Space of modular forms of level 31, weight 4, and Character 31.d

• Label: 31.4.d
• Level: $31$
• Weight: $4$
• Character orbit: 31.d
• Rep. character: $\chi_{31}(2,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $28$
• Newform subspaces: $1$
• Sturm bound: $10$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 31 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	31.d (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 31 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(10\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(31, [\chi])\).

	Total	New	Old
Modular forms	36	36	0
Cusp forms	28	28	0
Eisenstein series	8	8	0

Trace form

28 * q - 3 * q^2 - 7 * q^3 - 39 * q^4 + 38 * q^6 + 35 * q^7 - 17 * q^8 - 16 * q^9 + 54 * q^10 - 17 * q^11 - 130 * q^12 - 21 * q^13 + 2 * q^14 - 154 * q^15 + 169 * q^16 - 49 * q^17 + 6 * q^18 + 149 * q^19 + 361 * q^20 - 319 * q^21 - 176 * q^22 - 641 * q^23 - 425 * q^24 - 240 * q^25 + 1376 * q^26 + 809 * q^27 - 108 * q^28 + 115 * q^29 - 1470 * q^30 + 428 * q^31 + 1806 * q^32 + 817 * q^33 - 901 * q^34 - 816 * q^35 + 848 * q^36 + 476 * q^37 - 230 * q^38 - 329 * q^39 - 1674 * q^40 - 375 * q^41 + 860 * q^42 - 703 * q^43 - 604 * q^44 + 1078 * q^45 + 185 * q^46 - 953 * q^47 - 176 * q^48 - 1736 * q^49 - 866 * q^50 + 365 * q^51 + 157 * q^52 - 235 * q^53 - 3838 * q^54 - 830 * q^55 - 496 * q^56 + 3202 * q^57 + 2507 * q^58 + 775 * q^59 + 13 * q^60 - 192 * q^61 + 4148 * q^62 + 7012 * q^63 + 4651 * q^64 - 892 * q^65 - 5030 * q^66 - 240 * q^67 + 1890 * q^68 + 1957 * q^69 + 2605 * q^70 - 1459 * q^71 - 4822 * q^72 + 1303 * q^73 - 1787 * q^74 - 4013 * q^75 - 5975 * q^76 - 2413 * q^77 - 6977 * q^78 + 521 * q^79 - 550 * q^80 - 3064 * q^81 + 1926 * q^82 + 893 * q^83 + 1665 * q^84 - 6298 * q^85 - 3321 * q^86 + 802 * q^87 + 10756 * q^88 + 2031 * q^89 + 8334 * q^90 - 5375 * q^91 + 3902 * q^92 + 8981 * q^93 + 13970 * q^94 + 5474 * q^95 - 5690 * q^96 - 10071 * q^97 + 5060 * q^98 + 4004 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(31, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
31.4.d.a	$31$	$4$	31.d	31.d	$5$	$28$	$7$	$1.829$		None		✓	✓	✓	31.4.d.a	$2$	$0$	\(-3\)	\(-7\)	\(0\)	\(35\)		$\mathrm{SU}(2)[C_{5}]$