Space of modular forms of level 32, weight 24, and trivial character

• Label: 32.24.a
• Level: $32$
• Weight: $24$
• Character orbit: 32.a
• Rep. character: $\chi_{32}(1,\cdot)$
• Character field: $\Q$
• Dimension: $23$
• Newform subspaces: $5$
• Sturm bound: $96$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 32 = 2^{5} \)
Weight:	\( k \)	\(=\)	\( 24 \)
Character orbit:	\([\chi]\)	\(=\)	32.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(96\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{24}(\Gamma_0(32))\).

	Total	New	Old
Modular forms	96	23	73
Cusp forms	88	23	65
Eisenstein series	8	0	8

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

\(2\)	Dim
\(+\)	\(12\)
\(-\)	\(11\)

Trace form

\( 23 q - 35553398 q^{5} + 726786858563 q^{9} + O(q^{10}) \)

Decomposition of \(S_{24}^{\mathrm{new}}(\Gamma_0(32))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2
32.24.a.a	$32$	$24$	32.a	1.a	$1$	$1$	$1$	$107.265$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$1$	\(0\)	\(0\)	\(-206464378\)	\(0\)		$-$	$-$	$1$	$N(\mathrm{U}(1))$	\(q-206464378q^{5}-3^{23}q^{9}+7436301651582q^{13}+\cdots\)
32.24.a.b	$32$	$24$	32.a	1.a	$1$	$4$	$4$	$107.265$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$2$	$1$	\(0\)	\(0\)	\(19990040\)	\(0\)		$-$	$-$	$2^{30}\cdot 3^{7}\cdot 5$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(4997510+5\beta _{2})q^{5}+(8726\beta _{1}+\cdots)q^{7}+\cdots\)
32.24.a.c	$32$	$24$	32.a	1.a	$1$	$6$	$6$	$107.265$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-483920\)	\(-6100380\)	\(347289696\)		$-$	$-$	$2^{71}\cdot 3^{4}\cdot 5^{4}$	$\mathrm{SU}(2)$	\(q+(-80653+\beta _{1})q^{3}+(-1016775+\cdots)q^{5}+\cdots\)
32.24.a.d	$32$	$24$	32.a	1.a	$1$	$6$	$6$	$107.265$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$2$	$0$	\(0\)	\(0\)	\(163121700\)	\(0\)		$+$	$+$	$2^{71}\cdot 3^{6}\cdot 5^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(27186950+\beta _{2})q^{5}+(50^{2}\beta _{1}+\cdots)q^{7}+\cdots\)
32.24.a.e	$32$	$24$	32.a	1.a	$1$	$6$	$6$	$107.265$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(483920\)	\(-6100380\)	\(-347289696\)		$+$	$+$	$2^{71}\cdot 3^{4}\cdot 5^{4}$	$\mathrm{SU}(2)$	\(q+(80653-\beta _{1})q^{3}+(-1016775-135\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{24}^{\mathrm{old}}(\Gamma_0(32))\) into lower level spaces

\( S_{24}^{\mathrm{old}}(\Gamma_0(32)) \cong \) \(S_{24}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 5}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 2}\)