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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 251 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
832.1.c.a	$832$	$1$	832.c	52.b	$2$	$1$	$1$	$0.415$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-13}) $	$\Q(\sqrt{13}) $	✓		✓	✓	208.1.c.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{9}+q^{13}-2q^{17}+q^{25}+2q^{29}+\cdots$
832.1.t.a	$832$	$1$	832.t	13.d	$4$	$2$	$1$	$0.415$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None			✓	✓	416.1.t.a	$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q+(i-1)q^{5}-q^{9}+i q^{13}+2 i q^{17}+\cdots$
832.1.y.a	$832$	$1$	832.y	52.i	$6$	$2$	$1$	$0.415$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-1}) $	None			✓	✓	208.1.y.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{5}+\zeta_{6}^{2}q^{9}-\zeta_{6}q^{13}+\cdots$
832.1.bb.a	$832$	$1$	832.bb	52.j	$6$	$2$	$1$	$0.415$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-1}) $	None					52.1.j.a	$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q+q^{5}-\zeta_{6}q^{9}-\zeta_{6}^{2}q^{13}+\zeta_{6}q^{17}+\cdots$
832.1.bb.b	$832$	$1$	832.bb	52.j	$6$	$4$	$2$	$0.415$	$\Q(\zeta_{12})$	$A_{4}$	None	None			✓		416.1.bb.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}^{5}q^{3}+\zeta_{12}q^{7}-\zeta_{12}^{5}q^{11}+\cdots$
832.1.bl.a	$832$	$1$	832.bl	13.f	$12$	$4$	$1$	$0.415$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None			✓	✓	416.1.bl.a	$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q+(-\zeta_{12}+\zeta_{12}^{2})q^{5}-\zeta_{12}^{4}q^{9}-\zeta_{12}^{5}q^{13}+\cdots$
832.2.a.a	$832$	$2$	832.a	1.a	$1$	$1$	$1$	$6.644$	$\Q$	$_{}$	None	None	✓				26.2.a.b	$1$	$1$	$0$	$-3$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+q^{5}-q^{7}+6q^{9}-2q^{11}+\cdots$
832.2.a.b	$832$	$2$	832.a	1.a	$1$	$1$	$1$	$6.644$	$\Q$	$_{}$	None	None	✓				416.2.a.a	$1$	$1$	$0$	$-1$	$-1$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+3q^{7}-2q^{9}-2q^{11}+\cdots$
832.2.a.c	$832$	$2$	832.a	1.a	$1$	$1$	$1$	$6.644$	$\Q$	$_{}$	None	None	✓				104.2.a.a	$1$	$0$	$0$	$-1$	$1$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+5q^{7}-2q^{9}+2q^{11}+\cdots$
832.2.a.d	$832$	$2$	832.a	1.a	$1$	$1$	$1$	$6.644$	$\Q$	$_{}$	None	None	✓				26.2.a.a	$1$	$1$	$0$	$-1$	$3$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{5}-q^{7}-2q^{9}-6q^{11}+\cdots$
832.2.a.e	$832$	$2$	832.a	1.a	$1$	$1$	$1$	$6.644$	$\Q$	$_{}$	None	None	✓				52.2.a.a	$1$	$0$	$0$	$0$	$-2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-2q^{7}-3q^{9}+2q^{11}+q^{13}+\cdots$
832.2.a.f	$832$	$2$	832.a	1.a	$1$	$1$	$1$	$6.644$	$\Q$	$_{}$	None	None	✓				52.2.a.a	$1$	$1$	$0$	$0$	$-2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+2q^{7}-3q^{9}-2q^{11}+q^{13}+\cdots$
832.2.a.g	$832$	$2$	832.a	1.a	$1$	$1$	$1$	$6.644$	$\Q$	$_{}$	None	None	✓				416.2.a.a	$1$	$1$	$0$	$1$	$-1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-3q^{7}-2q^{9}+2q^{11}+\cdots$
