Space of modular forms of level 32, weight 30, and Character 32.b

• Label: 32.30.b
• Level: $32$
• Weight: $30$
• Character orbit: 32.b
• Rep. character: $\chi_{32}(17,\cdot)$
• Character field: $\Q$
• Dimension: $28$
• Newform subspaces: $1$
• Sturm bound: $120$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 32 = 2^{5} \)
Weight:	\( k \)	\(=\)	\( 30 \)
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:			\(120\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{30}(32, [\chi])\).

	Total	New	Old
Modular forms	120	30	90
Cusp forms	112	28	84
Eisenstein series	8	2	6

Trace form

28 * q - 1356446145696 * q^7 - 594796603828988 * q^9 + 116634443346832736 * q^15 + 236508787823771000 * q^17 - 149024448719096002016 * q^23 - 985560523954733380084 * q^25 + 7260046134127777257856 * q^31 - 2610896914152110428752 * q^33 - 74849868421738610351584 * q^39 - 80518000617380870331368 * q^41 - 121247766087237335010240 * q^47 + 8159536578855108935060412 * q^49 - 48823262031438992129145632 * q^55 - 36164170101969527032146832 * q^57 + 493740527299257821299206560 * q^63 + 275343801437622480199359040 * q^65 - 1637917847840158826077048224 * q^71 - 1631197084836886372704831464 * q^73 + 2323214658985225396749618624 * q^79 + 3743945936405161605092781740 * q^81 + 23673763728982249679638339488 * q^87 - 3845720546264709069323947304 * q^89 - 120167370974924948019325601696 * q^95 - 6191808951720963836806076616 * q^97

Decomposition of \(S_{30}^{\mathrm{new}}(32, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
32.30.b.a	$32$	$30$	32.b	8.b	$2$	$28$	$28$	$170.490$		None			✓	✓	8.30.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-13\!\cdots\!96\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{30}^{\mathrm{old}}(32, [\chi])\) into lower level spaces

\( S_{30}^{\mathrm{old}}(32, [\chi]) \simeq \) \(S_{30}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 3}\)