Space of modular forms of level 32, weight 20, and trivial character

• Label: 32.20.a
• Level: $32$
• Weight: $20$
• Character orbit: 32.a
• Rep. character: $\chi_{32}(1,\cdot)$
• Character field: $\Q$
• Dimension: $19$
• Newform subspaces: $5$
• Sturm bound: $80$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 32 = 2^{5} \)
Weight:	\( k \)	\(=\)	\( 20 \)
Character orbit:	\([\chi]\)	\(=\)	32.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(80\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{20}(\Gamma_0(32))\).

	Total	New	Old
Modular forms	80	19	61
Cusp forms	72	19	53
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
\(+\)	\(10\)
\(-\)	\(9\)

Trace form

\( 19 q - 3565918 q^{5} + 8979936575 q^{9} + O(q^{10}) \)

Decomposition of \(S_{20}^{\mathrm{new}}(\Gamma_0(32))\) 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
32.20.a.a	$32$	$20$	32.a	1.a	$1$	$1$	$1$	$73.221$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(5042902\)	\(0\)		$+$	$+$	$1$	$N(\mathrm{U}(1))$	\(q+5042902q^{5}-3^{19}q^{9}+13425142062q^{13}+\cdots\)
32.20.a.b	$32$	$20$	32.a	1.a	$1$	$4$	$4$	$73.221$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$2$	$0$	\(0\)	\(0\)	\(-5322920\)	\(0\)		$+$	$+$	$2^{30}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-1330730+5\beta _{2})q^{5}+\cdots\)
32.20.a.c	$32$	$20$	32.a	1.a	$1$	$4$	$4$	$73.221$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$2$	$1$	\(0\)	\(0\)	\(4924760\)	\(0\)		$-$	$-$	$2^{27}\cdot 3^{4}\cdot 5^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(1231190+\beta _{2})q^{5}+(830\beta _{1}+\cdots)q^{7}+\cdots\)
32.20.a.d	$32$	$20$	32.a	1.a	$1$	$5$	$5$	$73.221$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-6424\)	\(-4105330\)	\(107158480\)		$+$	$+$	$2^{48}\cdot 3^{4}\cdot 5^{2}$	$\mathrm{SU}(2)$	\(q+(-1285-\beta _{1})q^{3}+(-821058+39\beta _{1}+\cdots)q^{5}+\cdots\)
32.20.a.e	$32$	$20$	32.a	1.a	$1$	$5$	$5$	$73.221$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(6424\)	\(-4105330\)	\(-107158480\)		$-$	$-$	$2^{48}\cdot 3^{4}\cdot 5^{2}$	$\mathrm{SU}(2)$	\(q+(1285+\beta _{1})q^{3}+(-821058+39\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{20}^{\mathrm{old}}(\Gamma_0(32))\) into lower level spaces

\( S_{20}^{\mathrm{old}}(\Gamma_0(32)) \cong \) \(S_{20}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 5}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 2}\)