Space of modular forms of level 32, weight 4, and Character 32.b

• Label: 32.4.b
• Level: $32$
• Weight: $4$
• Character orbit: 32.b
• Rep. character: $\chi_{32}(17,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $16$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 32 = 2^{5} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	32.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(16\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(32, [\chi])\).

	Total	New	Old
Modular forms	16	4	12
Cusp forms	8	2	6
Eisenstein series	8	2	6

Trace form

2 * q + 16 * q^7 - 2 * q^9 - 112 * q^15 - 28 * q^17 + 304 * q^23 + 26 * q^25 - 448 * q^31 + 168 * q^33 + 560 * q^39 - 140 * q^41 - 672 * q^47 - 558 * q^49 + 336 * q^55 + 392 * q^57 - 16 * q^63 + 1120 * q^65 + 144 * q^71 - 588 * q^73 + 928 * q^79 - 1510 * q^81 - 1680 * q^87 + 532 * q^89 + 784 * q^95 + 1988 * q^97

Decomposition of \(S_{4}^{\mathrm{new}}(32, [\chi])\) 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				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
32.4.b.a	$32$	$4$	32.b	8.b	$2$	$2$	$2$	$1.888$	\(\Q(\sqrt{-7}) \)	None			✓	✓	8.4.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(16\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{3}-2\beta q^{5}+8q^{7}-q^{9}+3\beta q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(32, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(32, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 3}\)