Space of modular forms of level 32, weight 4, and trivial character

• Label: 32.4.a
• Level: $32$
• Weight: $4$
• Character orbit: 32.a
• Rep. character: $\chi_{32}(1,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $3$
• Sturm bound: $16$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 32 = 2^{5} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	32.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(16\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(32))\).

	Total	New	Old
Modular forms	16	3	13
Cusp forms	8	3	5
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
\(+\)	\(2\)
\(-\)	\(1\)

Trace form

\( 3 q + 2 q^{5} + 47 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(32))\) 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
32.4.a.a	$32$	$4$	32.a	1.a	$1$	$1$	$1$	$1.888$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-8\)	\(-10\)	\(-16\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-8q^{3}-10q^{5}-2^{4}q^{7}+37q^{9}+40q^{11}+\cdots\)
32.4.a.b	$32$	$4$	32.a	1.a	$1$	$1$	$1$	$1.888$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(22\)	\(0\)		$+$	$+$	$1$	$N(\mathrm{U}(1))$	\(q+22q^{5}-3^{3}q^{9}-18q^{13}-94q^{17}+\cdots\)
32.4.a.c	$32$	$4$	32.a	1.a	$1$	$1$	$1$	$1.888$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(8\)	\(-10\)	\(16\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+8q^{3}-10q^{5}+2^{4}q^{7}+37q^{9}-40q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(32))\) into lower level spaces

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