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Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Results (1-50 of 59 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	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	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1421.1.f.a	$1421$	$1$	1421.f	29.c	$4$	$2$	$1$	$0.709$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$0$		$1$		$q+(-1-i)q^{2}+iq^{4}-q^{8}-iq^{9}+\cdots$
1421.1.i.a	$1421$	$1$	1421.i	203.i	$6$	$2$	$1$	$0.709$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-203}) $	$\Q(\sqrt{29}) $		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{9}+\zeta_{6}^{2}q^{16}-\zeta_{6}^{2}q^{23}+\cdots$
1421.1.t.a	$1421$	$1$	1421.t	203.m	$12$	$4$	$1$	$0.709$	$\Q(\zeta_{12})$	$D_{4}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$2$	$0$	$0$	$0$		$1$		$q+(-\zeta_{12}-\zeta_{12}^{4})q^{2}+\zeta_{12}^{5}q^{4}+(-1+\cdots)q^{8}+\cdots$
1421.1.cl.a	$1421$	$1$	1421.cl	29.f	$28$	$12$	$1$	$0.709$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q+(\zeta_{28}^{3}-\zeta_{28}^{12})q^{2}+(\zeta_{28}+\zeta_{28}^{6}+\cdots)q^{4}+\cdots$
1421.1.cy.a	$1421$	$1$	1421.cy	203.u	$42$	$12$	$1$	$0.709$	$\Q(\zeta_{21})$	$D_{14}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{42}^{4}+\zeta_{42}^{16})q^{2}+(\zeta_{42}^{8}-\zeta_{42}^{11}+\cdots)q^{4}+\cdots$
1421.1.dj.a	$1421$	$1$	1421.dj	203.v	$42$	$12$	$1$	$0.709$	$\Q(\zeta_{21})$	$D_{7}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$2$	$0$	$0$	$0$		$1$		$q+(\zeta_{42}^{10}-\zeta_{42}^{13})q^{2}+(\zeta_{42}^{2}-\zeta_{42}^{5}+\cdots)q^{4}+\cdots$
1421.1.dr.a	$1421$	$1$	1421.dr	203.w	$84$	$24$	$1$	$0.709$	$\Q(\zeta_{84})$	$D_{28}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$-2$	$0$	$0$	$0$		$1$		$q+(-\zeta_{84}^{5}-\zeta_{84}^{20})q^{2}+(\zeta_{84}^{10}+\zeta_{84}^{25}+\cdots)q^{4}+\cdots$
1421.2.a.a	$1421$	$2$	1421.a	1.a	$1$	$1$	$1$	$11.347$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-2$	$-1$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-q^{3}+2q^{4}-2q^{5}+2q^{6}+\cdots$
1421.2.a.b	$1421$	$2$	1421.a	1.a	$1$	$1$	$1$	$11.347$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-2$	$1$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+q^{3}+2q^{4}+2q^{5}-2q^{6}+\cdots$
1421.2.a.c	$1421$	$2$	1421.a	1.a	$1$	$1$	$1$	$11.347$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-2$	$1$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+q^{3}+2q^{4}+4q^{5}-2q^{6}+\cdots$
1421.2.a.d	$1421$	$2$	1421.a	1.a	$1$	$1$	$1$	$11.347$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-1$	$1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}-q^{5}-q^{6}+3q^{8}+\cdots$
1421.2.a.e	$1421$	$2$	1421.a	1.a	$1$	$1$	$1$	$11.347$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$-3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-2q^{4}-3q^{5}+q^{9}+6q^{11}+\cdots$
1421.2.a.f	$1421$	$2$	1421.a	1.a	$1$	$1$	$1$	$11.347$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{4}+3q^{5}+q^{9}+6q^{11}+\cdots$
1421.2.a.g	$1421$	$2$	1421.a	1.a	$1$	$1$	$1$	$11.347$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$-2$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}-q^{4}-2q^{5}-2q^{6}-3q^{8}+\cdots$
1421.2.a.h	$1421$	$2$	1421.a	1.a	$1$	$1$	$1$	$11.347$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$2$	$-2$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-2q^{3}+2q^{4}-q^{5}-4q^{6}+\cdots$
1421.2.a.i	$1421$	$2$	1421.a	1.a	$1$	$1$	$1$	$11.347$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$2$	$2$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{3}+2q^{4}+q^{5}+4q^{6}+\cdots$
