841 T^{4} )^{2} \)
$31$ \( ( 1 - 46 T^{2} + 961 T^{4} )^{2} \)
$37$ \( ( 1 + 6 T + 37 T^{2} )^{4} \)
$41$ \( ( 1 + 16 T^{2} + 1681 T^{4} )^{2} \)
$43$ \( ( 1 - 22 T^{2} + 1849 T^{4} )^{2} \)
$47$ \( ( 1 + 62 T^{2} + 2209 T^{4} )^{2} \)
$53$ \( ( 1 - 88 T^{2} + 2809 T^{4} )^{2} \)
$59$ \( ( 1 - 10 T^{2} + 3481 T^{4} )^{2} \)
$61$ \( ( 1 + 2 T + 61 T^{2} )^{4} \)
$67$ \( ( 1 - 70 T^{2} + 4489 T^{4} )^{2} \)
$71$ \( ( 1 + 110 T^{2} + 5041 T^{4} )^{2} \)
$73$ \( ( 1 + 73 T^{2} )^{4} \)
$79$ \( ( 1 - 142 T^{2} + 6241 T^{4} )^{2} \)
$83$ \( ( 1 + 134 T^{2} + 6889 T^{4} )^{2} \)
$89$ \( ( 1 - 160 T^{2} + 7921 T^{4} )^{2} \)
$97$ \( ( 1 + 8 T + 97 T^{2} )^{4} \)
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