Space of modular forms of level 31, weight 2, and Character 31.d

• Label: 31.2.d
• Level: $31$
• Weight: $2$
• Character orbit: 31.d
• Rep. character: $\chi_{31}(2,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $5$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
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:			\(5\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(31, [\chi])\).

	Total	New	Old
Modular forms	12	12	0
Cusp forms	4	4	0
Eisenstein series	8	8	0

Trace form

4 * q - 3 * q^2 + q^3 + 3 * q^4 - 6 * q^5 - 2 * q^6 - 3 * q^7 - 5 * q^8 + 2 * q^9 + 2 * q^10 - 2 * q^11 + 2 * q^12 + 6 * q^13 + 6 * q^14 + q^15 + 9 * q^16 - 3 * q^17 + 6 * q^18 - 5 * q^19 - 7 * q^20 + 3 * q^21 - 6 * q^22 + 11 * q^23 + 5 * q^24 - 6 * q^25 - 12 * q^26 - 5 * q^27 - 6 * q^28 + 5 * q^29 - 2 * q^30 - 11 * q^31 - 18 * q^32 - 8 * q^33 + 11 * q^34 + 12 * q^35 + 4 * q^36 - 8 * q^37 + 10 * q^38 + 9 * q^39 + 10 * q^40 + 8 * q^41 - 6 * q^42 + q^43 + 6 * q^44 - 8 * q^45 - 7 * q^46 + 7 * q^47 + 6 * q^48 - 2 * q^49 + 12 * q^50 + 3 * q^51 - 3 * q^52 + 21 * q^53 + 10 * q^54 - 2 * q^55 - 20 * q^57 - 15 * q^58 + 5 * q^59 - 3 * q^60 + 8 * q^61 - 8 * q^62 - 24 * q^63 - 7 * q^64 - 9 * q^65 + 6 * q^66 - 8 * q^67 - 6 * q^68 - 11 * q^69 - 9 * q^70 - 7 * q^71 - 10 * q^72 + 21 * q^73 + 11 * q^74 - 9 * q^75 + 15 * q^76 + 24 * q^77 - 3 * q^78 - 6 * q^80 - q^81 + 4 * q^82 - 14 * q^83 - 9 * q^84 + 2 * q^85 - 7 * q^86 + 30 * q^87 + 20 * q^88 + 5 * q^89 - 4 * q^90 + 18 * q^91 + 22 * q^92 - 4 * q^93 - 14 * q^94 - 5 * q^95 - 2 * q^96 - 3 * q^97 + 4 * q^98 + 24 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(31, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
31.2.d.a	$31$	$2$	31.d	31.d	$5$	$4$	$1$	$0.248$	\(\Q(\zeta_{10})\)	None		✓	✓	✓	31.2.d.a	$2$	$0$	\(-3\)	\(1\)	\(-6\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1-\zeta_{10}^{2})q^{2}+(1-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{3}+\cdots\)