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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 62 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
1935.1.h.a	$1935$	$1$	1935.h	215.d	$2$	$3$	$3$	$0.966$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-215}) $	None	✓				215.1.d.a	$2$	$0$	$-1$	$0$	$3$	$1$		$1$		$q+\beta _{2}q^{2}+(\beta _{1}-\beta _{2})q^{4}+q^{5}+\beta _{1}q^{7}+\cdots$
1935.1.h.b	$1935$	$1$	1935.h	215.d	$2$	$3$	$3$	$0.966$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-215}) $	None	✓				215.1.d.a	$2$	$0$	$1$	$0$	$-3$	$-1$		$1$		$q-\beta _{2}q^{2}+(\beta _{1}-\beta _{2})q^{4}-q^{5}-\beta _{1}q^{7}+\cdots$
1935.1.x.a	$1935$	$1$	1935.x	1935.x	$6$	$2$	$1$	$0.966$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-215}) $	None		✓			1935.1.x.a	$4$	$0$	$-1$	$1$	$1$	$-1$		$1$		$q+\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}+\zeta_{6}q^{5}-q^{6}+\zeta_{6}^{2}q^{7}+\cdots$
1935.1.x.b	$1935$	$1$	1935.x	1935.x	$6$	$2$	$1$	$0.966$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-215}) $	None		✓			1935.1.x.a	$4$	$0$	$1$	$-1$	$-1$	$1$		$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{5}-q^{6}-\zeta_{6}^{2}q^{7}+\cdots$
1935.1.x.c	$1935$	$1$	1935.x	1935.x	$6$	$12$	$6$	$0.966$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-215}) $	None		✓			1935.1.x.c	$4$	$0$	$-1$	$1$	$-6$	$-1$		$1$		$q+(-\zeta_{42}^{3}+\zeta_{42}^{4})q^{2}-\zeta_{42}^{13}q^{3}+\cdots$
1935.1.x.d	$1935$	$1$	1935.x	1935.x	$6$	$12$	$6$	$0.966$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-215}) $	None		✓			1935.1.x.c	$4$	$0$	$1$	$-1$	$6$	$1$		$1$		$q+(\zeta_{42}^{3}-\zeta_{42}^{4})q^{2}+\zeta_{42}^{13}q^{3}+(\zeta_{42}^{6}+\cdots)q^{4}+\cdots$
1935.2.a.a	$1935$	$2$	1935.a	1.a	$1$	$1$	$1$	$15.451$	$\Q$	$_{}$	None	None	✓				645.2.a.f	$1$	$0$	$-2$	$0$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}-q^{5}+2q^{10}-5q^{11}+\cdots$
1935.2.a.b	$1935$	$2$	1935.a	1.a	$1$	$1$	$1$	$15.451$	$\Q$	$_{}$	None	None	✓	✓			1935.2.a.b	$1$	$1$	$-1$	$0$	$-1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-q^{5}-4q^{7}+3q^{8}+q^{10}+\cdots$
1935.2.a.c	$1935$	$2$	1935.a	1.a	$1$	$1$	$1$	$15.451$	$\Q$	$_{}$	None	None	✓	✓			1935.2.a.c	$1$	$1$	$-1$	$0$	$-1$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-q^{5}+4q^{7}+3q^{8}+q^{10}+\cdots$
1935.2.a.d	$1935$	$2$	1935.a	1.a	$1$	$1$	$1$	$15.451$	$\Q$	$_{}$	None	None	✓				645.2.a.e	$1$	$0$	$-1$	$0$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-q^{5}+4q^{7}+3q^{8}+q^{10}+\cdots$
1935.2.a.e	$1935$	$2$	1935.a	1.a	$1$	$1$	$1$	$15.451$	$\Q$	$_{}$	None	None	✓				645.2.a.d	$1$	$0$	$-1$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+q^{5}+3q^{8}-q^{10}-4q^{11}+\cdots$
