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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

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Results (1-50 of 190 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1088.1.g.a	$1088$	$1$	1088.g	68.d	$2$	$1$	$1$	$0.543$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-17}) $	$\Q(\sqrt{17}) $	✓				68.1.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-q^{9}+2q^{13}+q^{17}+q^{25}-q^{49}+\cdots$
1088.1.g.b	$1088$	$1$	1088.g	68.d	$2$	$2$	$2$	$0.543$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-17}) $	None	✓		✓		272.1.g.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta q^{3}-\beta q^{7}+q^{9}+\beta q^{11}-q^{17}+\cdots$
1088.1.n.a	$1088$	$1$	1088.n	136.j	$4$	$2$	$1$	$0.543$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{2}) $		✓			1088.1.n.a	$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q+(-1+i)q^{7}+iq^{9}+iq^{17}+(-1+\cdots)q^{23}+\cdots$
1088.1.n.b	$1088$	$1$	1088.n	136.j	$4$	$2$	$1$	$0.543$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{2}) $		✓			1088.1.n.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q+(1-i)q^{7}+iq^{9}+iq^{17}+(1-i+\cdots)q^{23}+\cdots$
1088.1.p.a	$1088$	$1$	1088.p	68.f	$4$	$2$	$1$	$0.543$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None			✓	✓	68.1.f.a	$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q+(1-i)q^{5}-iq^{9}-q^{17}-iq^{25}+\cdots$
1088.1.ba.a	$1088$	$1$	1088.ba	68.g	$8$	$4$	$1$	$0.543$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-1}) $	None			✓	✓	272.1.u.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{8}^{2}+\zeta_{8}^{3})q^{5}-\zeta_{8}q^{9}+(-\zeta_{8}+\cdots)q^{13}+\cdots$
1088.1.co.a	$1088$	$1$	1088.co	136.q	$16$	$8$	$1$	$0.543$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-2}) $	None		✓			1088.1.co.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{16}^{6}+\zeta_{16}^{7})q^{3}+(-\zeta_{16}^{4}+\zeta_{16}^{5}+\cdots)q^{9}+\cdots$
1088.1.co.b	$1088$	$1$	1088.co	136.q	$16$	$8$	$1$	$0.543$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-2}) $	None		✓			1088.1.co.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{16}^{6}-\zeta_{16}^{7})q^{3}+(-\zeta_{16}^{4}+\zeta_{16}^{5}+\cdots)q^{9}+\cdots$
1088.1.cz.a	$1088$	$1$	1088.cz	17.e	$16$	$8$	$1$	$0.543$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-1}) $	None			✓	✓	544.1.cd.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{16}^{2}-\zeta_{16}^{7})q^{5}-\zeta_{16}^{5}q^{9}+\cdots$
1088.2.a.a	$1088$	$2$	1088.a	1.a	$1$	$1$	$1$	$8.688$	$\Q$	$_{}$	None	None	✓				544.2.a.b	$1$	$2$	$0$	$-2$	$-4$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-4q^{5}-4q^{7}+q^{9}-2q^{11}+\cdots$
1088.2.a.b	$1088$	$2$	1088.a	1.a	$1$	$1$	$1$	$8.688$	$\Q$	$_{}$	None	None	✓				544.2.a.a	$1$	$1$	$0$	$-2$	$-2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-2q^{5}+2q^{7}+q^{9}+2q^{11}+\cdots$
1088.2.a.c	$1088$	$2$	1088.a	1.a	$1$	$1$	$1$	$8.688$	$\Q$	$_{}$	None	None	✓				136.2.a.b	$1$	$1$	$0$	$-2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{9}-2q^{11}+6q^{13}-q^{17}+\cdots$
1088.2.a.d	$1088$	$2$	1088.a	1.a	$1$	$1$	$1$	$8.688$	$\Q$	$_{}$	None	None	✓				34.2.a.a	$1$	$0$	$0$	$-2$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+4q^{7}+q^{9}+6q^{11}-2q^{13}+\cdots$
1088.2.a.e	$1088$	$2$	1088.a	1.a	$1$	$1$	$1$	$8.688$	$\Q$	$_{}$	None	None	✓				136.2.a.a	$1$	$1$	$0$	$-2$	$2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+2q^{5}+2q^{7}+q^{9}-6q^{11}+\cdots$
1088.2.a.f	$1088$	$2$	1088.a	1.a	$1$	$1$	$1$	$8.688$	$\Q$	$_{}$	None	None	✓				544.2.a.c	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}-3q^{9}+4q^{11}-2q^{13}-q^{17}+\cdots$
1088.2.a.g	$1088$	$2$	1088.a	1.a	$1$	$1$	$1$	$8.688$	$\Q$	$_{}$	None	None	✓				544.2.a.c	$1$	$1$	$0$	$0$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}-3q^{9}-4q^{11}-2q^{13}-q^{17}+\cdots$
