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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 297 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
256.1.c.a	$256$	$1$	256.c	4.b	$2$	$1$	$1$	$0.128$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-2}) $	$\Q(\sqrt{2}) $	✓		✓	✓	128.1.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{9}-2q^{17}-q^{25}-2q^{41}+q^{49}+\cdots$
256.2.a.a	$256$	$2$	256.a	1.a	$1$	$1$	$1$	$2.044$	$\Q$	$_{}$	$\Q(\sqrt{-2}) $	None	✓				64.2.b.a	$2$	$1$	$0$	$-2$	$0$	$0$	$+$	$1$	$N(\mathrm{U}(1))$	$q-2q^{3}+q^{9}-6q^{11}-6q^{17}-2q^{19}+\cdots$
256.2.a.b	$256$	$2$	256.a	1.a	$1$	$1$	$1$	$2.044$	$\Q$	$_{}$	$\Q(\sqrt{-1}) $	None	✓				128.2.b.b	$2$	$1$	$0$	$0$	$-4$	$0$	$+$	$1$	$N(\mathrm{U}(1))$	$q-4q^{5}-3q^{9}-4q^{13}-2q^{17}+11q^{25}+\cdots$
256.2.a.c	$256$	$2$	256.a	1.a	$1$	$1$	$1$	$2.044$	$\Q$	$_{}$	$\Q(\sqrt{-1}) $	None	✓				128.2.b.b	$2$	$0$	$0$	$0$	$4$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q+4q^{5}-3q^{9}+4q^{13}-2q^{17}+11q^{25}+\cdots$
256.2.a.d	$256$	$2$	256.a	1.a	$1$	$1$	$1$	$2.044$	$\Q$	$_{}$	$\Q(\sqrt{-2}) $	None	✓				64.2.b.a	$2$	$0$	$0$	$2$	$0$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q+2q^{3}+q^{9}+6q^{11}-6q^{17}+2q^{19}+\cdots$
256.2.a.e	$256$	$2$	256.a	1.a	$1$	$2$	$2$	$2.044$	$\Q(\sqrt{2}) $	$_{}$	$\Q(\sqrt{-2}) $	None	✓		✓		128.2.b.a	$4$	$0$	$0$	$0$	$0$	$0$	$-$	$2$	$N(\mathrm{U}(1))$	$q+\beta q^{3}+5q^{9}-\beta q^{11}+6q^{17}-3\beta q^{19}+\cdots$
256.2.b.a	$256$	$2$	256.b	8.b	$2$	$2$	$2$	$2.044$	$\Q(\sqrt{-1}) $	$_{}$	None	None					128.2.a.a	$2$	$0$	$0$	$0$	$0$	$-8$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}+\beta q^{5}-4 q^{7}-q^{9}+\beta q^{11}+\cdots$
256.2.b.b	$256$	$2$	256.b	8.b	$2$	$2$	$2$	$2.044$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None					32.2.a.a	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{5}+3 q^{9}+3\beta q^{13}+2 q^{17}+\cdots$
256.2.b.c	$256$	$2$	256.b	8.b	$2$	$2$	$2$	$2.044$	$\Q(\sqrt{-1}) $	$_{}$	None	None					128.2.a.a	$2$	$0$	$0$	$0$	$0$	$8$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}-\beta q^{5}+4 q^{7}-q^{9}+\beta q^{11}+\cdots$
256.2.e.a	$256$	$2$	256.e	16.e	$4$	$8$	$4$	$2.044$	$\Q(\zeta_{24})$	$_{}$	None	None		✓			256.2.e.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta_{2} q^{3}-\beta_{7} q^{5}+(-\beta_{6}-\beta_{3}+\beta_{2})q^{7}+\cdots$
256.2.e.b	$256$	$2$	256.e	16.e	$4$	$8$	$4$	$2.044$	$\Q(\zeta_{24})$	$_{}$	None	None		✓			256.2.e.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta_{2} q^{3}+\beta_{7} q^{5}+(\beta_{6}+\beta_{3}-\beta_{2})q^{7}+\cdots$
256.2.g.a	$256$	$2$	256.g	32.g	$8$	$4$	$1$	$2.044$	$\Q(\zeta_{8})$	$_{}$	None	None					32.2.g.a	$2$	$0$	$0$	$0$	$4$	$-4$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+(\zeta_{8}+\zeta_{8}^{2})q^{3}+(1+\zeta_{8}+2\zeta_{8}^{2}-2\zeta_{8}^{3})q^{5}+\cdots$