1935.2.a.f	$1935$	$2$	1935.a	1.a	$1$	$1$	$1$	$15.451$	$\Q$	$_{}$	None	None	✓				645.2.a.c	$1$	$0$	$0$	$0$	$-1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-q^{5}-2q^{7}+5q^{11}-5q^{13}+\cdots$
1935.2.a.g	$1935$	$2$	1935.a	1.a	$1$	$1$	$1$	$15.451$	$\Q$	$_{}$	None	None	✓				215.2.a.a	$1$	$1$	$0$	$0$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+q^{5}-2q^{7}+q^{11}-q^{13}+\cdots$
1935.2.a.h	$1935$	$2$	1935.a	1.a	$1$	$1$	$1$	$15.451$	$\Q$	$_{}$	None	None	✓	✓			1935.2.a.b	$1$	$0$	$1$	$0$	$1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+q^{5}-4q^{7}-3q^{8}+q^{10}+\cdots$
1935.2.a.i	$1935$	$2$	1935.a	1.a	$1$	$1$	$1$	$15.451$	$\Q$	$_{}$	None	None	✓	✓			1935.2.a.c	$1$	$0$	$1$	$0$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+q^{5}+4q^{7}-3q^{8}+q^{10}+\cdots$
1935.2.a.j	$1935$	$2$	1935.a	1.a	$1$	$1$	$1$	$15.451$	$\Q$	$_{}$	None	None	✓				645.2.a.b	$1$	$0$	$2$	$0$	$-1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}-q^{5}-4q^{7}-2q^{10}+\cdots$
1935.2.a.k	$1935$	$2$	1935.a	1.a	$1$	$1$	$1$	$15.451$	$\Q$	$_{}$	None	None	✓				645.2.a.a	$1$	$0$	$2$	$0$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}-q^{5}+4q^{7}-2q^{10}+\cdots$
1935.2.a.l	$1935$	$2$	1935.a	1.a	$1$	$2$	$2$	$15.451$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				645.2.a.g	$1$	$1$	$0$	$0$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{5}-\beta q^{7}-2\beta q^{8}+\beta q^{10}+\cdots$
1935.2.a.m	$1935$	$2$	1935.a	1.a	$1$	$2$	$2$	$15.451$	$\Q(\sqrt{6}) $	$_{}$	None	None	✓	✓			1935.2.a.m	$1$	$1$	$0$	$0$	$-2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+4q^{4}-q^{5}+(-2-\beta )q^{7}+\cdots$
1935.2.a.n	$1935$	$2$	1935.a	1.a	$1$	$2$	$2$	$15.451$	$\Q(\sqrt{6}) $	$_{}$	None	None	✓	✓			1935.2.a.m	$1$	$0$	$0$	$0$	$2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+4q^{4}+q^{5}+(-2+\beta )q^{7}+\cdots$
1935.2.a.o	$1935$	$2$	1935.a	1.a	$1$	$3$	$3$	$15.451$	3.3.316.1	$_{}$	None	None	✓		✓		645.2.a.j	$1$	$1$	$-1$	$0$	$3$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots$
1935.2.a.p	$1935$	$2$	1935.a	1.a	$1$	$3$	$3$	$15.451$	3.3.148.1	$_{}$	None	None	✓				645.2.a.i	$1$	$1$	$0$	$0$	$-3$	$-8$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+(1-\beta _{1}-\beta _{2})q^{4}-q^{5}+(-3+\cdots)q^{7}+\cdots$
1935.2.a.q	$1935$	$2$	1935.a	1.a	$1$	$3$	$3$	$15.451$	3.3.148.1	$_{}$	None	None	✓				645.2.a.h	$1$	$0$	$2$	$0$	$3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots$
1935.2.a.r	$1935$	$2$	1935.a	1.a	$1$	$3$	$3$	$15.451$	3.3.321.1	$_{}$	None	None	✓				215.2.a.b	$1$	$0$	$2$	$0$	$-3$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots$
1935.2.a.s	$1935$	$2$	1935.a	1.a	$1$	$5$	$5$	$15.451$	5.5.230224.1	$_{}$	None	None	✓	✓	✓	✓	1935.2.a.s	$1$	$1$	$-3$	$0$	$5$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots$
