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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 94 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
1275.1.c.a	$1275$	$1$	1275.c	51.c	$2$	$1$	$1$	$0.636$	$\Q$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-51}) $	$\Q(\sqrt{85}) $	✓				255.1.h.e	$4$	$0$	$0$	$-1$	$0$	$0$		$1$		$q-q^{3}+q^{4}+q^{9}-q^{12}+q^{16}+q^{17}+\cdots$
1275.1.c.b	$1275$	$1$	1275.c	51.c	$2$	$1$	$1$	$0.636$	$\Q$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-51}) $	$\Q(\sqrt{85}) $	✓				255.1.h.e	$4$	$0$	$0$	$1$	$0$	$0$		$1$		$q+q^{3}+q^{4}+q^{9}+q^{12}+q^{16}-q^{17}+\cdots$
1275.1.c.c	$1275$	$1$	1275.c	51.c	$2$	$2$	$2$	$0.636$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-255}) $	None					255.1.h.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{2}-i q^{3}-q^{6}-i q^{7}-i q^{8}+\cdots$
1275.1.c.d	$1275$	$1$	1275.c	51.c	$2$	$2$	$2$	$0.636$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-255}) $	None					255.1.h.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+i q^{2}-i q^{3}+q^{6}-i q^{7}+i q^{8}+\cdots$
1275.1.t.a	$1275$	$1$	1275.t	51.f	$4$	$4$	$2$	$0.636$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-15}) $	None			✓	✓	255.1.i.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{8}-\zeta_{8}^{3})q^{2}-\zeta_{8}^{3}q^{3}+q^{4}+(1+\cdots)q^{6}+\cdots$
1275.1.y.a	$1275$	$1$	1275.y	51.g	$8$	$8$	$2$	$0.636$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-15}) $	None			✓	✓	255.1.y.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{16}-\zeta_{16}^{3})q^{2}+\zeta_{16}^{7}q^{3}+(\zeta_{16}^{2}+\cdots)q^{4}+\cdots$
1275.1.bf.a	$1275$	$1$	1275.bf	1275.af	$10$	$8$	$2$	$0.636$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-51}) $	None		✓	✓	✓	1275.1.bf.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{20}^{9}q^{3}-\zeta_{20}^{4}q^{4}+\zeta_{20}^{5}q^{5}+\cdots$
1275.1.bg.a	$1275$	$1$	1275.bg	1275.ag	$10$	$4$	$1$	$0.636$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-51}) $	None		✓			1275.1.bg.a	$4$	$0$	$0$	$-1$	$4$	$0$		$1$		$q-\zeta_{10}^{3}q^{3}-\zeta_{10}^{3}q^{4}+q^{5}-\zeta_{10}q^{9}+\cdots$
1275.1.bg.b	$1275$	$1$	1275.bg	1275.ag	$10$	$4$	$1$	$0.636$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-51}) $	None		✓			1275.1.bg.a	$4$	$0$	$0$	$1$	$-4$	$0$		$1$		$q+\zeta_{10}^{3}q^{3}-\zeta_{10}^{3}q^{4}-q^{5}-\zeta_{10}q^{9}+\cdots$
1275.1.bk.a	$1275$	$1$	1275.bk	255.ac	$16$	$16$	$2$	$0.636$	$\Q(\zeta_{32})$	$D_{16}$	$\Q(\sqrt{-15}) $	None		✓	✓	✓	1275.1.bk.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{32}^{5}+\zeta_{32}^{15})q^{2}+\zeta_{32}^{9}q^{3}+(-\zeta_{32}^{4}+\cdots)q^{4}+\cdots$
1275.1.br.a	$1275$	$1$	1275.br	255.aj	$16$	$16$	$2$	$0.636$	$\Q(\zeta_{32})$	$D_{16}$	$\Q(\sqrt{-15}) $	None		✓	✓	✓	1275.1.bk.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{32}+\zeta_{32}^{11})q^{2}-\zeta_{32}^{7}q^{3}+\cdots$
1275.2.a.a	$1275$	$2$	1275.a	1.a	$1$	$1$	$1$	$10.181$	$\Q$	$_{}$	None	None	✓	✓			1275.2.a.a	$1$	$1$	$-2$	$-1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-q^{3}+2q^{4}+2q^{6}+q^{7}+q^{9}+\cdots$
1275.2.a.b	$1275$	$2$	1275.a	1.a	$1$	$1$	$1$	$10.181$	$\Q$	$_{}$	None	None	✓				255.2.b.a	$1$	$0$	$-1$	$-1$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+q^{6}+4q^{7}+3q^{8}+\cdots$
1275.2.a.c	$1275$	$2$	1275.a	1.a	$1$	$1$	$1$	$10.181$	$\Q$	$_{}$	None	None	✓	✓			1275.2.a.c	$1$	$1$	$0$	$-1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}-q^{7}+q^{9}+2q^{11}+2q^{12}+\cdots$
1275.2.a.d	$1275$	$2$	1275.a	1.a	$1$	$1$	$1$	$10.181$	$\Q$	$_{}$	None	None	✓				51.2.a.a	$1$	$0$	$0$	$-1$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}+4q^{7}+q^{9}-3q^{11}+\cdots$
