Space of modular forms of level 80, weight 11, and Character 80.i

• Label: 80.11.i
• Level: $80$
• Weight: $11$
• Character orbit: 80.i
• Rep. character: $\chi_{80}(13,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $236$
• Newform subspaces: $1$
• Sturm bound: $132$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	80.i (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 80 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(132\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(80, [\chi])\).

	Total	New	Old
Modular forms	244	244	0
Cusp forms	236	236	0
Eisenstein series	8	8	0

Trace form

236 * q - 2 * q^2 + 1220 * q^4 - 2 * q^5 - 4 * q^6 - 69128 * q^8 - 4487724 * q^9 + 2046 * q^10 - 4 * q^11 + 738232 * q^12 - 4 * q^15 - 2041064 * q^16 - 4 * q^17 + 5924662 * q^18 - 5107040 * q^19 + 2913160 * q^20 - 4 * q^21 + 9808012 * q^22 + 236196 * q^24 - 6048244 * q^26 + 15215716 * q^28 - 30527308 * q^30 - 8 * q^31 - 82944132 * q^32 - 4 * q^33 - 150787640 * q^34 - 14674464 * q^35 - 100247348 * q^36 - 209466216 * q^38 + 472392 * q^39 + 282957456 * q^40 + 681994816 * q^42 + 31808124 * q^43 - 908940840 * q^44 - 19413154 * q^45 - 430213844 * q^46 - 4 * q^47 + 1394077780 * q^48 + 981313210 * q^50 + 373209116 * q^51 + 1025053488 * q^52 - 4 * q^53 + 1241604372 * q^54 + 1974486356 * q^56 + 236196 * q^57 + 624139296 * q^58 + 749542720 * q^59 + 5795514376 * q^60 - 1673280164 * q^61 - 438403556 * q^62 - 1129901000 * q^63 - 2847240880 * q^64 - 4 * q^65 + 4226634996 * q^66 - 5418553252 * q^67 + 3281041848 * q^68 + 1698475716 * q^69 - 5980058172 * q^70 + 2490447808 * q^72 - 894454032 * q^73 - 3678024964 * q^74 + 241008096 * q^75 + 10579892476 * q^76 + 1129900992 * q^77 + 4072424540 * q^78 + 28086184324 * q^80 + 79033779748 * q^81 - 26176518000 * q^82 - 2938554144 * q^84 + 19531248 * q^85 - 2548694284 * q^86 + 236196 * q^87 + 2506934416 * q^88 - 484086218 * q^90 + 6679066556 * q^91 - 35385670492 * q^92 - 8232256100 * q^94 - 6725122180 * q^95 + 7881918696 * q^96 - 4 * q^97 - 23474977278 * q^98 - 28071956444 * q^99

Decomposition of \(S_{11}^{\mathrm{new}}(80, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
80.11.i.a	$80$	$11$	80.i	80.i	$4$	$236$	$118$	$50.829$		None		✓	✓	✓	80.11.i.a	$2$	$0$	\(-2\)	\(0\)	\(-2\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$