256.2.g.b	$256$	$2$	256.g	32.g	$8$	$4$	$1$	$2.044$	$\Q(\zeta_{8})$	$_{}$	None	None					32.2.g.a	$2$	$0$	$0$	$0$	$4$	$4$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+(-\zeta_{8}-\zeta_{8}^{2})q^{3}+(1+\zeta_{8}+2\zeta_{8}^{2}+\cdots)q^{5}+\cdots$
256.2.g.c	$256$	$2$	256.g	32.g	$8$	$8$	$2$	$2.044$	8.0.18939904.2	$_{}$	None	None					32.2.g.b	$2$	$0$	$0$	$-4$	$0$	$8$		$2^{3}$	$\mathrm{SU}(2)[C_{8}]$	$q+(-1+\beta _{1}+\beta _{6}-\beta _{7})q^{3}+(\beta _{4}-\beta _{7})q^{5}+\cdots$
256.2.g.d	$256$	$2$	256.g	32.g	$8$	$8$	$2$	$2.044$	8.0.18939904.2	$_{}$	None	None					32.2.g.b	$2$	$0$	$0$	$4$	$0$	$-8$		$2^{3}$	$\mathrm{SU}(2)[C_{8}]$	$q+(\beta _{2}+\beta _{6}-\beta _{7})q^{3}+(\beta _{6}+\beta _{7})q^{5}+\cdots$
256.2.i.a	$256$	$2$	256.i	64.i	$16$	$56$	$7$	$2.044$		$_{}$	None	None			✓	✓	64.2.i.a	$2$	$0$	$0$	$8$	$-8$	$8$			$\mathrm{SU}(2)[C_{16}]$
256.2.m.a	$256$	$2$	256.m	256.m	$64$	$992$	$31$	$2.044$		$_{}$	None	None		✓	✓	✓	256.2.m.a	$2$	$0$	$-32$	$-32$	$-32$	$-32$			$\mathrm{SU}(2)[C_{64}]$
256.3.c.a	$256$	$3$	256.c	4.b	$2$	$1$	$1$	$6.975$	$\Q$	$_{}$	$\Q(\sqrt{-1}) $	None	✓				128.3.d.a	$2$	$0$	$0$	$0$	$-8$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-8q^{5}+9q^{9}+24q^{13}+30q^{17}+\cdots$
256.3.c.b	$256$	$3$	256.c	4.b	$2$	$1$	$1$	$6.975$	$\Q$	$_{}$	$\Q(\sqrt{-1}) $	None	✓				128.3.d.a	$2$	$0$	$0$	$0$	$8$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+8q^{5}+9q^{9}-24q^{13}+30q^{17}+\cdots$
256.3.c.c	$256$	$3$	256.c	4.b	$2$	$2$	$2$	$6.975$	$\Q(\sqrt{-2}) $	$_{}$	None	None					128.3.d.c	$2$	$0$	$0$	$0$	$-8$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}-4q^{5}+4\beta q^{7}+q^{9}-5\beta q^{11}+\cdots$
256.3.c.d	$256$	$3$	256.c	4.b	$2$	$2$	$2$	$6.975$	$\Q(\sqrt{-2}) $	$_{}$	$\Q(\sqrt{-2}) $	None					128.3.d.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{3}-23q^{9}+3\beta q^{11}-2q^{17}+\cdots$
256.3.c.e	$256$	$3$	256.c	4.b	$2$	$2$	$2$	$6.975$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-2}) $	None					8.3.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{3}+5 q^{9}+7\beta q^{11}+2 q^{17}+\cdots$
256.3.c.f	$256$	$3$	256.c	4.b	$2$	$2$	$2$	$6.975$	$\Q(\sqrt{-2}) $	$_{}$	None	None					128.3.d.c	$2$	$0$	$0$	$0$	$8$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}+4q^{5}-4\beta q^{7}+q^{9}-5\beta q^{11}+\cdots$
256.3.c.g	$256$	$3$	256.c	4.b	$2$	$4$	$4$	$6.975$	$\Q(\zeta_{12})$	$_{}$	None	None			✓		64.3.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_{2} q^{3}-\beta_1 q^{5}-\beta_{3} q^{7}-3 q^{9}+\cdots$
256.3.d.a	$256$	$3$	256.d	8.d	$2$	$2$	$2$	$6.975$	$\Q(\sqrt{-1}) $	$_{}$	None	None					32.3.c.a	$2$	$0$	$0$	$-8$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-4 q^{3}+\beta q^{5}-4\beta q^{7}+7 q^{9}-4 q^{11}+\cdots$
