Space of modular forms of level 80, weight 10, and Character 80.s

• Label: 80.10.s
• Level: $80$
• Weight: $10$
• Character orbit: 80.s
• Rep. character: $\chi_{80}(3,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $212$
• Newform subspaces: $1$
• Sturm bound: $120$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	80.s (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 80 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(120\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(80, [\chi])\).

	Total	New	Old
Modular forms	220	220	0
Cusp forms	212	212	0
Eisenstein series	8	8	0

Trace form

212 * q - 2 * q^2 - 4 * q^3 - 684 * q^4 - 2 * q^5 - 4 * q^6 - 4 * q^7 + 712 * q^8 + 1338444 * q^9 + 1022 * q^10 - 4 * q^11 - 155360 * q^12 - 78732 * q^15 + 534200 * q^16 - 4 * q^17 - 759866 * q^18 + 480888 * q^19 + 360352 * q^20 - 4 * q^21 - 1659308 * q^22 - 4 * q^23 - 78732 * q^24 + 6874252 * q^26 - 78736 * q^27 + 282588 * q^28 - 8081124 * q^30 - 3431972 * q^32 - 4 * q^33 + 14019176 * q^34 - 15214060 * q^35 - 18999476 * q^36 + 66252864 * q^38 + 38890752 * q^40 - 82908936 * q^42 - 144493960 * q^44 - 3945618 * q^45 + 13958060 * q^46 + 112458264 * q^47 + 269076820 * q^48 - 11251806 * q^50 - 90014332 * q^51 - 87877584 * q^52 - 4 * q^53 + 49163684 * q^54 - 4 * q^55 - 87069868 * q^56 - 78732 * q^57 + 534661688 * q^58 - 144037616 * q^59 - 425720880 * q^60 + 90121100 * q^61 + 26063004 * q^62 - 78732 * q^63 + 317209104 * q^64 - 4 * q^65 + 193062388 * q^66 - 1095329816 * q^68 + 382281444 * q^69 - 884221412 * q^70 - 238101480 * q^71 + 440475536 * q^72 + 241709752 * q^73 - 652460148 * q^74 - 1034969596 * q^75 + 214323196 * q^76 - 161414432 * q^77 - 115110388 * q^78 - 426894316 * q^80 + 7748409772 * q^81 - 647768040 * q^82 - 795523164 * q^83 + 1454815008 * q^84 + 3906248 * q^85 + 1472476340 * q^86 - 2350951628 * q^87 + 296521744 * q^88 - 6912111786 * q^90 + 1393037580 * q^91 + 1769972156 * q^92 - 3013336692 * q^94 - 2812876760 * q^95 + 5969986888 * q^96 - 4 * q^97 - 2904618678 * q^98 - 778491244 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(80, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
80.10.s.a	$80$	$10$	80.s	80.s	$4$	$212$	$106$	$41.203$		None		✓	✓	✓	80.10.j.a	$2$	$0$	\(-2\)	\(-4\)	\(-2\)	\(-4\)		$\mathrm{SU}(2)[C_{4}]$