Space of modular forms of level 32, weight 2, and trivial character

• Label: 32.2.a
• Level: $32$
• Weight: $2$
• Character orbit: 32.a
• Rep. character: $\chi_{32}(1,\cdot)$
• Character field: $\Q$
• Dimension: $1$
• Newform subspaces: $1$
• Sturm bound: $8$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 32 = 2^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	32.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(8\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(32))\).

	Total	New	Old
Modular forms	8	1	7
Cusp forms	1	1	0
Eisenstein series	7	0	7

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
\(-\)	\(1\)

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(32))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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
32.2.a.a	$32$	$2$	32.a	1.a	$1$	$1$	$1$	$0.256$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	✓	✓	✓	32.2.a.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{5}-3q^{9}+6q^{13}+2q^{17}-q^{25}+\cdots\)