1421.2.a.j	$1421$	$2$	1421.a	1.a	$1$	$2$	$2$	$11.347$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$-2$	$-2$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(-1+\beta )q^{3}+(1-2\beta )q^{4}+\cdots$
1421.2.a.k	$1421$	$2$	1421.a	1.a	$1$	$2$	$2$	$11.347$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$1$	$-2$	$1$	$-3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1-\beta )q^{3}-q^{4}+(-1-\beta )q^{5}+\cdots$
1421.2.a.l	$1421$	$2$	1421.a	1.a	$1$	$2$	$2$	$11.347$	$\Q(\sqrt{7}) $	$_{}$	None	None	✓	$2$	$1$	$2$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta q^{3}-q^{4}+\beta q^{5}-\beta q^{6}-3q^{8}+\cdots$
1421.2.a.m	$1421$	$2$	1421.a	1.a	$1$	$2$	$2$	$11.347$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$4$	$-2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(-1+\beta )q^{3}+2q^{4}-2\beta q^{5}+\cdots$
1421.2.a.n	$1421$	$2$	1421.a	1.a	$1$	$3$	$3$	$11.347$	3.3.148.1	$_{}$	None	None	✓	$1$	$0$	$-1$	$3$	$5$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots$
1421.2.a.o	$1421$	$2$	1421.a	1.a	$1$	$4$	$4$	$11.347$	$\Q(\sqrt{2}, \sqrt{7})$	$_{}$	None	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-2q^{4}+\beta _{2}q^{5}+(1+\beta _{3})q^{9}+\cdots$
1421.2.a.p	$1421$	$2$	1421.a	1.a	$1$	$4$	$4$	$11.347$	$\Q(\zeta_{24})^+$	$_{}$	None	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+\beta _{3}q^{3}+q^{4}-\beta _{3}q^{5}+(-\beta _{1}+\cdots)q^{6}+\cdots$
1421.2.a.q	$1421$	$2$	1421.a	1.a	$1$	$5$	$5$	$11.347$	5.5.2626356.1	$_{}$	None	None	✓	$1$	$0$	$2$	$2$	$-5$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{4}q^{3}+(2+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
1421.2.a.r	$1421$	$2$	1421.a	1.a	$1$	$8$	$8$	$11.347$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-2$	$-5$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1+\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots$
1421.2.a.s	$1421$	$2$	1421.a	1.a	$1$	$8$	$8$	$11.347$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$-2$	$5$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1-\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots$
1421.2.a.t	$1421$	$2$	1421.a	1.a	$1$	$8$	$8$	$11.347$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{5}q^{3}+(1+\beta _{2})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots$
1421.2.a.u	$1421$	$2$	1421.a	1.a	$1$	$8$	$8$	$11.347$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{5}q^{3}+(1+\beta _{2})q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots$
1421.2.a.v	$1421$	$2$	1421.a	1.a	$1$	$10$	$10$	$11.347$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{4}q^{2}-\beta _{1}q^{3}+(2-\beta _{7})q^{4}+\beta _{6}q^{5}+\cdots$
1421.2.a.w	$1421$	$2$	1421.a	1.a	$1$	$20$	$20$	$11.347$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None	✓	$2$	$0$	$4$	$0$	$0$	$0$	$-$	$2^{6}$	$\mathrm{SU}(2)$	$q+\beta _{6}q^{2}-\beta _{1}q^{3}+(2+\beta _{9})q^{4}+\beta _{12}q^{5}+\cdots$
1421.2.b.a	$1421$	$2$	1421.b	29.b	$2$	$2$	$2$	$11.347$	$\Q(\sqrt{-7}) $	$_{}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q-\beta q^{2}-5q^{4}+3\beta q^{8}+3q^{9}-2\beta q^{11}+\cdots$
1421.2.b.b	$1421$	$2$	1421.b	29.b	$2$	$2$	$2$	$11.347$	$\Q(\sqrt{-5}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$6$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}+\beta q^{3}-3q^{4}+3q^{5}-5q^{6}+\cdots$
1421.2.b.c	$1421$	$2$	1421.b	29.b	$2$	$2$	$2$	$11.347$	$\Q(\sqrt{-5}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{3}+2q^{4}-2q^{5}-2q^{9}-2\beta q^{11}+\cdots$