1088.2.a.h	$1088$	$2$	1088.a	1.a	$1$	$1$	$1$	$8.688$	$\Q$	$_{}$	None	None	✓				17.2.a.a	$1$	$1$	$0$	$0$	$2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-4q^{7}-3q^{9}+2q^{13}+q^{17}+\cdots$
1088.2.a.i	$1088$	$2$	1088.a	1.a	$1$	$1$	$1$	$8.688$	$\Q$	$_{}$	None	None	✓				17.2.a.a	$1$	$0$	$0$	$0$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+4q^{7}-3q^{9}+2q^{13}+q^{17}+\cdots$
1088.2.a.j	$1088$	$2$	1088.a	1.a	$1$	$1$	$1$	$8.688$	$\Q$	$_{}$	None	None	✓				544.2.a.b	$1$	$0$	$0$	$2$	$-4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-4q^{5}+4q^{7}+q^{9}+2q^{11}+\cdots$
1088.2.a.k	$1088$	$2$	1088.a	1.a	$1$	$1$	$1$	$8.688$	$\Q$	$_{}$	None	None	✓				544.2.a.a	$1$	$1$	$0$	$2$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{5}-2q^{7}+q^{9}-2q^{11}+\cdots$
1088.2.a.l	$1088$	$2$	1088.a	1.a	$1$	$1$	$1$	$8.688$	$\Q$	$_{}$	None	None	✓				34.2.a.a	$1$	$1$	$0$	$2$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-4q^{7}+q^{9}-6q^{11}-2q^{13}+\cdots$
1088.2.a.m	$1088$	$2$	1088.a	1.a	$1$	$1$	$1$	$8.688$	$\Q$	$_{}$	None	None	✓				136.2.a.b	$1$	$0$	$0$	$2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{9}+2q^{11}+6q^{13}-q^{17}+\cdots$
1088.2.a.n	$1088$	$2$	1088.a	1.a	$1$	$1$	$1$	$8.688$	$\Q$	$_{}$	None	None	✓				136.2.a.a	$1$	$0$	$0$	$2$	$2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+2q^{5}-2q^{7}+q^{9}+6q^{11}+\cdots$
1088.2.a.o	$1088$	$2$	1088.a	1.a	$1$	$2$	$2$	$8.688$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓		✓		136.2.a.c	$1$	$1$	$0$	$-2$	$-4$	$-2$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}-2q^{5}+(-1-\beta )q^{7}+\cdots$
1088.2.a.p	$1088$	$2$	1088.a	1.a	$1$	$2$	$2$	$8.688$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓		✓		68.2.a.a	$1$	$1$	$0$	$-2$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}-2\beta q^{5}+(-1+\beta )q^{7}+\cdots$
1088.2.a.q	$1088$	$2$	1088.a	1.a	$1$	$2$	$2$	$8.688$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				544.2.a.g	$2$	$0$	$0$	$0$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+2q^{5}+3\beta q^{7}-q^{9}+\beta q^{11}+\cdots$
1088.2.a.r	$1088$	$2$	1088.a	1.a	$1$	$2$	$2$	$8.688$	$\Q(\sqrt{10}) $	$_{}$	None	None	✓				544.2.a.h	$2$	$0$	$0$	$0$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+2q^{5}-\beta q^{7}+7q^{9}+\beta q^{11}+\cdots$
1088.2.a.s	$1088$	$2$	1088.a	1.a	$1$	$2$	$2$	$8.688$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				136.2.a.c	$1$	$0$	$0$	$2$	$-4$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}-2q^{5}+(1+\beta )q^{7}+(3+2\beta )q^{9}+\cdots$
1088.2.a.t	$1088$	$2$	1088.a	1.a	$1$	$2$	$2$	$8.688$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				68.2.a.a	$1$	$0$	$0$	$2$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+2\beta q^{5}+(1+\beta )q^{7}+(1+\cdots)q^{9}+\cdots$
1088.2.a.u	$1088$	$2$	1088.a	1.a	$1$	$3$	$3$	$8.688$	3.3.148.1	$_{}$	None	None	✓				544.2.a.i	$1$	$0$	$0$	$-2$	$2$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(1-\beta _{2})q^{7}+\cdots$
1088.2.a.v	$1088$	$2$	1088.a	1.a	$1$	$3$	$3$	$8.688$	3.3.148.1	$_{}$	None	None	✓				544.2.a.i	$1$	$0$	$0$	$2$	$2$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(-1+\beta _{2})q^{7}+\cdots$
1088.2.b.a	$1088$	$2$	1088.b	17.b	$2$	$2$	$2$	$8.688$	$\Q(\sqrt{-2}) $	$_{}$	None	None					34.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}+\beta q^{5}-5q^{9}-\beta q^{11}-2q^{13}+\cdots$
1088.2.b.b	$1088$	$2$	1088.b	17.b	$2$	$2$	$2$	$8.688$	$\Q(\sqrt{-2}) $	$_{}$	None	None					34.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}-\beta q^{5}-5q^{9}-\beta q^{11}-2q^{13}+\cdots$
1088.2.b.c	$1088$	$2$	1088.b	17.b	$2$	$2$	$2$	$8.688$	$\Q(\sqrt{-1}) $	$_{}$	None	None					136.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}-iq^{7}-q^{9}+iq^{11}+2q^{13}+\cdots$
