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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 (46 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
3627.1.c.a	$3627$	$1$	3627.c	403.b	$2$	$1$	$1$	$1.810$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-403}) $	$\Q(\sqrt{1209}) $	✓	✓			3627.1.c.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{4}-q^{13}+q^{16}+q^{25}+q^{31}+\cdots$
3627.1.c.b	$3627$	$1$	3627.c	403.b	$2$	$1$	$1$	$1.810$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-403}) $	$\Q(\sqrt{1209}) $	✓	✓			3627.1.c.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{4}+q^{13}+q^{16}+q^{25}-q^{31}+\cdots$
3627.1.bv.a	$3627$	$1$	3627.bv	403.n	$6$	$2$	$1$	$1.810$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	3627.1.bv.a	$4$	$0$	$0$	$0$	$0$	$1$		$1$		$q-\zeta_{6}^{2}q^{4}+\zeta_{6}q^{7}-\zeta_{6}q^{13}-\zeta_{6}q^{16}+\cdots$
3627.1.cg.a	$3627$	$1$	3627.cg	3627.bg	$6$	$8$	$4$	$1.810$	8.0.12960000.1	$A_{5}$	None	None		✓	✓	✓	3627.1.cg.a	$4$	$0$	$-2$	$0$	$-2$	$0$		$1$		$q+(-1+\beta _{4}+\beta _{5})q^{2}+\beta _{7}q^{3}+(-\beta _{2}+\cdots)q^{4}+\cdots$
3627.1.ch.a	$3627$	$1$	3627.ch	403.o	$6$	$2$	$1$	$1.810$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	3627.1.bv.a	$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q+\zeta_{6}q^{4}-q^{7}+\zeta_{6}q^{13}+\zeta_{6}^{2}q^{16}+\cdots$
3627.1.cl.a	$3627$	$1$	3627.cl	403.p	$6$	$4$	$2$	$1.810$	$\Q(\zeta_{12})$	$A_{4}$	None	None			✓	✓	403.1.p.a	$4$	$0$	$2$	$0$	$0$	$2$		$1$		$q+\zeta_{12}^{2}q^{2}-\zeta_{12}^{4}q^{7}+q^{8}+\zeta_{12}^{5}q^{11}+\cdots$
3627.1.dg.a	$3627$	$1$	3627.dg	403.u	$6$	$2$	$1$	$1.810$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	3627.1.dg.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{6}q^{4}+(-\zeta_{6}-\zeta_{6}^{2})q^{7}-\zeta_{6}q^{13}+\cdots$
3627.1.dj.a	$3627$	$1$	3627.dj	1209.al	$6$	$4$	$2$	$1.810$	$\Q(\sqrt{-2}, \sqrt{-3})$	$S_{4}$	None	None		✓	✓	✓	3627.1.dj.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(1-\beta _{2})q^{7}+(1-\beta _{2}+\cdots)q^{13}+\cdots$
3627.1.dq.a	$3627$	$1$	3627.dq	403.q	$6$	$2$	$1$	$1.810$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	3627.1.dg.a	$4$	$0$	$0$	$0$	$0$	$3$		$1$		$q+\zeta_{6}^{2}q^{4}+(1-\zeta_{6}^{2})q^{7}+\zeta_{6}q^{13}+\cdots$
3627.1.dz.a	$3627$	$1$	3627.dz	1209.ao	$6$	$4$	$2$	$1.810$	$\Q(\sqrt{-2}, \sqrt{-3})$	$S_{4}$	None	None		✓	✓	✓	3627.1.dj.a	$4$	$0$	$0$	$0$	$0$	$-4$		$1$		$q+(\beta _{1}-\beta _{3})q^{2}+(1-\beta _{2})q^{4}-q^{7}+(1+\cdots)q^{13}+\cdots$
3627.1.ed.a	$3627$	$1$	3627.ed	3627.dd	$6$	$8$	$4$	$1.810$	8.0.12960000.1	$A_{5}$	None	None		✓	✓	✓	3627.1.cg.a	$4$	$0$	$4$	$0$	$-2$	$0$		$1$		$q-\beta _{2}q^{2}+(-\beta _{3}-\beta _{7})q^{3}-\beta _{2}q^{4}+\cdots$
3627.1.es.a	$3627$	$1$	3627.es	403.z	$10$	$4$	$1$	$1.810$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-3}) $	None		✓			3627.1.es.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{10}q^{4}+(\zeta_{10}^{3}+\zeta_{10}^{4})q^{7}-\zeta_{10}^{3}q^{13}+\cdots$
3627.1.es.b	$3627$	$1$	3627.es	403.z	$10$	$4$	$1$	$1.810$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-3}) $	None		✓			3627.1.es.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{10}q^{4}+(-\zeta_{10}^{3}-\zeta_{10}^{4})q^{7}+\zeta_{10}q^{13}+\cdots$
3627.1.fm.a	$3627$	$1$	3627.fm	403.ac	$12$	$4$	$1$	$1.810$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	3627.1.fm.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q+\zeta_{12}^{5}q^{4}+(-\zeta_{12}+\zeta_{12}^{2})q^{7}-\zeta_{12}^{5}q^{13}+\cdots$
3627.1.gh.a	$3627$	$1$	3627.gh	403.ah	$12$	$4$	$1$	$1.810$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	3627.1.fm.a	$4$	$0$	$0$	$0$	$0$	$-4$		$1$		$q-\zeta_{12}^{5}q^{4}+(-1+\zeta_{12}^{5})q^{7}+\zeta_{12}q^{13}+\cdots$
