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

• Label: 80.11.p
• Level: $80$
• Weight: $11$
• Character orbit: 80.p
• Rep. character: $\chi_{80}(17,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $58$
• Newform subspaces: $7$
• Sturm bound: $132$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	80.p (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(132\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	252	62	190
Cusp forms	228	58	170
Eisenstein series	24	4	20

Trace form

58 * q + 2 * q^3 - 2 * q^5 + 2 * q^7 + 4 * q^11 + 145666 * q^13 - 2076430 * q^15 + 452882 * q^17 + 5907276 * q^21 + 16246034 * q^23 - 738494 * q^25 - 31101232 * q^27 - 58368316 * q^31 + 45212092 * q^33 + 34205714 * q^35 - 115197222 * q^37 + 146547276 * q^41 + 15904066 * q^43 - 287129892 * q^45 - 809409358 * q^47 - 837310556 * q^51 + 146769866 * q^53 + 695258068 * q^55 - 1248755536 * q^57 - 1673280164 * q^61 - 3169541982 * q^63 - 2057629078 * q^65 + 1481541746 * q^67 - 3514702876 * q^71 - 1713824550 * q^73 + 372363538 * q^75 - 564950500 * q^77 - 19069766222 * q^81 - 3336135086 * q^83 - 5320742142 * q^85 - 5069347664 * q^87 - 25370032316 * q^91 + 264102604 * q^93 + 13740861360 * q^95 + 9668205978 * q^97

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.p.a	$80$	$11$	80.p	5.c	$4$	$2$	$1$	$50.829$	\(\Q(\sqrt{-1}) \)	None					10.11.c.b	$2$	$0$	\(0\)	\(-114\)	\(5850\)	\(-13906\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(57 i-57)q^{3}+(1100 i+2925)q^{5}+\cdots\)
80.11.p.b	$80$	$11$	80.p	5.c	$4$	$2$	$1$	$50.829$	\(\Q(\sqrt{-1}) \)	None					10.11.c.a	$2$	$0$	\(0\)	\(366\)	\(-3750\)	\(16814\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-183 i+183)q^{3}+(-2500 i-1875)q^{5}+\cdots\)
80.11.p.c	$80$	$11$	80.p	5.c	$4$	$6$	$3$	$50.829$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None					10.11.c.c	$2$	$0$	\(0\)	\(-128\)	\(5460\)	\(-13512\)	$2^{8}\cdot 5^{6}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-21-21\beta _{1}-\beta _{3})q^{3}+(910+896\beta _{1}+\cdots)q^{5}+\cdots\)
80.11.p.d	$80$	$11$	80.p	5.c	$4$	$8$	$4$	$50.829$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None					5.11.c.a	$2$	$0$	\(0\)	\(-60\)	\(-5340\)	\(14500\)	$2^{14}\cdot 3^{2}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-7-7\beta _{1}+\beta _{2})q^{3}+(-665-10^{3}\beta _{1}+\cdots)q^{5}+\cdots\)
80.11.p.e	$80$	$11$	80.p	5.c	$4$	$10$	$5$	$50.829$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None					20.11.f.a	$2$	$0$	\(0\)	\(-62\)	\(894\)	\(-22286\)	$2^{22}\cdot 3^{2}\cdot 5^{6}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-6-6\beta _{1}-\beta _{2})q^{3}+(90-174\beta _{1}+\cdots)q^{5}+\cdots\)
80.11.p.f	$80$	$11$	80.p	5.c	$4$	$14$	$7$	$50.829$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None					40.11.l.a	$2$	$0$	\(0\)	\(190\)	\(-510\)	\(4646\)	$2^{47}\cdot 3^{4}\cdot 5^{14}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(14-14\beta _{1}-\beta _{2})q^{3}+(-6^{2}-271\beta _{1}+\cdots)q^{5}+\cdots\)
80.11.p.g	$80$	$11$	80.p	5.c	$4$	$16$	$8$	$50.829$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None			✓		40.11.l.b	$2$	$0$	\(0\)	\(-190\)	\(-2606\)	\(13746\)	$2^{62}\cdot 3^{2}\cdot 5^{14}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-12+12\beta _{1}+\beta _{2})q^{3}+(-163+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{11}^{\mathrm{old}}(80, [\chi])\) into lower level spaces

\( S_{11}^{\mathrm{old}}(80, [\chi]) \simeq \) \(S_{11}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)