1275.2.a.e	$1275$	$2$	1275.a	1.a	$1$	$1$	$1$	$10.181$	$\Q$	$_{}$	None	None	✓	✓			1275.2.a.c	$1$	$0$	$0$	$1$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}+q^{7}+q^{9}+2q^{11}-2q^{12}+\cdots$
1275.2.a.f	$1275$	$2$	1275.a	1.a	$1$	$1$	$1$	$10.181$	$\Q$	$_{}$	None	None	✓				255.2.b.a	$1$	$0$	$1$	$1$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+q^{6}-4q^{7}-3q^{8}+\cdots$
1275.2.a.g	$1275$	$2$	1275.a	1.a	$1$	$1$	$1$	$10.181$	$\Q$	$_{}$	None	None	✓	✓			1275.2.a.a	$1$	$0$	$2$	$1$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+q^{3}+2q^{4}+2q^{6}-q^{7}+q^{9}+\cdots$
1275.2.a.h	$1275$	$2$	1275.a	1.a	$1$	$2$	$2$	$10.181$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				255.2.a.b	$1$	$1$	$-3$	$2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{2}+q^{3}+3\beta q^{4}+(-1+\cdots)q^{6}+\cdots$
1275.2.a.i	$1275$	$2$	1275.a	1.a	$1$	$2$	$2$	$10.181$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				255.2.b.b	$1$	$1$	$-1$	$2$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots$
1275.2.a.j	$1275$	$2$	1275.a	1.a	$1$	$2$	$2$	$10.181$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓				255.2.a.a	$1$	$0$	$-1$	$2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+q^{3}+(1+\beta )q^{4}-\beta q^{6}+(1+\cdots)q^{7}+\cdots$
1275.2.a.k	$1275$	$2$	1275.a	1.a	$1$	$2$	$2$	$10.181$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			1275.2.a.k	$1$	$0$	$0$	$-2$	$0$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}-\beta q^{6}+(3+\beta )q^{7}-2\beta q^{8}+\cdots$
1275.2.a.l	$1275$	$2$	1275.a	1.a	$1$	$2$	$2$	$10.181$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			1275.2.a.k	$1$	$1$	$0$	$2$	$0$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+\beta q^{6}+(-3+\beta )q^{7}+\cdots$
1275.2.a.m	$1275$	$2$	1275.a	1.a	$1$	$2$	$2$	$10.181$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓		✓		255.2.b.b	$1$	$1$	$1$	$-2$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots$
1275.2.a.n	$1275$	$2$	1275.a	1.a	$1$	$2$	$2$	$10.181$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓				51.2.a.b	$1$	$0$	$1$	$2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+(2+\beta )q^{4}+\beta q^{6}+(4+\cdots)q^{8}+\cdots$
1275.2.a.o	$1275$	$2$	1275.a	1.a	$1$	$3$	$3$	$10.181$	3.3.148.1	$_{}$	None	None	✓	✓	✓		1275.2.a.o	$1$	$1$	$-2$	$3$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots$
1275.2.a.p	$1275$	$2$	1275.a	1.a	$1$	$3$	$3$	$10.181$	3.3.229.1	$_{}$	None	None	✓				255.2.a.c	$1$	$1$	$0$	$-3$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots$
1275.2.a.q	$1275$	$2$	1275.a	1.a	$1$	$3$	$3$	$10.181$	3.3.148.1	$_{}$	None	None	✓	✓			1275.2.a.q	$1$	$1$	$0$	$-3$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}-q^{3}+(1-\beta _{1}-\beta _{2})q^{4}-\beta _{2}q^{6}+\cdots$
1275.2.a.r	$1275$	$2$	1275.a	1.a	$1$	$3$	$3$	$10.181$	3.3.148.1	$_{}$	None	None	✓	✓			1275.2.a.q	$1$	$0$	$0$	$3$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+q^{3}+(1-\beta _{1}-\beta _{2})q^{4}-\beta _{2}q^{6}+\cdots$
1275.2.a.s	$1275$	$2$	1275.a	1.a	$1$	$3$	$3$	$10.181$	3.3.148.1	$_{}$	None	None	✓	✓			1275.2.a.o	$1$	$0$	$2$	$-3$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}-q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots$
1275.2.a.t	$1275$	$2$	1275.a	1.a	$1$	$4$	$4$	$10.181$	4.4.13768.1	$_{}$	None	None	✓		✓		255.2.a.d	$1$	$0$	$-1$	$-4$	$0$	$-4$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}-q^{3}+(2-\beta _{1})q^{4}-\beta _{3}q^{6}+\cdots$
1275.2.a.u	$1275$	$2$	1275.a	1.a	$1$	$5$	$5$	$10.181$	5.5.3717884.1	$_{}$	None	None	✓		✓		255.2.b.c	$1$	$0$	$-2$	$-5$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
1275.2.a.v	$1275$	$2$	1275.a	1.a	$1$	$5$	$5$	$10.181$	5.5.3717884.1	$_{}$	None	None	✓		✓		255.2.b.c	$1$	$0$	$2$	$5$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