3627.1.hi.a	$3627$	$1$	3627.hi	403.am	$20$	$8$	$1$	$1.810$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-3}) $	None		✓			3627.1.hi.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q-\zeta_{20}q^{4}+(-\zeta_{20}^{3}-\zeta_{20}^{4})q^{7}-\zeta_{20}^{3}q^{13}+\cdots$
3627.1.hi.b	$3627$	$1$	3627.hi	403.am	$20$	$8$	$1$	$1.810$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-3}) $	None		✓			3627.1.hi.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q-\zeta_{20}q^{4}+(-\zeta_{20}^{8}+\zeta_{20}^{9})q^{7}+\zeta_{20}q^{13}+\cdots$
3627.1.it.a	$3627$	$1$	3627.it	403.au	$30$	$8$	$1$	$1.810$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	3627.1.it.a	$4$	$0$	$0$	$0$	$0$	$-3$		$1$		$q-\zeta_{30}^{13}q^{4}+(\zeta_{30}^{7}-\zeta_{30}^{9})q^{7}-\zeta_{30}^{8}q^{13}+\cdots$
3627.1.jd.a	$3627$	$1$	3627.jd	403.ar	$30$	$8$	$1$	$1.810$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	3627.1.it.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{30}^{13}q^{4}+(-\zeta_{30}^{7}-\zeta_{30}^{14})q^{7}+\cdots$
3627.1.jh.a	$3627$	$1$	3627.jh	403.av	$30$	$8$	$1$	$1.810$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	3627.1.jh.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q-\zeta_{30}^{4}q^{4}+(-\zeta_{30}+\zeta_{30}^{2})q^{7}+\zeta_{30}^{7}q^{13}+\cdots$
3627.1.jt.a	$3627$	$1$	3627.jt	403.ax	$30$	$8$	$1$	$1.810$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	3627.1.jh.a	$4$	$0$	$0$	$0$	$0$	$-1$		$1$		$q-\zeta_{30}^{14}q^{4}+(-\zeta_{30}^{11}+\zeta_{30}^{12}+\cdots)q^{7}+\cdots$
3627.1.ll.a	$3627$	$1$	3627.ll	403.ba	$60$	$16$	$1$	$1.810$	$\Q(\zeta_{60})$	$D_{60}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	3627.1.ll.a	$4$	$0$	$0$	$0$	$0$	$4$		$1$		$q-\zeta_{60}^{29}q^{4}+(-\zeta_{60}^{11}-\zeta_{60}^{12}+\cdots)q^{7}+\cdots$
3627.1.mf.a	$3627$	$1$	3627.mf	403.bf	$60$	$16$	$1$	$1.810$	$\Q(\zeta_{60})$	$D_{60}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	3627.1.ll.a	$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-\zeta_{60}q^{4}+(-\zeta_{60}^{4}-\zeta_{60}^{23})q^{7}+\cdots$
3627.2.a.a	$3627$	$2$	3627.a	1.a	$1$	$1$	$1$	$28.962$	$\Q$	$_{}$	None	None	✓				1209.2.a.b	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-2q^{7}-q^{11}+q^{13}+4q^{16}+\cdots$
3627.2.a.b	$3627$	$2$	3627.a	1.a	$1$	$1$	$1$	$28.962$	$\Q$	$_{}$	None	None	✓				1209.2.a.a	$1$	$1$	$2$	$0$	$-2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}-2q^{5}+2q^{7}-4q^{10}+\cdots$
3627.2.a.c	$3627$	$2$	3627.a	1.a	$1$	$2$	$2$	$28.962$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				403.2.a.a	$1$	$1$	$-3$	$0$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{2}+3\beta q^{4}+(1-2\beta )q^{5}+\cdots$
3627.2.a.d	$3627$	$2$	3627.a	1.a	$1$	$2$	$2$	$28.962$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				1209.2.a.e	$1$	$1$	$-2$	$0$	$-1$	$1$	$+$	$3$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+(-1-\beta )q^{5}+(1+\beta )q^{7}+\cdots$
3627.2.a.e	$3627$	$2$	3627.a	1.a	$1$	$2$	$2$	$28.962$	$\Q(\sqrt{21}) $	$_{}$	None	None	✓				1209.2.a.g	$1$	$0$	$-2$	$0$	$3$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+(1+\beta )q^{5}+(1+\beta )q^{7}+\cdots$
3627.2.a.f	$3627$	$2$	3627.a	1.a	$1$	$2$	$2$	$28.962$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				1209.2.a.f	$1$	$1$	$-2$	$0$	$2$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(2-2\beta )q^{4}+(1-\beta )q^{5}+\cdots$
3627.2.a.g	$3627$	$2$	3627.a	1.a	$1$	$2$	$2$	$28.962$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				1209.2.a.d	$1$	$1$	$0$	$0$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-\beta q^{5}-2q^{7}-2\beta q^{8}-2q^{10}+\cdots$
3627.2.a.h	$3627$	$2$	3627.a	1.a	$1$	$2$	$2$	$28.962$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				1209.2.a.c	$1$	$1$	$0$	$0$	$-1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-2\beta )q^{2}+3q^{4}-\beta q^{5}+(-2+\beta )q^{7}+\cdots$