832.2.a.h	$832$	$2$	832.a	1.a	$1$	$1$	$1$	$6.644$	$\Q$	$_{}$	None	None	✓				104.2.a.a	$1$	$1$	$0$	$1$	$1$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-5q^{7}-2q^{9}-2q^{11}+\cdots$
832.2.a.i	$832$	$2$	832.a	1.a	$1$	$1$	$1$	$6.644$	$\Q$	$_{}$	None	None	✓				26.2.a.a	$1$	$0$	$0$	$1$	$3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{5}+q^{7}-2q^{9}+6q^{11}+\cdots$
832.2.a.j	$832$	$2$	832.a	1.a	$1$	$1$	$1$	$6.644$	$\Q$	$_{}$	None	None	✓				26.2.a.b	$1$	$0$	$0$	$3$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+q^{5}+q^{7}+6q^{9}+2q^{11}+\cdots$
832.2.a.k	$832$	$2$	832.a	1.a	$1$	$2$	$2$	$6.644$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓		✓		104.2.a.b	$1$	$1$	$0$	$-1$	$-3$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(-2+\beta )q^{5}-\beta q^{7}+(1+\beta )q^{9}+\cdots$
832.2.a.l	$832$	$2$	832.a	1.a	$1$	$2$	$2$	$6.644$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓				416.2.a.c	$1$	$0$	$0$	$-1$	$3$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(2-\beta )q^{5}+(2-\beta )q^{7}+(1+\beta )q^{9}+\cdots$
832.2.a.m	$832$	$2$	832.a	1.a	$1$	$2$	$2$	$6.644$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓		✓		416.2.a.d	$2$	$1$	$0$	$0$	$-6$	$0$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{3}-3q^{5}+\beta q^{7}+2q^{9}+2\beta q^{11}+\cdots$
832.2.a.n	$832$	$2$	832.a	1.a	$1$	$2$	$2$	$6.644$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓				104.2.a.b	$1$	$0$	$0$	$1$	$-3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(-2+\beta )q^{5}+\beta q^{7}+(1+\beta )q^{9}+\cdots$
832.2.a.o	$832$	$2$	832.a	1.a	$1$	$2$	$2$	$6.644$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓				416.2.a.c	$1$	$0$	$0$	$1$	$3$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(2-\beta )q^{5}+(-2+\beta )q^{7}+(1+\cdots)q^{9}+\cdots$
832.2.a.p	$832$	$2$	832.a	1.a	$1$	$4$	$4$	$6.644$	4.4.13448.1	$_{}$	None	None	✓		✓		416.2.a.f	$2$	$0$	$0$	$0$	$2$	$0$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}-\beta _{3}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots$
832.2.b.a	$832$	$2$	832.b	8.b	$2$	$4$	$4$	$6.644$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			832.2.b.a	$2$	$0$	$0$	$0$	$0$	$-12$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta_{2}+\beta_1)q^{3}+(2\beta_{2}-\beta_1)q^{5}+\cdots$
832.2.b.b	$832$	$2$	832.b	8.b	$2$	$4$	$4$	$6.644$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			832.2.b.a	$2$	$0$	$0$	$0$	$0$	$12$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta_{2}+\beta_1)q^{3}+(-2\beta_{2}+\beta_1)q^{5}+\cdots$
832.2.b.c	$832$	$2$	832.b	8.b	$2$	$8$	$8$	$6.644$	8.0.195105024.2	$_{}$	None	None		✓			832.2.b.c	$2$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{3}-\beta _{4}q^{5}+(-\beta _{1}-\beta _{7})q^{7}+\cdots$
832.2.b.d	$832$	$2$	832.b	8.b	$2$	$8$	$8$	$6.644$	8.0.195105024.2	$_{}$	None	None		✓			832.2.b.c	$2$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{3}+\beta _{4}q^{5}+(\beta _{1}+\beta _{7})q^{7}+(-1+\cdots)q^{9}+\cdots$
