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

• Label: 32.7.h
• Level: $32$
• Weight: $7$
• Character orbit: 32.h
• Rep. character: $\chi_{32}(3,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $92$
• Newform subspaces: $1$
• Sturm bound: $28$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 32 = 2^{5} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	32.h (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 32 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(28\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	100	100	0
Cusp forms	92	92	0
Eisenstein series	8	8	0

Trace form

92 * 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 + 2996 * q^10 - 4 * q^11 - 3892 * q^12 - 4 * q^13 - 8532 * q^14 - 8 * q^15 + 14096 * q^16 + 24296 * q^18 - 4 * q^19 - 14004 * q^20 - 4 * q^21 - 19552 * q^22 + 13116 * q^23 - 43568 * q^24 - 4 * q^25 + 5296 * q^26 - 68644 * q^27 + 85496 * q^28 - 4 * q^29 + 102980 * q^30 - 58904 * q^32 - 8 * q^33 - 139248 * q^34 + 162332 * q^35 - 328464 * q^36 - 4 * q^37 + 457684 * q^38 - 254404 * q^39 + 430952 * q^40 - 4 * q^41 - 256504 * q^42 + 145436 * q^43 - 808764 * q^44 - 2920 * q^45 - 197284 * q^46 - 8 * q^47 + 349488 * q^48 + 1254548 * q^50 - 157792 * q^51 - 71644 * q^52 + 443676 * q^53 - 455840 * q^54 - 232708 * q^55 - 619736 * q^56 - 4 * q^57 - 290272 * q^58 + 886140 * q^59 + 803000 * q^60 - 652996 * q^61 + 1415352 * q^62 - 1533928 * q^64 - 8 * q^65 - 308980 * q^66 - 1509604 * q^67 + 447632 * q^68 + 1083452 * q^69 - 676264 * q^70 - 267012 * q^71 - 1219564 * q^72 - 4 * q^73 - 661588 * q^74 + 2083672 * q^75 + 873980 * q^76 - 932964 * q^77 + 1480180 * q^78 - 1721864 * q^79 - 2377928 * q^80 - 1407364 * q^82 + 3074396 * q^83 + 2103584 * q^84 + 62496 * q^85 + 2146368 * q^86 - 2029892 * q^87 + 2855072 * q^88 - 4 * q^89 + 2497832 * q^90 - 3700804 * q^91 - 540888 * q^92 + 2912 * q^93 - 2438936 * q^94 + 3127168 * q^96 - 8 * q^97 + 2073880 * q^98 + 5967768 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
32.7.h.a	$32$	$7$	32.h	32.h	$8$	$92$	$23$	$7.362$		None		✓	✓	✓	32.7.h.a	$2$	$0$	\(-4\)	\(-4\)	\(-4\)	\(-4\)		$\mathrm{SU}(2)[C_{8}]$