Space of modular forms of level 32, weight 6, and trivial character

• Label: 32.6.a
• Level: $32$
• Weight: $6$
• Character orbit: 32.a
• Rep. character: $\chi_{32}(1,\cdot)$
• Character field: $\Q$
• Dimension: $5$
• Newform subspaces: $4$
• Sturm bound: $24$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 32 = 2^{5} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	32.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(24\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(32))\).

	Total	New	Old
Modular forms	24	5	19
Cusp forms	16	5	11
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
\(+\)	\(2\)
\(-\)	\(3\)

Trace form

5 * q + 38 * q^5 + 449 * q^9 + 110 * q^13 + 1610 * q^17 - 5888 * q^21 - 4277 * q^25 + 3678 * q^29 + 13184 * q^33 - 7258 * q^37 - 30766 * q^41 + 63214 * q^45 + 57789 * q^49 - 76490 * q^53 - 132992 * q^57 + 108510 * q^61 + 113476 * q^65 - 226560 * q^69 - 120318 * q^73 + 195328 * q^77 + 270029 * q^81 - 131124 * q^85 - 174702 * q^89 + 152576 * q^93 + 359642 * q^97

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(32))\) 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
32.6.a.a	$32$	$6$	32.a	1.a	$1$	$1$	$1$	$5.132$	\(\Q\)	None	✓	✓			32.6.a.a	$1$	$1$	\(0\)	\(-8\)	\(14\)	\(-208\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-8q^{3}+14q^{5}-208q^{7}-179q^{9}+\cdots\)
32.6.a.b	$32$	$6$	32.a	1.a	$1$	$1$	$1$	$5.132$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	✓			32.6.a.b	$2$	$1$	\(0\)	\(0\)	\(-82\)	\(0\)		$+$	$+$	$1$	$N(\mathrm{U}(1))$	\(q-82q^{5}-3^{5}q^{9}-1194q^{13}+2242q^{17}+\cdots\)
32.6.a.c	$32$	$6$	32.a	1.a	$1$	$1$	$1$	$5.132$	\(\Q\)	None	✓	✓			32.6.a.a	$1$	$0$	\(0\)	\(8\)	\(14\)	\(208\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+8q^{3}+14q^{5}+208q^{7}-179q^{9}+\cdots\)
32.6.a.d	$32$	$6$	32.a	1.a	$1$	$2$	$2$	$5.132$	\(\Q(\sqrt{3}) \)	None	✓	✓	✓		32.6.a.d	$2$	$0$	\(0\)	\(0\)	\(92\)	\(0\)		$-$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+46q^{5}-6\beta q^{7}+525q^{9}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(32))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(32)) \simeq \) \(S_{6}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 2}\)