832.2.e.a	$832$	$2$	832.e	104.e	$2$	$4$	$4$	$6.644$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			832.2.e.a	$4$	$0$	$0$	$0$	$-12$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_1 q^{3}-3 q^{5}-\beta_1 q^{7}+2 q^{9}+\cdots$
832.2.e.b	$832$	$2$	832.e	104.e	$2$	$4$	$4$	$6.644$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			832.2.e.a	$4$	$0$	$0$	$0$	$12$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_1 q^{3}+3 q^{5}+\beta_1 q^{7}+2 q^{9}+\cdots$
832.2.e.c	$832$	$2$	832.e	104.e	$2$	$8$	$8$	$6.644$	8.0.3317760000.2	$_{}$	None	None		✓			832.2.e.c	$8$	$0$	$0$	$0$	$0$	$0$		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+\beta _{2}q^{7}-q^{9}-\beta _{4}q^{11}+(\beta _{5}+\cdots)q^{13}+\cdots$
832.2.e.d	$832$	$2$	832.e	104.e	$2$	$12$	$12$	$6.644$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	$\Q(\sqrt{-26}) $	None		✓	✓		832.2.e.d	$8$	$0$	$0$	$0$	$0$	$0$		$2^{14}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{2}q^{3}-\beta _{5}q^{5}-\beta _{3}q^{7}+(-3-\beta _{7}+\cdots)q^{9}+\cdots$
832.2.f.a	$832$	$2$	832.f	13.b	$2$	$2$	$2$	$6.644$	$\Q(\sqrt{-1}) $	$_{}$	None	None					416.2.f.a	$2$	$0$	$0$	$-6$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-3 q^{3}-3 i q^{5}+i q^{7}+6 q^{9}+4 i q^{11}+\cdots$
832.2.f.b	$832$	$2$	832.f	13.b	$2$	$2$	$2$	$6.644$	$\Q(\sqrt{-1}) $	$_{}$	None	None					26.2.b.a	$2$	$0$	$0$	$-2$	$0$	$0$		$3$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+\beta q^{5}-\beta q^{7}-2 q^{9}+(-\beta-2)q^{13}+\cdots$
832.2.f.c	$832$	$2$	832.f	13.b	$2$	$2$	$2$	$6.644$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None					416.2.f.b	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q-2\beta q^{5}-3 q^{9}+(-\beta+3)q^{13}+\cdots$
832.2.f.d	$832$	$2$	832.f	13.b	$2$	$2$	$2$	$6.644$	$\Q(\sqrt{-1}) $	$_{}$	None	None					26.2.b.a	$2$	$0$	$0$	$2$	$0$	$0$		$3$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+\beta q^{5}+\beta q^{7}-2 q^{9}+(-\beta-2)q^{13}+\cdots$
832.2.f.e	$832$	$2$	832.f	13.b	$2$	$2$	$2$	$6.644$	$\Q(\sqrt{-1}) $	$_{}$	None	None					416.2.f.a	$2$	$0$	$0$	$6$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3 q^{3}-3 i q^{5}-i q^{7}+6 q^{9}-4 i q^{11}+\cdots$
832.2.f.f	$832$	$2$	832.f	13.b	$2$	$4$	$4$	$6.644$	$\Q(i, \sqrt{17})$	$_{}$	None	None					104.2.f.a	$2$	$0$	$0$	$-2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta _{3})q^{3}-\beta _{1}q^{5}+(-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$
832.2.f.g	$832$	$2$	832.f	13.b	$2$	$4$	$4$	$6.644$	$\Q(i, \sqrt{13})$	$_{}$	$\Q(\sqrt{-13}) $	None					416.2.f.d	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{7}-3q^{9}+(-\beta _{1}-\beta _{2})q^{11}+\cdots$
832.2.f.h	$832$	$2$	832.f	13.b	$2$	$4$	$4$	$6.644$	$\Q(i, \sqrt{5})$	$_{}$	None	None					416.2.f.e	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}+\beta _{1}q^{5}+\beta _{2}q^{7}+2q^{9}+(-2+\cdots)q^{13}+\cdots$
