Properties

Label 96.4.a
Level $96$
Weight $4$
Character orbit 96.a
Rep. character $\chi_{96}(1,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $6$
Sturm bound $64$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 96 = 2^{5} \cdot 3 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 96.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(64\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(96))\).

Total New Old
Modular forms 56 6 50
Cusp forms 40 6 34
Eisenstein series 16 0 16

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
\(+\)\(+\)$+$\(2\)
\(+\)\(-\)$-$\(1\)
\(-\)\(+\)$-$\(1\)
\(-\)\(-\)$+$\(2\)
Plus space\(+\)\(4\)
Minus space\(-\)\(2\)

Trace form

\( 6 q - 4 q^{5} + 54 q^{9} + O(q^{10}) \) \( 6 q - 4 q^{5} + 54 q^{9} + 164 q^{13} + 156 q^{17} - 120 q^{21} - 150 q^{25} + 284 q^{29} + 24 q^{33} - 636 q^{37} - 1300 q^{41} - 36 q^{45} + 854 q^{49} - 212 q^{53} + 168 q^{57} - 1324 q^{61} - 280 q^{65} + 1212 q^{73} + 3872 q^{77} + 486 q^{81} + 2456 q^{85} + 220 q^{89} - 2760 q^{93} - 2260 q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(96))\) 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
96.4.a.a 96.a 1.a $1$ $5.664$ \(\Q\) None \(0\) \(-3\) \(-14\) \(36\) $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}-14q^{5}+6^{2}q^{7}+9q^{9}+6^{2}q^{11}+\cdots\)
96.4.a.b 96.a 1.a $1$ $5.664$ \(\Q\) None \(0\) \(-3\) \(2\) \(-12\) $-$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+2q^{5}-12q^{7}+9q^{9}-60q^{11}+\cdots\)
96.4.a.c 96.a 1.a $1$ $5.664$ \(\Q\) None \(0\) \(-3\) \(10\) \(-4\) $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+10q^{5}-4q^{7}+9q^{9}+20q^{11}+\cdots\)
96.4.a.d 96.a 1.a $1$ $5.664$ \(\Q\) None \(0\) \(3\) \(-14\) \(-36\) $+$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}-14q^{5}-6^{2}q^{7}+9q^{9}-6^{2}q^{11}+\cdots\)
96.4.a.e 96.a 1.a $1$ $5.664$ \(\Q\) None \(0\) \(3\) \(2\) \(12\) $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+2q^{5}+12q^{7}+9q^{9}+60q^{11}+\cdots\)
96.4.a.f 96.a 1.a $1$ $5.664$ \(\Q\) None \(0\) \(3\) \(10\) \(4\) $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+10q^{5}+4q^{7}+9q^{9}-20q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(96))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(96)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 2}\)