Properties

Label 96.2.d
Level 96
Weight 2
Character orbit d
Rep. character \(\chi_{96}(49,\cdot)\)
Character field \(\Q\)
Dimension 2
Newform subspaces 1
Sturm bound 32
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 96 = 2^{5} \cdot 3 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 96.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 8 \)
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 2 22
Cusp forms 8 2 6
Eisenstein series 16 0 16

Trace form

\( 2q + 4q^{7} - 2q^{9} + O(q^{10}) \) \( 2q + 4q^{7} - 2q^{9} - 4q^{15} - 4q^{17} - 8q^{23} + 2q^{25} - 4q^{31} + 8q^{39} + 4q^{41} + 24q^{47} - 6q^{49} + 8q^{57} - 4q^{63} + 16q^{65} - 24q^{71} - 12q^{73} - 20q^{79} + 2q^{81} + 12q^{87} - 20q^{89} + 16q^{95} - 4q^{97} + O(q^{100}) \)

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.d.a \(2\) \(0.767\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(4\) \(q+iq^{3}+2iq^{5}+2q^{7}-q^{9}-4iq^{13}+\cdots\)

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
$3$ \( 1 + T^{2} \)
$5$ \( ( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} ) \)
$7$ \( ( 1 - 2 T + 7 T^{2} )^{2} \)
$11$ \( ( 1 - 11 T^{2} )^{2} \)
$13$ \( ( 1 - 6 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} ) \)
$17$ \( ( 1 + 2 T + 17 T^{2} )^{2} \)
$19$ \( 1 - 22 T^{2} + 361 T^{4} \)
$23$ \( ( 1 + 4 T + 23 T^{2} )^{2} \)
$29$ \( 1 - 22 T^{2} + 841 T^{4} \)
$31$ \( ( 1 + 2 T + 31 T^{2} )^{2} \)
$37$ \( 1 - 10 T^{2} + 1369 T^{4} \)
$41$ \( ( 1 - 2 T + 41 T^{2} )^{2} \)
$43$ \( 1 - 70 T^{2} + 1849 T^{4} \)
$47$ \( ( 1 - 12 T + 47 T^{2} )^{2} \)
$53$ \( 1 - 70 T^{2} + 2809 T^{4} \)
$59$ \( 1 - 102 T^{2} + 3481 T^{4} \)
$61$ \( ( 1 - 61 T^{2} )^{2} \)
$67$ \( 1 + 10 T^{2} + 4489 T^{4} \)
$71$ \( ( 1 + 12 T + 71 T^{2} )^{2} \)
$73$ \( ( 1 + 6 T + 73 T^{2} )^{2} \)
$79$ \( ( 1 + 10 T + 79 T^{2} )^{2} \)
$83$ \( 1 + 90 T^{2} + 6889 T^{4} \)
$89$ \( ( 1 + 10 T + 89 T^{2} )^{2} \)
$97$ \( ( 1 + 2 T + 97 T^{2} )^{2} \)
show more
show less