Space of modular forms of level 32, weight 2, and Character 32.g

• Label: 32.2.g
• Level: $32$
• Weight: $2$
• Character orbit: 32.g
• Rep. character: $\chi_{32}(5,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $8$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 32 = 2^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	32.g (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 32 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(8\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(32, [\chi])\).

	Total	New	Old
Modular forms	20	20	0
Cusp forms	12	12	0
Eisenstein series	8	8	0

Trace form

12 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 + 4 * q^10 - 4 * q^11 + 12 * q^12 - 4 * q^13 + 12 * q^14 + 16 * q^16 + 16 * q^18 - 4 * q^19 + 12 * q^20 - 4 * q^21 + 8 * q^22 + 4 * q^23 - 16 * q^24 - 4 * q^25 - 24 * q^26 + 20 * q^27 - 24 * q^28 - 4 * q^29 - 36 * q^30 + 16 * q^31 - 24 * q^32 - 8 * q^33 - 16 * q^34 + 20 * q^35 - 32 * q^36 - 4 * q^37 + 4 * q^38 + 20 * q^39 + 8 * q^40 - 4 * q^41 + 16 * q^42 + 4 * q^43 + 36 * q^44 + 8 * q^45 + 28 * q^46 + 48 * q^48 + 36 * q^50 - 8 * q^51 + 4 * q^52 + 12 * q^53 + 8 * q^54 - 36 * q^55 + 8 * q^56 - 4 * q^57 - 8 * q^58 - 36 * q^59 - 8 * q^60 + 28 * q^61 - 24 * q^62 - 48 * q^63 - 40 * q^64 - 8 * q^65 - 28 * q^66 - 44 * q^67 + 16 * q^68 + 28 * q^69 - 16 * q^70 - 36 * q^71 + 20 * q^72 - 4 * q^73 + 12 * q^74 - 16 * q^75 - 4 * q^76 + 12 * q^77 + 36 * q^78 - 8 * q^80 - 4 * q^82 + 36 * q^83 + 16 * q^84 + 16 * q^85 - 24 * q^86 + 52 * q^87 - 4 * q^89 + 8 * q^90 + 44 * q^91 - 40 * q^92 - 16 * q^93 + 8 * q^94 + 56 * q^95 - 8 * q^97 - 24 * q^98 + 48 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(32, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
32.2.g.a	$32$	$2$	32.g	32.g	$8$	$4$	$1$	$0.256$	\(\Q(\zeta_{8})\)	None		✓			32.2.g.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}+(\zeta_{8}+\zeta_{8}^{2})q^{3}+\cdots\)
32.2.g.b	$32$	$2$	32.g	32.g	$8$	$8$	$2$	$0.256$	8.0.18939904.2	None		✓	✓		32.2.g.b	$2$	$0$	\(-4\)	\(-4\)	\(0\)	\(-8\)	$2$	$\mathrm{SU}(2)[C_{8}]$	\(q-\beta _{2}q^{2}+(\beta _{1}+\beta _{3}+\beta _{5}+\beta _{7})q^{3}+\cdots\)