Space of modular forms of level 80, weight 2, and Character 80.s

• Label: 80.2.s
• Level: $80$
• Weight: $2$
• Character orbit: 80.s
• Rep. character: $\chi_{80}(3,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $20$
• Newform subspaces: $2$
• Sturm bound: $24$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	80.s (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 80 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(24\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(80, [\chi])\).

	Total	New	Old
Modular forms	28	28	0
Cusp forms	20	20	0
Eisenstein series	8	8	0

Trace form

20 * q - 2 * q^2 - 4 * q^3 + 4 * q^4 - 2 * q^5 - 4 * q^6 - 4 * q^7 - 8 * q^8 + 12 * q^9 + 2 * q^10 - 4 * q^11 - 12 * q^15 - 8 * q^16 - 4 * q^17 - 26 * q^18 - 8 * q^19 - 8 * q^20 - 4 * q^21 + 12 * q^22 - 4 * q^23 - 12 * q^24 - 20 * q^26 - 16 * q^27 + 28 * q^28 + 36 * q^30 + 28 * q^32 - 4 * q^33 + 24 * q^34 + 20 * q^35 - 4 * q^36 + 24 * q^38 + 32 * q^40 - 16 * q^42 - 40 * q^44 - 18 * q^45 + 12 * q^46 + 24 * q^47 + 20 * q^48 - 6 * q^50 + 4 * q^51 + 16 * q^52 - 4 * q^53 - 4 * q^54 - 4 * q^55 + 20 * q^56 - 12 * q^57 + 48 * q^58 + 16 * q^59 + 12 * q^61 - 36 * q^62 - 12 * q^63 + 16 * q^64 - 4 * q^65 + 4 * q^66 - 56 * q^68 - 28 * q^69 - 52 * q^70 + 24 * q^71 - 64 * q^72 - 8 * q^73 - 36 * q^74 + 4 * q^75 - 4 * q^76 - 32 * q^77 - 28 * q^78 - 76 * q^80 - 20 * q^81 + 40 * q^82 + 36 * q^83 + 48 * q^84 + 8 * q^85 - 28 * q^86 + 52 * q^87 - 16 * q^88 - 6 * q^90 + 12 * q^91 - 4 * q^92 - 28 * q^94 + 40 * q^95 - 56 * q^96 - 4 * q^97 - 78 * q^98 + 20 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(80, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
80.2.s.a	$80$	$2$	80.s	80.s	$4$	$2$	$1$	$0.639$	\(\Q(\sqrt{-1}) \)	None		✓			80.2.j.a	$2$	$1$	\(-2\)	\(-4\)	\(-4\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(i-1)q^{2}-2 q^{3}-2 i q^{4}+(i-2)q^{5}+\cdots\)
80.2.s.b	$80$	$2$	80.s	80.s	$4$	$18$	$9$	$0.639$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None		✓	✓		80.2.j.b	$2$	$0$	\(0\)	\(0\)	\(2\)	\(2\)	$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}-\beta _{3}q^{3}+\beta _{13}q^{4}+\beta _{17}q^{5}+\cdots\)