1088.2.b.d	$1088$	$2$	1088.b	17.b	$2$	$2$	$2$	$8.688$	$\Q(\sqrt{-1}) $	$_{}$	None	None					136.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}-iq^{7}-q^{9}+iq^{11}+2q^{13}+\cdots$
1088.2.b.e	$1088$	$2$	1088.b	17.b	$2$	$2$	$2$	$8.688$	$\Q(\sqrt{-2}) $	$_{}$	None	None					68.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}+2\beta q^{5}+3\beta q^{7}+q^{9}-\beta q^{11}+\cdots$
1088.2.b.f	$1088$	$2$	1088.b	17.b	$2$	$2$	$2$	$8.688$	$\Q(\sqrt{-2}) $	$_{}$	None	None					68.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}-2\beta q^{5}+3\beta q^{7}+q^{9}-\beta q^{11}+\cdots$
1088.2.b.g	$1088$	$2$	1088.b	17.b	$2$	$2$	$2$	$8.688$	$\Q(\sqrt{-2}) $	$_{}$	None	None					136.2.b.b	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{5}+\beta q^{7}+3q^{9}+2\beta q^{11}-2q^{13}+\cdots$
1088.2.b.h	$1088$	$2$	1088.b	17.b	$2$	$2$	$2$	$8.688$	$\Q(\sqrt{-2}) $	$_{}$	None	None					136.2.b.b	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{5}+\beta q^{7}+3q^{9}+2\beta q^{11}-2q^{13}+\cdots$
1088.2.b.i	$1088$	$2$	1088.b	17.b	$2$	$2$	$2$	$8.688$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None					544.2.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-iq^{5}+3q^{9}+6q^{13}+(1+i)q^{17}+\cdots$
1088.2.b.j	$1088$	$2$	1088.b	17.b	$2$	$4$	$4$	$8.688$	4.0.2312.1	$_{}$	$\Q(\sqrt{-17}) $	None					544.2.b.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{7}+(-4-\beta _{3})q^{9}+\cdots$
1088.2.b.k	$1088$	$2$	1088.b	17.b	$2$	$4$	$4$	$8.688$	4.0.2312.1	$_{}$	$\Q(\sqrt{-17}) $	None					544.2.b.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{3}+\beta _{1}q^{7}+(-2+\beta _{2})q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots$
1088.2.b.l	$1088$	$2$	1088.b	17.b	$2$	$4$	$4$	$8.688$	4.0.2048.2	$_{}$	None	None					544.2.b.d	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}+(\beta _{1}+\beta _{2})q^{5}+\beta _{1}q^{7}+(-1+\cdots)q^{9}+\cdots$
1088.2.b.m	$1088$	$2$	1088.b	17.b	$2$	$4$	$4$	$8.688$	4.0.2048.2	$_{}$	None	None					544.2.b.d	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}+(-\beta _{1}-\beta _{2})q^{5}+\beta _{1}q^{7}+\cdots$
1088.2.c.a	$1088$	$2$	1088.c	8.b	$2$	$2$	$2$	$8.688$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			1088.2.c.a	$2$	$0$	$0$	$0$	$0$	$-8$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{5}-4q^{7}+3q^{9}+2iq^{11}+2iq^{13}+\cdots$
1088.2.c.b	$1088$	$2$	1088.c	8.b	$2$	$2$	$2$	$8.688$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			1088.2.c.a	$2$	$0$	$0$	$0$	$0$	$8$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{5}+4q^{7}+3q^{9}+2iq^{11}-2iq^{13}+\cdots$
1088.2.c.c	$1088$	$2$	1088.c	8.b	$2$	$4$	$4$	$8.688$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			1088.2.c.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{8}q^{3}-\zeta_{8}^{2}q^{5}-\zeta_{8}^{3}q^{7}-q^{9}+\cdots$
1088.2.c.d	$1088$	$2$	1088.c	8.b	$2$	$12$	$12$	$8.688$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓			1088.2.c.d	$4$	$0$	$0$	$0$	$0$	$0$		$2^{16}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{8}q^{3}-\beta _{6}q^{5}+\beta _{3}q^{7}+(-2-\beta _{5}+\cdots)q^{9}+\cdots$
1088.2.c.e	$1088$	$2$	1088.c	8.b	$2$	$12$	$12$	$8.688$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓			1088.2.c.e	$4$	$0$	$0$	$0$	$0$	$0$		$2^{15}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{6}q^{3}+\beta _{5}q^{5}+\beta _{3}q^{7}+(-1+\beta _{1}+\cdots)q^{9}+\cdots$
1088.2.h.a	$1088$	$2$	1088.h	136.h	$2$	$4$	$4$	$8.688$	$\Q(\zeta_{8})$	$_{}$	$\Q(\sqrt{-2}) $	None		✓			1088.2.h.a	$8$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{U}(1)[D_{2}]$	$q-\zeta_{8}^{3}q^{3}+5q^{9}-\zeta_{8}^{3}q^{11}+(3+\zeta_{8}^{2}+\cdots)q^{17}+\cdots$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.