256.3.d.b	$256$	$3$	256.d	8.d	$2$	$2$	$2$	$6.975$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None					16.3.c.a	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+3\beta q^{5}-9 q^{9}+5\beta q^{13}-30 q^{17}+\cdots$
256.3.d.c	$256$	$3$	256.d	8.d	$2$	$2$	$2$	$6.975$	$\Q(\sqrt{-1}) $	$_{}$	None	None					32.3.c.a	$2$	$0$	$0$	$8$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+4 q^{3}+\beta q^{5}+4\beta q^{7}+7 q^{9}+4 q^{11}+\cdots$
256.3.d.d	$256$	$3$	256.d	8.d	$2$	$4$	$4$	$6.975$	$\Q(\zeta_{8})$	$_{}$	None	None					128.3.c.a	$2$	$0$	$0$	$-8$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta_{2}-2)q^{3}+(-\beta_{3}-\beta_1)q^{5}+\cdots$
256.3.d.e	$256$	$3$	256.d	8.d	$2$	$4$	$4$	$6.975$	$\Q(\zeta_{8})$	$_{}$	None	None					128.3.c.a	$2$	$0$	$0$	$8$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta_{2}+2)q^{3}+(-\beta_{3}+\beta_1)q^{5}+\cdots$
256.3.f.a	$256$	$3$	256.f	16.f	$4$	$8$	$4$	$6.975$	$\Q(\zeta_{24})$	$_{}$	None	None		✓			256.3.f.a	$4$	$0$	$0$	$0$	$-16$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta_{2} q^{3}+(\beta_{4}-2\beta_1-2)q^{5}+(\beta_{5}-3\beta_{3}-2\beta_{2})q^{7}+\cdots$
256.3.f.b	$256$	$3$	256.f	16.f	$4$	$8$	$4$	$6.975$	8.0.8540717056.1	$_{}$	None	None		✓			256.3.f.b	$4$	$0$	$0$	$0$	$-16$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{2}q^{3}+(-2-2\beta _{1}-\beta _{6})q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots$
256.3.f.c	$256$	$3$	256.f	16.f	$4$	$8$	$4$	$6.975$	8.0.8540717056.1	$_{}$	None	None		✓			256.3.f.b	$4$	$0$	$0$	$0$	$16$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{2}q^{3}+(2+2\beta _{1}+\beta _{6})q^{5}+(\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots$
256.3.f.d	$256$	$3$	256.f	16.f	$4$	$8$	$4$	$6.975$	$\Q(\zeta_{24})$	$_{}$	None	None		✓			256.3.f.a	$4$	$0$	$0$	$0$	$16$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta_{2} q^{3}+(-\beta_{4}+2\beta_1+2)q^{5}+\cdots$
256.3.h.a	$256$	$3$	256.h	32.h	$8$	$28$	$7$	$6.975$		$_{}$	None	None					32.3.h.a	$2$	$0$	$0$	$-4$	$4$	$4$			$\mathrm{SU}(2)[C_{8}]$
256.3.h.b	$256$	$3$	256.h	32.h	$8$	$28$	$7$	$6.975$		$_{}$	None	None					32.3.h.a	$2$	$0$	$0$	$4$	$4$	$-4$			$\mathrm{SU}(2)[C_{8}]$
256.3.j.a	$256$	$3$	256.j	64.j	$16$	$120$	$15$	$6.975$		$_{}$	None	None			✓	✓	64.3.j.a	$2$	$0$	$0$	$8$	$-8$	$8$			$\mathrm{SU}(2)[C_{16}]$
256.3.n.a	$256$	$3$	256.n	256.n	$64$	$2016$	$63$	$6.975$		$_{}$	None	None		✓	✓	✓	256.3.n.a	$2$	$0$	$-32$	$-32$	$-32$	$-32$			$\mathrm{SU}(2)[C_{64}]$
256.4.a.a	$256$	$4$	256.a	1.a	$1$	$1$	$1$	$15.104$	$\Q$	$_{}$	$\Q(\sqrt{-2}) $	None	✓				64.4.b.a	$2$	$1$	$0$	$-10$	$0$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q-10q^{3}+73q^{9}+18q^{11}+90q^{17}+\cdots$