1275.2.b.a	$1275$	$2$	1275.b	5.b	$2$	$2$	$2$	$10.181$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			1275.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 i q^{2}-i q^{3}-2 q^{4}+2 q^{6}-i q^{7}+\cdots$
1275.2.b.b	$1275$	$2$	1275.b	5.b	$2$	$2$	$2$	$10.181$	$\Q(\sqrt{-1}) $	$_{}$	None	None					51.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{3}+2 q^{4}-4 i q^{7}-q^{9}-3 q^{11}+\cdots$
1275.2.b.c	$1275$	$2$	1275.b	5.b	$2$	$2$	$2$	$10.181$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			1275.2.a.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+2 q^{4}-i q^{7}-q^{9}+2 q^{11}+\cdots$
1275.2.b.d	$1275$	$2$	1275.b	5.b	$2$	$4$	$4$	$10.181$	$\Q(i, \sqrt{17})$	$_{}$	None	None					51.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{3}+(-3+\beta _{3})q^{4}+(1+\cdots)q^{6}+\cdots$
1275.2.b.e	$1275$	$2$	1275.b	5.b	$2$	$4$	$4$	$10.181$	$\Q(i, \sqrt{5})$	$_{}$	None	None					255.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}-\beta _{3})q^{2}-\beta _{3}q^{3}+3\beta _{2}q^{4}+(-1+\cdots)q^{6}+\cdots$
1275.2.b.f	$1275$	$2$	1275.b	5.b	$2$	$4$	$4$	$10.181$	$\Q(i, \sqrt{13})$	$_{}$	None	None					255.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-2+\beta _{3})q^{4}+(-1+\cdots)q^{6}+\cdots$
1275.2.b.g	$1275$	$2$	1275.b	5.b	$2$	$4$	$4$	$10.181$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			1275.2.a.k	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_{2} q^{2}-\beta_1 q^{3}-\beta_{3} q^{6}+(-\beta_{2}-3\beta_1)q^{7}+\cdots$
1275.2.b.h	$1275$	$2$	1275.b	5.b	$2$	$6$	$6$	$10.181$	6.0.350464.1	$_{}$	None	None		✓			1275.2.a.o	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{3}+\beta _{4})q^{2}-\beta _{3}q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots$
1275.2.b.i	$1275$	$2$	1275.b	5.b	$2$	$6$	$6$	$10.181$	6.0.3356224.1	$_{}$	None	None					255.2.a.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-1+\beta _{2})q^{4}-\beta _{4}q^{6}+\cdots$
1275.2.b.j	$1275$	$2$	1275.b	5.b	$2$	$6$	$6$	$10.181$	6.0.350464.1	$_{}$	None	None		✓			1275.2.a.q	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{2}+\beta _{3}q^{3}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
1275.2.b.k	$1275$	$2$	1275.b	5.b	$2$	$8$	$8$	$10.181$	8.0.$\cdots$.1	$_{}$	None	None			✓		255.2.a.d	$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}-\beta _{4}q^{3}+(-2-\beta _{1})q^{4}-\beta _{6}q^{6}+\cdots$
1275.2.d.a	$1275$	$2$	1275.d	85.c	$2$	$2$	$2$	$10.181$	$\Q(\sqrt{-1}) $	$_{}$	None	None					51.2.d.a	$2$	$0$	$0$	$-2$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 i q^{2}-q^{3}-2 q^{4}-2 i q^{6}+2 q^{7}+\cdots$
1275.2.d.b	$1275$	$2$	1275.d	85.c	$2$	$2$	$2$	$10.181$	$\Q(\sqrt{-1}) $	$_{}$	None	None					51.2.d.b	$2$	$0$	$0$	$-2$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{3}+q^{4}-i q^{6}-4 q^{7}+\cdots$
1275.2.d.c	$1275$	$2$	1275.d	85.c	$2$	$2$	$2$	$10.181$	$\Q(\sqrt{-1}) $	$_{}$	None	None					51.2.d.a	$2$	$0$	$0$	$2$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 i q^{2}+q^{3}-2 q^{4}+2 i q^{6}-2 q^{7}+\cdots$
1275.2.d.d	$1275$	$2$	1275.d	85.c	$2$	$2$	$2$	$10.181$	$\Q(\sqrt{-1}) $	$_{}$	None	None					51.2.d.b	$2$	$0$	$0$	$2$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}+q^{3}+q^{4}+i q^{6}+4 q^{7}+\cdots$
1275.2.d.e	$1275$	$2$	1275.d	85.c	$2$	$4$	$4$	$10.181$	$\Q(i, \sqrt{13})$	$_{}$	None	None					255.2.g.a	$2$	$0$	$0$	$-4$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-q^{3}+(-2+\beta _{3})q^{4}-\beta _{1}q^{6}+\cdots$
1275.2.d.f	$1275$	$2$	1275.d	85.c	$2$	$4$	$4$	$10.181$	$\Q(i, \sqrt{13})$	$_{}$	None	None					255.2.g.a	$2$	$0$	$0$	$4$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+q^{3}+(-2+\beta _{3})q^{4}+\beta _{1}q^{6}+\cdots$

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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.