Properties

Label 96.2.c
Level 96
Weight 2
Character orbit c
Rep. character \(\chi_{96}(95,\cdot)\)
Character field \(\Q\)
Dimension 4
Newform subspaces 1
Sturm bound 32
Trace bound 0

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Defining parameters

Level: \( N \) = \( 96 = 2^{5} \cdot 3 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 96.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 12 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(32\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(96, [\chi])\).

Total New Old
Modular forms 24 4 20
Cusp forms 8 4 4
Eisenstein series 16 0 16

Trace form

\( 4q + 4q^{9} + O(q^{10}) \) \( 4q + 4q^{9} - 8q^{13} - 8q^{21} - 12q^{25} - 16q^{33} + 24q^{37} + 32q^{45} + 12q^{49} + 24q^{57} - 8q^{61} - 32q^{69} - 24q^{73} - 28q^{81} - 8q^{93} + 40q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(96, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
96.2.c.a \(4\) \(0.767\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{3}+\zeta_{8}^{3}q^{5}+(-\zeta_{8}+\zeta_{8}^{2})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(96, [\chi])\) into lower level spaces

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

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ 1
$3$ \( 1 - 2 T^{2} + 9 T^{4} \)
$5$ \( ( 1 - 2 T^{2} + 25 T^{4} )^{2} \)
$7$ \( ( 1 - 10 T^{2} + 49 T^{4} )^{2} \)
$11$ \( ( 1 + 14 T^{2} + 121 T^{4} )^{2} \)
$13$ \( ( 1 + 2 T + 13 T^{2} )^{4} \)
$17$ \( ( 1 - 17 T^{2} )^{4} \)
$19$ \( ( 1 - 2 T^{2} + 361 T^{4} )^{2} \)
$23$ \( ( 1 + 14 T^{2} + 529 T^{4} )^{2} \)
$29$ \( ( 1 - 50 T^{2} + 841 T^{4} )^{2} \)
$31$ \( ( 1 - 58 T^{2} + 961 T^{4} )^{2} \)
$37$ \( ( 1 - 6 T + 37 T^{2} )^{4} \)
$41$ \( ( 1 - 50 T^{2} + 1681 T^{4} )^{2} \)
$43$ \( ( 1 - 82 T^{2} + 1849 T^{4} )^{2} \)
$47$ \( ( 1 - 34 T^{2} + 2209 T^{4} )^{2} \)
$53$ \( ( 1 - 34 T^{2} + 2809 T^{4} )^{2} \)
$59$ \( ( 1 + 110 T^{2} + 3481 T^{4} )^{2} \)
$61$ \( ( 1 + 2 T + 61 T^{2} )^{4} \)
$67$ \( ( 1 - 130 T^{2} + 4489 T^{4} )^{2} \)
$71$ \( ( 1 + 110 T^{2} + 5041 T^{4} )^{2} \)
$73$ \( ( 1 + 6 T + 73 T^{2} )^{4} \)
$79$ \( ( 1 + 38 T^{2} + 6241 T^{4} )^{2} \)
$83$ \( ( 1 + 158 T^{2} + 6889 T^{4} )^{2} \)
$89$ \( ( 1 + 110 T^{2} + 7921 T^{4} )^{2} \)
$97$ \( ( 1 - 10 T + 97 T^{2} )^{4} \)
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