3627.2.a.i	$3627$	$2$	3627.a	1.a	$1$	$4$	$4$	$28.962$	$\Q(\sqrt{3}, \sqrt{7})$	$_{}$	None	None	✓	✓			3627.2.a.i	$2$	$1$	$0$	$0$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}-\beta _{2}q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots$
3627.2.a.j	$3627$	$2$	3627.a	1.a	$1$	$5$	$5$	$28.962$	5.5.135076.1	$_{}$	None	None	✓				1209.2.a.h	$1$	$1$	$1$	$0$	$4$	$-10$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(1-\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots$
3627.2.a.k	$3627$	$2$	3627.a	1.a	$1$	$6$	$6$	$28.962$	6.6.41295872.1	$_{}$	None	None	✓				1209.2.a.j	$1$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{4}q^{5}+(\beta _{1}+\beta _{5})q^{7}+\cdots$
3627.2.a.l	$3627$	$2$	3627.a	1.a	$1$	$6$	$6$	$28.962$	6.6.20329488.1	$_{}$	None	None	✓				1209.2.a.i	$1$	$0$	$1$	$0$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1+\beta _{5})q^{5}+\cdots$
3627.2.a.m	$3627$	$2$	3627.a	1.a	$1$	$6$	$6$	$28.962$	6.6.5748973.1	$_{}$	None	None	✓				403.2.a.b	$1$	$0$	$2$	$0$	$9$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{4}q^{2}+(1-\beta _{1}-\beta _{2}+\beta _{3}-\beta _{5})q^{4}+\cdots$
3627.2.a.n	$3627$	$2$	3627.a	1.a	$1$	$7$	$7$	$28.962$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓				403.2.a.c	$1$	$1$	$-2$	$0$	$-11$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{2}+(\beta _{1}+\beta _{4}+\beta _{6})q^{4}+(-2+\cdots)q^{5}+\cdots$
3627.2.a.o	$3627$	$2$	3627.a	1.a	$1$	$8$	$8$	$28.962$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓				1209.2.a.k	$1$	$0$	$-2$	$0$	$-2$	$10$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\beta _{7}q^{5}+\cdots$
3627.2.a.p	$3627$	$2$	3627.a	1.a	$1$	$8$	$8$	$28.962$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓		✓		403.2.a.e	$1$	$1$	$1$	$0$	$-11$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1-\beta _{3}-\beta _{7})q^{5}+\cdots$
3627.2.a.q	$3627$	$2$	3627.a	1.a	$1$	$8$	$8$	$28.962$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓				403.2.a.d	$1$	$0$	$5$	$0$	$15$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+(2+\cdots)q^{5}+\cdots$
3627.2.a.r	$3627$	$2$	3627.a	1.a	$1$	$10$	$10$	$28.962$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	3627.2.a.r	$2$	$1$	$0$	$0$	$0$	$-10$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{3}+\beta _{7})q^{5}+\cdots$
3627.2.a.s	$3627$	$2$	3627.a	1.a	$1$	$11$	$11$	$28.962$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	$_{}$	None	None	✓		✓		1209.2.a.m	$1$	$1$	$-3$	$0$	$-6$	$4$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1-\beta _{3})q^{5}+\cdots$
3627.2.a.t	$3627$	$2$	3627.a	1.a	$1$	$11$	$11$	$28.962$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	$_{}$	None	None	✓		✓		1209.2.a.l	$1$	$0$	$2$	$0$	$-3$	$3$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{5}q^{5}-\beta _{8}q^{7}+\cdots$
3627.2.a.u	$3627$	$2$	3627.a	1.a	$1$	$12$	$12$	$28.962$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	✓	✓		3627.2.a.u	$2$	$1$	$0$	$0$	$0$	$-10$	$+$	$2^{4}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{3}+\beta _{4})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
3627.2.a.v	$3627$	$2$	3627.a	1.a	$1$	$14$	$14$	$28.962$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	3627.2.a.v	$2$	$0$	$0$	$0$	$0$	$2$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}-\beta _{13}q^{7}+\cdots$
3627.2.a.w	$3627$	$2$	3627.a	1.a	$1$	$20$	$20$	$28.962$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	3627.2.a.w	$2$	$0$	$0$	$0$	$0$	$6$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{13}q^{5}+\beta _{11}q^{7}+\cdots$

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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.