256.4.a.b	$256$	$4$	256.a	1.a	$1$	$1$	$1$	$15.104$	$\Q$	$_{}$	None	None	✓				128.4.b.a	$1$	$1$	$0$	$-8$	$-12$	$32$	$-$	$1$	$\mathrm{SU}(2)$	$q-8q^{3}-12q^{5}+2^{5}q^{7}+37q^{9}+8q^{11}+\cdots$
256.4.a.c	$256$	$4$	256.a	1.a	$1$	$1$	$1$	$15.104$	$\Q$	$_{}$	None	None	✓				128.4.b.a	$1$	$0$	$0$	$-8$	$12$	$-32$	$+$	$1$	$\mathrm{SU}(2)$	$q-8q^{3}+12q^{5}-2^{5}q^{7}+37q^{9}+8q^{11}+\cdots$
256.4.a.d	$256$	$4$	256.a	1.a	$1$	$1$	$1$	$15.104$	$\Q$	$_{}$	$\Q(\sqrt{-1}) $	None	✓				128.4.b.c	$2$	$0$	$0$	$0$	$-4$	$0$	$+$	$1$	$N(\mathrm{U}(1))$	$q-4q^{5}-3^{3}q^{9}+92q^{13}+94q^{17}+\cdots$
256.4.a.e	$256$	$4$	256.a	1.a	$1$	$1$	$1$	$15.104$	$\Q$	$_{}$	$\Q(\sqrt{-1}) $	None	✓				128.4.b.c	$2$	$1$	$0$	$0$	$4$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q+4q^{5}-3^{3}q^{9}-92q^{13}+94q^{17}+\cdots$
256.4.a.f	$256$	$4$	256.a	1.a	$1$	$1$	$1$	$15.104$	$\Q$	$_{}$	None	None	✓				128.4.b.a	$1$	$1$	$0$	$8$	$-12$	$-32$	$-$	$1$	$\mathrm{SU}(2)$	$q+8q^{3}-12q^{5}-2^{5}q^{7}+37q^{9}-8q^{11}+\cdots$
256.4.a.g	$256$	$4$	256.a	1.a	$1$	$1$	$1$	$15.104$	$\Q$	$_{}$	None	None	✓				128.4.b.a	$1$	$0$	$0$	$8$	$12$	$32$	$+$	$1$	$\mathrm{SU}(2)$	$q+8q^{3}+12q^{5}+2^{5}q^{7}+37q^{9}-8q^{11}+\cdots$
256.4.a.h	$256$	$4$	256.a	1.a	$1$	$1$	$1$	$15.104$	$\Q$	$_{}$	$\Q(\sqrt{-2}) $	None	✓				64.4.b.a	$2$	$0$	$0$	$10$	$0$	$0$	$+$	$1$	$N(\mathrm{U}(1))$	$q+10q^{3}+73q^{9}-18q^{11}+90q^{17}+\cdots$
256.4.a.i	$256$	$4$	256.a	1.a	$1$	$2$	$2$	$15.104$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				64.4.b.b	$2$	$0$	$0$	$-4$	$0$	$0$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q-2q^{3}-\beta q^{5}-2\beta q^{7}-23q^{9}+42q^{11}+\cdots$
256.4.a.j	$256$	$4$	256.a	1.a	$1$	$2$	$2$	$15.104$	$\Q(\sqrt{7}) $	$_{}$	None	None	✓				8.4.b.a	$2$	$1$	$0$	$0$	$0$	$-16$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{3}-2\beta q^{5}-8q^{7}+q^{9}+3\beta q^{11}+\cdots$
256.4.a.k	$256$	$4$	256.a	1.a	$1$	$2$	$2$	$15.104$	$\Q(\sqrt{2}) $	$_{}$	$\Q(\sqrt{-2}) $	None	✓				128.4.b.b	$4$	$1$	$0$	$0$	$0$	$0$	$-$	$2$	$N(\mathrm{U}(1))$	$q+\beta q^{3}-19q^{9}-5^{2}\beta q^{11}-90q^{17}+\cdots$
256.4.a.l	$256$	$4$	256.a	1.a	$1$	$2$	$2$	$15.104$	$\Q(\sqrt{7}) $	$_{}$	None	None	✓				8.4.b.a	$2$	$0$	$0$	$0$	$0$	$16$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{3}+2\beta q^{5}+8q^{7}+q^{9}+3\beta q^{11}+\cdots$
256.4.a.m	$256$	$4$	256.a	1.a	$1$	$2$	$2$	$15.104$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				64.4.b.b	$2$	$1$	$0$	$4$	$0$	$0$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+2q^{3}-\beta q^{5}+2\beta q^{7}-23q^{9}-42q^{11}+\cdots$

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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.