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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 301 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
800.1.e.a	$800$	$1$	800.e	40.e	$2$	$2$	$2$	$0.399$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-2}) $	None			✓	✓	200.1.g.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{3}+q^{11}-i q^{17}-q^{19}-i q^{27}+\cdots$
800.1.g.a	$800$	$1$	800.g	8.d	$2$	$1$	$1$	$0.399$	$\Q$	$D_{3}$	$\Q(\sqrt{-2}) $	None	✓				200.1.g.a	$2$	$0$	$0$	$-1$	$0$	$0$		$1$		$q-q^{3}+q^{11}+q^{17}+q^{19}+q^{27}+\cdots$
800.1.g.b	$800$	$1$	800.g	8.d	$2$	$1$	$1$	$0.399$	$\Q$	$D_{3}$	$\Q(\sqrt{-2}) $	None	✓				200.1.g.a	$2$	$0$	$0$	$1$	$0$	$0$		$1$		$q+q^{3}+q^{11}-q^{17}+q^{19}-q^{27}+\cdots$
800.1.p.a	$800$	$1$	800.p	5.c	$4$	$2$	$1$	$0.399$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-5}) $	None		✓			800.1.p.a	$4$	$0$	$0$	$-2$	$0$	$2$		$1$		$q+(i-1)q^{3}+(i+1)q^{7}-i q^{9}-2 q^{21}+\cdots$
800.1.p.b	$800$	$1$	800.p	5.c	$4$	$2$	$1$	$0.399$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None					160.1.p.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+i q^{9}+(-i+1)q^{13}+(i+1)q^{17}+\cdots$
800.1.p.c	$800$	$1$	800.p	5.c	$4$	$2$	$1$	$0.399$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-5}) $	None		✓			800.1.p.a	$4$	$0$	$0$	$2$	$0$	$-2$		$1$		$q+(-i+1)q^{3}+(-i-1)q^{7}-i q^{9}+\cdots$
800.1.bh.a	$800$	$1$	800.bh	100.j	$10$	$8$	$2$	$0.399$	$\Q(\zeta_{20})$	$A_{5}$	None	None		✓	✓	✓	800.1.bh.a	$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-\zeta_{20}^{7}q^{3}+\zeta_{20}^{4}q^{5}+(\zeta_{20}+\zeta_{20}^{9}+\cdots)q^{7}+\cdots$
800.1.bo.a	$800$	$1$	800.bo	25.f	$20$	$8$	$1$	$0.399$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	800.1.bo.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{20}^{7}q^{5}+\zeta_{20}q^{9}+(-\zeta_{20}^{8}+\zeta_{20}^{9}+\cdots)q^{13}+\cdots$
800.2.a.a	$800$	$2$	800.a	1.a	$1$	$1$	$1$	$6.388$	$\Q$	$_{}$	None	None	✓				160.2.a.a	$1$	$1$	$0$	$-2$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-2q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots$
800.2.a.b	$800$	$2$	800.a	1.a	$1$	$1$	$1$	$6.388$	$\Q$	$_{}$	None	None	✓	✓			800.2.a.b	$1$	$1$	$0$	$-1$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{7}-2q^{9}-5q^{11}+5q^{17}+\cdots$
800.2.a.c	$800$	$2$	800.a	1.a	$1$	$1$	$1$	$6.388$	$\Q$	$_{}$	None	None	✓	✓			800.2.a.b	$1$	$0$	$0$	$-1$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{7}-2q^{9}+5q^{11}-5q^{17}+\cdots$
800.2.a.d	$800$	$2$	800.a	1.a	$1$	$1$	$1$	$6.388$	$\Q$	$_{}$	$\Q(\sqrt{-1}) $	None	✓				32.2.a.a	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$N(\mathrm{U}(1))$	$q-3q^{9}-6q^{13}-2q^{17}-10q^{29}+\cdots$
800.2.a.e	$800$	$2$	800.a	1.a	$1$	$1$	$1$	$6.388$	$\Q$	$_{}$	$\Q(\sqrt{-1}) $	None	✓				160.2.c.a	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$N(\mathrm{U}(1))$	$q-3q^{9}-4q^{13}-8q^{17}+10q^{29}+\cdots$
800.2.a.f	$800$	$2$	800.a	1.a	$1$	$1$	$1$	$6.388$	$\Q$	$_{}$	$\Q(\sqrt{-1}) $	None	✓				160.2.c.a	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q-3q^{9}+4q^{13}+8q^{17}+10q^{29}+\cdots$
800.2.a.g	$800$	$2$	800.a	1.a	$1$	$1$	$1$	$6.388$	$\Q$	$_{}$	None	None	✓	✓			800.2.a.b	$1$	$1$	$0$	$1$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{7}-2q^{9}-5q^{11}-5q^{17}+\cdots$
800.2.a.h	$800$	$2$	800.a	1.a	$1$	$1$	$1$	$6.388$	$\Q$	$_{}$	None	None	✓	✓			800.2.a.b	$1$	$0$	$0$	$1$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{7}-2q^{9}+5q^{11}+5q^{17}+\cdots$
800.2.a.i	$800$	$2$	800.a	1.a	$1$	$1$	$1$	$6.388$	$\Q$	$_{}$	None	None	✓				160.2.a.a	$1$	$0$	$0$	$2$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+2q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots$
