Space of modular forms of level 31, weight 5, and Character 31.h

• Label: 31.5.h
• Level: $31$
• Weight: $5$
• Character orbit: 31.h
• Rep. character: $\chi_{31}(3,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $80$
• Newform subspaces: $1$
• Sturm bound: $13$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 31 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	31.h (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 31 \)
Character field:			\(\Q(\zeta_{30})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(13\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(31, [\chi])\).

	Total	New	Old
Modular forms	96	96	0
Cusp forms	80	80	0
Eisenstein series	16	16	0

Trace form

80 * q - 6 * q^2 - 16 * q^3 - 138 * q^4 - q^5 - 9 * q^6 + 288 * q^7 - 221 * q^8 - 182 * q^9 + 102 * q^10 - 49 * q^11 - 159 * q^12 + 527 * q^13 - 740 * q^14 + 1060 * q^15 - 1970 * q^16 + 848 * q^17 + 3 * q^18 + 1534 * q^19 + 1165 * q^20 + 1367 * q^21 + 4579 * q^22 - 1375 * q^23 - 3828 * q^24 - 5997 * q^25 - 2547 * q^26 - 3235 * q^27 - 1564 * q^28 - 1150 * q^29 - 3587 * q^31 + 15718 * q^32 - 5029 * q^33 + 5958 * q^34 + 4959 * q^35 + 13555 * q^36 + 3462 * q^37 + 6118 * q^38 - 8143 * q^39 - 13011 * q^40 - 7290 * q^41 - 24735 * q^42 + 4687 * q^43 + 17051 * q^44 - 6093 * q^45 - 16530 * q^46 - 4302 * q^47 + 40344 * q^48 + 14300 * q^49 + 30081 * q^50 + 1348 * q^51 - 14433 * q^52 + 17996 * q^53 - 42200 * q^54 - 5289 * q^55 - 32470 * q^56 - 35847 * q^57 - 38475 * q^58 + 3552 * q^59 - 26585 * q^60 - 6327 * q^62 + 35814 * q^63 + 231 * q^64 + 18280 * q^65 + 85992 * q^66 + 2185 * q^67 + 56694 * q^68 + 57836 * q^69 + 6338 * q^70 - 3708 * q^71 - 25127 * q^72 + 5344 * q^73 + 5247 * q^74 + 13921 * q^75 - 10354 * q^76 - 37000 * q^77 - 98345 * q^78 + 53300 * q^79 + 65286 * q^80 + 20439 * q^81 - 26142 * q^82 - 59542 * q^83 - 77120 * q^84 + 4525 * q^85 - 100990 * q^86 - 55761 * q^87 - 82191 * q^88 - 26395 * q^89 - 61689 * q^90 - 12450 * q^91 + 9029 * q^93 + 67112 * q^94 - 3972 * q^95 + 210490 * q^96 + 5883 * q^97 + 107722 * q^98 + 75228 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(31, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
31.5.h.a	$31$	$5$	31.h	31.h	$30$	$80$	$10$	$3.204$		None		✓	✓	✓	31.5.h.a	$2$	$0$	\(-6\)	\(-16\)	\(-1\)	\(288\)		$\mathrm{SU}(2)[C_{30}]$