832.2.f.i	$832$	$2$	832.f	13.b	$2$	$4$	$4$	$6.644$	$\Q(i, \sqrt{17})$	$_{}$	None	None					104.2.f.a	$2$	$0$	$0$	$2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-\beta _{3})q^{3}-\beta _{1}q^{5}+(\beta _{1}-\beta _{2})q^{7}+\cdots$
832.2.i.a	$832$	$2$	832.i	13.c	$3$	$2$	$1$	$6.644$	$\Q(\sqrt{-3}) $	$_{}$	None	None					52.2.e.a	$2$	$0$	$0$	$-3$	$-4$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-3+3\zeta_{6})q^{3}-2q^{5}+\zeta_{6}q^{7}-6\zeta_{6}q^{9}+\cdots$
832.2.i.b	$832$	$2$	832.i	13.c	$3$	$2$	$1$	$6.644$	$\Q(\sqrt{-3}) $	$_{}$	None	None					416.2.i.a	$2$	$1$	$0$	$-2$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{3}-q^{5}-\zeta_{6}q^{9}+(-4+\cdots)q^{11}+\cdots$
832.2.i.c	$832$	$2$	832.i	13.c	$3$	$2$	$1$	$6.644$	$\Q(\sqrt{-3}) $	$_{}$	None	None					52.2.e.b	$2$	$0$	$0$	$-2$	$6$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{3}+3q^{5}+4\zeta_{6}q^{7}+\cdots$
832.2.i.d	$832$	$2$	832.i	13.c	$3$	$2$	$1$	$6.644$	$\Q(\sqrt{-3}) $	$_{}$	None	None					104.2.i.a	$2$	$1$	$0$	$-1$	$-4$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}-2q^{5}-\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots$
832.2.i.e	$832$	$2$	832.i	13.c	$3$	$2$	$1$	$6.644$	$\Q(\sqrt{-3}) $	$_{}$	None	None					26.2.c.a	$2$	$0$	$0$	$0$	$2$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{5}-4\zeta_{6}q^{7}+3\zeta_{6}q^{9}+(4-4\zeta_{6})q^{11}+\cdots$
832.2.i.f	$832$	$2$	832.i	13.c	$3$	$2$	$1$	$6.644$	$\Q(\sqrt{-3}) $	$_{}$	None	None					26.2.c.a	$2$	$0$	$0$	$0$	$2$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{5}+4\zeta_{6}q^{7}+3\zeta_{6}q^{9}+(-4+4\zeta_{6})q^{11}+\cdots$
832.2.i.g	$832$	$2$	832.i	13.c	$3$	$2$	$1$	$6.644$	$\Q(\sqrt{-3}) $	$_{}$	None	None					104.2.i.a	$2$	$0$	$0$	$1$	$-4$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}-2q^{5}+\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots$
832.2.i.h	$832$	$2$	832.i	13.c	$3$	$2$	$1$	$6.644$	$\Q(\sqrt{-3}) $	$_{}$	None	None					416.2.i.a	$2$	$0$	$0$	$2$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{3}-q^{5}-\zeta_{6}q^{9}+(4-4\zeta_{6})q^{11}+\cdots$
832.2.i.i	$832$	$2$	832.i	13.c	$3$	$2$	$1$	$6.644$	$\Q(\sqrt{-3}) $	$_{}$	None	None					52.2.e.b	$2$	$0$	$0$	$2$	$6$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{3}+3q^{5}-4\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots$
832.2.i.j	$832$	$2$	832.i	13.c	$3$	$2$	$1$	$6.644$	$\Q(\sqrt{-3}) $	$_{}$	None	None					52.2.e.a	$2$	$0$	$0$	$3$	$-4$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(3-3\zeta_{6})q^{3}-2q^{5}-\zeta_{6}q^{7}-6\zeta_{6}q^{9}+\cdots$
832.2.i.k	$832$	$2$	832.i	13.c	$3$	$4$	$2$	$6.644$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None					416.2.i.c	$2$	$0$	$0$	$-2$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{1}-\beta _{2})q^{3}-2\beta _{3}q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$

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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.