800.2.a.j	$800$	$2$	800.a	1.a	$1$	$2$	$2$	$6.388$	$\Q(\sqrt{5}) $	$_{}$	$\Q(\sqrt{-5}) $	None	✓		✓		160.2.c.b	$2$	$1$	$0$	$-2$	$0$	$-6$	$+$	$2$	$N(\mathrm{U}(1))$	$q+(-1-\beta )q^{3}+(-3+\beta )q^{7}+(3+2\beta )q^{9}+\cdots$
800.2.a.k	$800$	$2$	800.a	1.a	$1$	$2$	$2$	$6.388$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓			800.2.a.k	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{3}-2\beta q^{7}+2q^{9}+\beta q^{11}-4q^{13}+\cdots$
800.2.a.l	$800$	$2$	800.a	1.a	$1$	$2$	$2$	$6.388$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓			800.2.a.k	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{3}-2\beta q^{7}+2q^{9}-\beta q^{11}+4q^{13}+\cdots$
800.2.a.m	$800$	$2$	800.a	1.a	$1$	$2$	$2$	$6.388$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				160.2.a.c	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{3}-\beta q^{7}+5q^{9}+2\beta q^{11}+2q^{13}+\cdots$
800.2.a.n	$800$	$2$	800.a	1.a	$1$	$2$	$2$	$6.388$	$\Q(\sqrt{5}) $	$_{}$	$\Q(\sqrt{-5}) $	None	✓				160.2.c.b	$2$	$0$	$0$	$2$	$0$	$6$	$-$	$2$	$N(\mathrm{U}(1))$	$q+(1+\beta )q^{3}+(3-\beta )q^{7}+(3+2\beta )q^{9}+\cdots$
800.2.c.a	$800$	$2$	800.c	5.b	$2$	$2$	$2$	$6.388$	$\Q(\sqrt{-1}) $	$_{}$	None	None					160.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}-\beta q^{7}-q^{9}-4 q^{11}+3\beta q^{13}+\cdots$
800.2.c.b	$800$	$2$	800.c	5.b	$2$	$2$	$2$	$6.388$	$\Q(\sqrt{-1}) $	$_{}$	None	None					160.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}-\beta q^{7}-q^{9}+4 q^{11}-3\beta q^{13}+\cdots$
800.2.c.c	$800$	$2$	800.c	5.b	$2$	$2$	$2$	$6.388$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			800.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+2 i q^{7}+2 q^{9}-5 q^{11}+\cdots$
800.2.c.d	$800$	$2$	800.c	5.b	$2$	$2$	$2$	$6.388$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			800.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+2 i q^{7}+2 q^{9}+5 q^{11}+\cdots$
800.2.c.e	$800$	$2$	800.c	5.b	$2$	$2$	$2$	$6.388$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None					32.2.a.a	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+3 q^{9}+3\beta q^{13}-\beta q^{17}+10 q^{29}+\cdots$
800.2.c.f	$800$	$2$	800.c	5.b	$2$	$4$	$4$	$6.388$	$\Q(\zeta_{8})$	$_{}$	None	None					160.2.a.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_{2} q^{3}+\beta_{2} q^{7}-5 q^{9}+\beta_{3} q^{11}+\cdots$
800.2.c.g	$800$	$2$	800.c	5.b	$2$	$4$	$4$	$6.388$	$\Q(i, \sqrt{5})$	$_{}$	None	None		✓			800.2.a.k	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}-2\beta _{2}q^{7}-2q^{9}+\beta _{3}q^{11}+\cdots$
800.2.d.a	$800$	$2$	800.d	8.b	$2$	$2$	$2$	$6.388$	$\Q(\sqrt{-7}) $	$_{}$	None	None					200.2.d.b	$2$	$1$	$0$	$0$	$0$	$-8$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{3}-4q^{7}-4q^{9}+\beta q^{11}-3q^{17}+\cdots$
800.2.d.b	$800$	$2$	800.d	8.b	$2$	$2$	$2$	$6.388$	$\Q(\sqrt{-1}) $	$_{}$	None	None					200.2.d.a	$2$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}-2 q^{7}+2 q^{9}-5 i q^{11}+\cdots$
800.2.d.c	$800$	$2$	800.d	8.b	$2$	$2$	$2$	$6.388$	$\Q(\sqrt{-1}) $	$_{}$	None	None					200.2.d.a	$2$	$0$	$0$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+2 q^{7}+2 q^{9}+5 i q^{11}+\cdots$
800.2.d.d	$800$	$2$	800.d	8.b	$2$	$2$	$2$	$6.388$	$\Q(\sqrt{-7}) $	$_{}$	None	None					200.2.d.b	$2$	$0$	$0$	$0$	$0$	$8$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{3}+4q^{7}-4q^{9}-\beta q^{11}+3q^{17}+\cdots$
800.2.d.e	$800$	$2$	800.d	8.b	$2$	$4$	$4$	$6.388$	$\Q(\zeta_{12})$	$_{}$	None	None					40.2.d.a	$2$	$0$	$0$	$0$	$0$	$-4$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_{3} q^{3}+(-\beta_1-1)q^{7}+(2\beta_1-1)q^{9}+\cdots$