1935.2.a.t	$1935$	$2$	1935.a	1.a	$1$	$5$	$5$	$15.451$	5.5.220036.1	$_{}$	None	None	✓		✓		645.2.a.l	$1$	$1$	$-2$	$0$	$-5$	$2$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}+(\beta _{1}-\beta _{3})q^{4}-q^{5}+\beta _{2}q^{7}+\cdots$
1935.2.a.u	$1935$	$2$	1935.a	1.a	$1$	$5$	$5$	$15.451$	5.5.1933097.1	$_{}$	None	None	✓		✓		215.2.a.c	$1$	$0$	$-2$	$0$	$-5$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}+(1-\beta _{3}+\cdots)q^{7}+\cdots$
1935.2.a.v	$1935$	$2$	1935.a	1.a	$1$	$5$	$5$	$15.451$	5.5.1240016.1	$_{}$	None	None	✓	✓	✓		1935.2.a.v	$1$	$1$	$-1$	$0$	$-5$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}-q^{5}+(1+\cdots)q^{7}+\cdots$
1935.2.a.w	$1935$	$2$	1935.a	1.a	$1$	$5$	$5$	$15.451$	5.5.1240016.1	$_{}$	None	None	✓	✓	✓		1935.2.a.v	$1$	$0$	$1$	$0$	$5$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+q^{5}+(1+\cdots)q^{7}+\cdots$
1935.2.a.x	$1935$	$2$	1935.a	1.a	$1$	$5$	$5$	$15.451$	5.5.230224.1	$_{}$	None	None	✓	✓	✓	✓	1935.2.a.s	$1$	$0$	$3$	$0$	$-5$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots$
1935.2.a.y	$1935$	$2$	1935.a	1.a	$1$	$5$	$5$	$15.451$	5.5.135076.1	$_{}$	None	None	✓				645.2.a.k	$1$	$0$	$4$	$0$	$5$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{3})q^{2}+(3-\beta _{1}+\beta _{2}+\beta _{4})q^{4}+\cdots$
1935.2.a.z	$1935$	$2$	1935.a	1.a	$1$	$6$	$6$	$15.451$	6.6.32503921.1	$_{}$	None	None	✓		✓		215.2.a.d	$1$	$0$	$-3$	$0$	$6$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
1935.2.b.a	$1935$	$2$	1935.b	5.b	$2$	$4$	$4$	$15.451$	$\Q(\zeta_{12})$	$_{}$	None	None					645.2.b.b	$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+2\zeta_{12}^{2})q^{2}-q^{4}+(-1+2\zeta_{12}+\cdots)q^{5}+\cdots$
1935.2.b.b	$1935$	$2$	1935.b	5.b	$2$	$4$	$4$	$15.451$	$\Q(\zeta_{8})$	$_{}$	None	None					645.2.b.a	$2$	$0$	$0$	$0$	$4$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\zeta_{8}+\zeta_{8}^{2})q^{2}+(-1-2\zeta_{8}^{3})q^{4}+\cdots$
1935.2.b.c	$1935$	$2$	1935.b	5.b	$2$	$6$	$6$	$15.451$	6.0.1827904.1	$_{}$	None	None					215.2.b.a	$2$	$0$	$0$	$0$	$12$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-1-\beta _{2}+\beta _{3})q^{4}+(2+\beta _{4}+\cdots)q^{5}+\cdots$
1935.2.b.d	$1935$	$2$	1935.b	5.b	$2$	$14$	$14$	$15.451$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	$_{}$	None	None					215.2.b.b	$2$	$0$	$0$	$0$	$-8$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}+\beta _{9})q^{2}+(-1+\beta _{4}+\beta _{8})q^{4}+\cdots$
1935.2.b.e	$1935$	$2$	1935.b	5.b	$2$	$16$	$16$	$15.451$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None					645.2.b.c	$2$	$0$	$0$	$0$	$-2$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{3}+\beta _{10})q^{5}+(\beta _{12}+\cdots)q^{7}+\cdots$
