Space of modular forms of level 32, weight 7, and Character 32.d

• Label: 32.7.d
• Level: $32$
• Weight: $7$
• Character orbit: 32.d
• Rep. character: $\chi_{32}(15,\cdot)$
• Character field: $\Q$
• Dimension: $5$
• Newform subspaces: $2$
• Sturm bound: $28$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 32 = 2^{5} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	32.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(28\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(32, [\chi])\).

	Total	New	Old
Modular forms	28	7	21
Cusp forms	20	5	15
Eisenstein series	8	2	6

Trace form

\( 5 q + 2 q^{3} + 727 q^{9} + O(q^{10}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(32, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
32.7.d.a	$32$	$7$	32.d	8.d	$2$	$1$	$1$	$7.362$	\(\Q\)	\(\Q(\sqrt{-2}) \)	✓	$2$	$0$	\(0\)	\(-46\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-46q^{3}+1387q^{9}+2338q^{11}-1726q^{17}+\cdots\)
32.7.d.b	$32$	$7$	32.d	8.d	$2$	$4$	$4$	$7.362$	4.0.3803625.2	None		$2$	$0$	\(0\)	\(48\)	\(0\)	\(0\)	$2^{13}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(12-\beta _{1})q^{3}-\beta _{2}q^{5}+(\beta _{2}-\beta _{3})q^{7}+\cdots\)

Decomposition of \(S_{7}^{\mathrm{old}}(32, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(32, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 2}\)