800.2.d.f	$800$	$2$	800.d	8.b	$2$	$4$	$4$	$6.388$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	None	None					40.2.f.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-\beta _{2}q^{7}+q^{9}+\beta _{3}q^{11}-2\beta _{2}q^{17}+\cdots$
800.2.f.a	$800$	$2$	800.f	40.f	$2$	$2$	$2$	$6.388$	$\Q(\sqrt{-1}) $	$_{}$	None	None					200.2.d.a	$2$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}-2 i q^{7}-2 q^{9}+5 i q^{11}+\cdots$
800.2.f.b	$800$	$2$	800.f	40.f	$2$	$2$	$2$	$6.388$	$\Q(\sqrt{-1}) $	$_{}$	None	None					200.2.d.a	$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+2 i q^{7}-2 q^{9}+5 i q^{11}+\cdots$
800.2.f.c	$800$	$2$	800.f	40.f	$2$	$4$	$4$	$6.388$	$\Q(\zeta_{12})$	$_{}$	None	None					40.2.d.a	$2$	$0$	$0$	$-4$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta_1-1)q^{3}+\beta_{3} q^{7}+(2\beta_1+1)q^{9}+\cdots$
800.2.f.d	$800$	$2$	800.f	40.f	$2$	$4$	$4$	$6.388$	$\Q(i, \sqrt{7})$	$_{}$	None	None					200.2.d.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{3}+4\beta _{1}q^{7}+4q^{9}-\beta _{3}q^{11}+\cdots$
800.2.f.e	$800$	$2$	800.f	40.f	$2$	$4$	$4$	$6.388$	$\Q(\zeta_{12})$	$_{}$	None	None					40.2.d.a	$2$	$0$	$0$	$4$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta_1+1)q^{3}-\beta_{3} q^{7}+(2\beta_1+1)q^{9}+\cdots$
800.2.n.a	$800$	$2$	800.n	20.e	$4$	$2$	$1$	$6.388$	$\Q(\sqrt{-1}) $	$_{}$	None	None					160.2.n.a	$2$	$0$	$0$	$-4$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-2 i-2)q^{3}+(2 i-2)q^{7}+5 i q^{9}+\cdots$
800.2.n.b	$800$	$2$	800.n	20.e	$4$	$2$	$1$	$6.388$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			800.2.n.b	$2$	$1$	$0$	$-2$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-i-1)q^{3}+(i-1)q^{7}-i q^{9}+\cdots$
800.2.n.c	$800$	$2$	800.n	20.e	$4$	$2$	$1$	$6.388$	$\Q(\sqrt{-1}) $	$_{}$	None	None					160.2.n.b	$2$	$0$	$0$	$-2$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-i-1)q^{3}+(i-1)q^{7}-i q^{9}+\cdots$
800.2.n.d	$800$	$2$	800.n	20.e	$4$	$2$	$1$	$6.388$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			800.2.n.b	$2$	$0$	$0$	$-2$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-i-1)q^{3}+(i-1)q^{7}-i q^{9}+\cdots$
800.2.n.e	$800$	$2$	800.n	20.e	$4$	$2$	$1$	$6.388$	$\Q(\sqrt{-1}) $	$_{}$	None	None					160.2.n.c	$2$	$0$	$0$	$-2$	$0$	$6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-i-1)q^{3}+(-3 i+3)q^{7}-i q^{9}+\cdots$
800.2.n.f	$800$	$2$	800.n	20.e	$4$	$2$	$1$	$6.388$	$\Q(\sqrt{-1}) $	$_{}$	None	None					160.2.n.c	$2$	$0$	$0$	$2$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(i+1)q^{3}+(3 i-3)q^{7}-i q^{9}+\cdots$
800.2.n.g	$800$	$2$	800.n	20.e	$4$	$2$	$1$	$6.388$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			800.2.n.b	$2$	$0$	$0$	$2$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(i+1)q^{3}+(-i+1)q^{7}-i q^{9}+\cdots$
800.2.n.h	$800$	$2$	800.n	20.e	$4$	$2$	$1$	$6.388$	$\Q(\sqrt{-1}) $	$_{}$	None	None					160.2.n.b	$2$	$0$	$0$	$2$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(i+1)q^{3}+(-i+1)q^{7}-i q^{9}+\cdots$
800.2.n.i	$800$	$2$	800.n	20.e	$4$	$2$	$1$	$6.388$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			800.2.n.b	$2$	$0$	$0$	$2$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(i+1)q^{3}+(-i+1)q^{7}-i q^{9}+\cdots$
800.2.n.j	$800$	$2$	800.n	20.e	$4$	$2$	$1$	$6.388$	$\Q(\sqrt{-1}) $	$_{}$	None	None					160.2.n.a	$2$	$0$	$0$	$4$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(2 i+2)q^{3}+(-2 i+2)q^{7}+5 i q^{9}+\cdots$

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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.