1935.2.b.f	$1935$	$2$	1935.b	5.b	$2$	$20$	$20$	$15.451$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None					645.2.b.d	$2$	$0$	$0$	$0$	$-4$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-2+\beta _{2}-\beta _{3})q^{4}+\beta _{8}q^{5}+\cdots$
1935.2.b.g	$1935$	$2$	1935.b	5.b	$2$	$40$	$40$	$15.451$		$_{}$	None	None		✓	✓		1935.2.b.g	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1935.2.d.a	$1935$	$2$	1935.d	645.d	$2$	$88$	$88$	$15.451$		$_{}$	None	None		✓	✓	✓	1935.2.d.a	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1935.2.g.a	$1935$	$2$	1935.g	129.d	$2$	$2$	$2$	$15.451$	$\Q(\sqrt{-2}) $	$_{}$	None	None		✓			1935.2.g.a	$2$	$1$	$-2$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}-q^{4}+q^{5}+2\beta q^{7}+3q^{8}-q^{10}+\cdots$
1935.2.g.b	$1935$	$2$	1935.g	129.d	$2$	$2$	$2$	$15.451$	$\Q(\sqrt{-2}) $	$_{}$	None	None		✓			1935.2.g.a	$2$	$0$	$2$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}-q^{4}-q^{5}-2\beta q^{7}-3q^{8}-q^{10}+\cdots$
1935.2.g.c	$1935$	$2$	1935.g	129.d	$2$	$26$	$26$	$15.451$		$_{}$	None	None		✓			1935.2.g.c	$2$	$0$	$-2$	$0$	$-26$	$0$			$\mathrm{SU}(2)[C_{2}]$
1935.2.g.d	$1935$	$2$	1935.g	129.d	$2$	$26$	$26$	$15.451$		$_{}$	None	None		✓			1935.2.g.c	$2$	$0$	$2$	$0$	$26$	$0$			$\mathrm{SU}(2)[C_{2}]$
1935.4.a.a	$1935$	$4$	1935.a	1.a	$1$	$1$	$1$	$114.169$	$\Q$	$_{}$	None	None	✓	✓			1935.4.a.a	$1$	$2$	$-3$	$0$	$-5$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{2}+q^{4}-5q^{5}+4q^{7}+21q^{8}+\cdots$
1935.4.a.b	$1935$	$4$	1935.a	1.a	$1$	$1$	$1$	$114.169$	$\Q$	$_{}$	None	None	✓	✓			1935.4.a.a	$1$	$1$	$3$	$0$	$5$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{2}+q^{4}+5q^{5}+4q^{7}-21q^{8}+\cdots$
1935.4.a.c	$1935$	$4$	1935.a	1.a	$1$	$6$	$6$	$114.169$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	$_{}$	None	None	✓				215.4.a.a	$1$	$1$	$5$	$0$	$-30$	$-34$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}-5q^{5}+\cdots$
1935.4.a.d	$1935$	$4$	1935.a	1.a	$1$	$8$	$8$	$114.169$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓				645.4.a.b	$1$	$1$	$-2$	$0$	$40$	$-5$	$-$	$2^{3}\cdot 5$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2})q^{4}+5q^{5}+\cdots$
1935.4.a.e	$1935$	$4$	1935.a	1.a	$1$	$8$	$8$	$114.169$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓				215.4.a.b	$1$	$1$	$1$	$0$	$40$	$-36$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(3+\beta _{2})q^{4}+5q^{5}+(-4+\cdots)q^{7}+\cdots$
1935.4.a.f	$1935$	$4$	1935.a	1.a	$1$	$8$	$8$	$114.169$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓				645.4.a.a	$1$	$0$	$6$	$0$	$-40$	$-35$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(3-\beta _{1}+\beta _{2})q^{4}-5q^{5}+\cdots$

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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.