Properties

Label 96.2.f
Level 96
Weight 2
Character orbit f
Rep. character \(\chi_{96}(47,\cdot)\)
Character field \(\Q\)
Dimension 2
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.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 24 \)
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 6 18
Cusp forms 8 2 6
Eisenstein series 16 4 12

Trace form

\( 2q + 2q^{3} - 2q^{9} + O(q^{10}) \) \( 2q + 2q^{3} - 2q^{9} - 4q^{19} - 10q^{25} - 10q^{27} + 8q^{33} + 20q^{43} + 14q^{49} + 16q^{51} - 4q^{57} - 28q^{67} + 4q^{73} - 10q^{75} - 14q^{81} - 20q^{97} + 16q^{99} + O(q^{100}) \)

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.f.a \(2\) \(0.767\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) \(0\) \(2\) \(0\) \(0\) \(q+(1+\beta )q^{3}+(-1+2\beta )q^{9}-2\beta q^{11}+\cdots\)

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

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

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ 1
$3$ \( 1 - 2 T + 3 T^{2} \)
$5$ \( ( 1 + 5 T^{2} )^{2} \)
$7$ \( ( 1 - 7 T^{2} )^{2} \)
$11$ \( ( 1 - 6 T + 11 T^{2} )( 1 + 6 T + 11 T^{2} ) \)
$13$ \( ( 1 - 13 T^{2} )^{2} \)
$17$ \( ( 1 - 6 T + 17 T^{2} )( 1 + 6 T + 17 T^{2} ) \)
$19$ \( ( 1 + 2 T + 19 T^{2} )^{2} \)
$23$ \( ( 1 + 23 T^{2} )^{2} \)
$29$ \( ( 1 + 29 T^{2} )^{2} \)
$31$ \( ( 1 - 31 T^{2} )^{2} \)
$37$ \( ( 1 - 37 T^{2} )^{2} \)
$41$ \( ( 1 - 6 T + 41 T^{2} )( 1 + 6 T + 41 T^{2} ) \)
$43$ \( ( 1 - 10 T + 43 T^{2} )^{2} \)
$47$ \( ( 1 + 47 T^{2} )^{2} \)
$53$ \( ( 1 + 53 T^{2} )^{2} \)
$59$ \( ( 1 - 6 T + 59 T^{2} )( 1 + 6 T + 59 T^{2} ) \)
$61$ \( ( 1 - 61 T^{2} )^{2} \)
$67$ \( ( 1 + 14 T + 67 T^{2} )^{2} \)
$71$ \( ( 1 + 71 T^{2} )^{2} \)
$73$ \( ( 1 - 2 T + 73 T^{2} )^{2} \)
$79$ \( ( 1 - 79 T^{2} )^{2} \)
$83$ \( ( 1 - 18 T + 83 T^{2} )( 1 + 18 T + 83 T^{2} ) \)
$89$ \( ( 1 - 18 T + 89 T^{2} )( 1 + 18 T + 89 T^{2} ) \)
$97$ \( ( 1 + 10 T + 97 T^{2} )^{2} \)
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