Properties

Label 96.2.a
Level $96$
Weight $2$
Character orbit 96.a
Rep. character $\chi_{96}(1,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $2$
Sturm bound $32$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 96 = 2^{5} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 96.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(32\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(96))\).

Total New Old
Modular forms 24 2 22
Cusp forms 9 2 7
Eisenstein series 15 0 15

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)FrickeDim.
\(+\)\(-\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(1\)
Plus space\(+\)\(0\)
Minus space\(-\)\(2\)

Trace form

\( 2 q + 4 q^{5} + 2 q^{9} + O(q^{10}) \) \( 2 q + 4 q^{5} + 2 q^{9} - 4 q^{13} - 12 q^{17} - 8 q^{21} - 2 q^{25} + 4 q^{29} + 8 q^{33} - 4 q^{37} + 4 q^{41} + 4 q^{45} + 18 q^{49} + 20 q^{53} - 8 q^{57} + 12 q^{61} - 8 q^{65} - 12 q^{73} - 32 q^{77} + 2 q^{81} - 24 q^{85} + 20 q^{89} + 8 q^{93} - 28 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(96))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3
96.2.a.a 96.a 1.a $1$ $0.767$ \(\Q\) None \(0\) \(-1\) \(2\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}+4q^{7}+q^{9}-4q^{11}+\cdots\)
96.2.a.b 96.a 1.a $1$ $0.767$ \(\Q\) None \(0\) \(1\) \(2\) \(-4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}-4q^{7}+q^{9}+4q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(96))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(96)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 2}\)