1421.2.b.d	$1421$	$2$	1421.b	29.b	$2$	$4$	$4$	$11.347$	4.0.7168.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{1}q^{3}+(-1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
1421.2.b.e	$1421$	$2$	1421.b	29.b	$2$	$4$	$4$	$11.347$	4.0.7168.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{1}q^{3}+(-1+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$
1421.2.b.f	$1421$	$2$	1421.b	29.b	$2$	$4$	$4$	$11.347$	4.0.94192.1	$_{}$	$\Q(\sqrt{-203}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{3}+2q^{4}+(-3+\beta _{2})q^{9}+2\beta _{1}q^{12}+\cdots$
1421.2.b.g	$1421$	$2$	1421.b	29.b	$2$	$6$	$6$	$11.347$	6.0.16516096.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$-8$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{2}-\beta _{1}q^{3}+(-1+\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots$
1421.2.b.h	$1421$	$2$	1421.b	29.b	$2$	$6$	$6$	$11.347$	6.0.25809920.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$8$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{5}q^{3}+(-1+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots$
1421.2.b.i	$1421$	$2$	1421.b	29.b	$2$	$12$	$12$	$11.347$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{9}q^{2}-\beta _{8}q^{3}+(-1-\beta _{5})q^{4}-\beta _{2}q^{5}+\cdots$
1421.2.b.j	$1421$	$2$	1421.b	29.b	$2$	$18$	$18$	$11.347$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{11}q^{3}+(-1+\beta _{2})q^{4}+\cdots$
1421.2.b.k	$1421$	$2$	1421.b	29.b	$2$	$18$	$18$	$11.347$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{11}q^{3}+(-1+\beta _{2})q^{4}+\cdots$
1421.2.b.l	$1421$	$2$	1421.b	29.b	$2$	$20$	$20$	$11.347$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{16}q^{2}+\beta _{13}q^{3}+(-1-\beta _{8})q^{4}+\cdots$
1421.4.a.a	$1421$	$4$	1421.a	1.a	$1$	$1$	$1$	$83.842$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$4$	$-14$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+4q^{3}-7q^{4}-14q^{5}+4q^{6}+\cdots$
1421.4.a.b	$1421$	$4$	1421.a	1.a	$1$	$1$	$1$	$83.842$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$4$	$-8$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+4q^{2}-8q^{3}+8q^{4}-2q^{5}-2^{5}q^{6}+\cdots$
1421.4.a.c	$1421$	$4$	1421.a	1.a	$1$	$2$	$2$	$83.842$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$-2$	$10$	$10$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(5+3\beta )q^{3}+(-5-2\beta )q^{4}+\cdots$
1421.4.a.d	$1421$	$4$	1421.a	1.a	$1$	$2$	$2$	$83.842$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$2$	$1$	$6$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{2}+6\beta q^{3}+q^{4}-8\beta q^{5}+18\beta q^{6}+\cdots$
1421.4.a.e	$1421$	$4$	1421.a	1.a	$1$	$5$	$5$	$83.842$	5.5.13458092.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-8$	$-10$	$0$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{3}+\beta _{4})q^{3}+\cdots$
1421.4.a.f	$1421$	$4$	1421.a	1.a	$1$	$7$	$7$	$83.842$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-2$	$2$	$24$	$0$	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1-\beta _{1}-\beta _{3})q^{3}+(1+\beta _{1}+\cdots)q^{4}+\cdots$
1421.4.a.g	$1421$	$4$	1421.a	1.a	$1$	$10$	$10$	$83.842$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$-4$	$8$	$24$	$0$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{6})q^{3}+(5+\beta _{2})q^{4}+\cdots$
1421.4.a.h	$1421$	$4$	1421.a	1.a	$1$	$11$	$11$	$83.842$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$2$	$-4$	$-16$	$0$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{3}q^{3}+(5+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$

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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.