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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 104 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
203.1.c.a	$203$	$1$	203.c	203.c	$2$	$1$	$1$	$0.101$	$\Q$	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-203}) $	$\Q(\sqrt{29}) $	✓	$4$	$0$	$0$	$0$	$0$	$-1$		$1$		$q+q^{4}-q^{7}-q^{9}+q^{16}-2q^{23}+q^{25}+\cdots$
203.1.n.a	$203$	$1$	203.n	203.n	$14$	$6$	$1$	$0.101$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$-1$		$1$		$q+(-\zeta_{14}^{3}+\zeta_{14}^{6})q^{2}+(\zeta_{14}^{2}-\zeta_{14}^{5}+\cdots)q^{4}+\cdots$
203.1.o.a	$203$	$1$	203.o	203.o	$14$	$6$	$1$	$0.101$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$1$		$1$		$q+(\zeta_{14}^{5}+\zeta_{14}^{6})q^{2}+(-\zeta_{14}^{3}-\zeta_{14}^{4}+\cdots)q^{4}+\cdots$
203.2.a.a	$203$	$2$	203.a	1.a	$1$	$1$	$1$	$1.621$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-2$	$-1$	$-4$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-q^{3}+2q^{4}-4q^{5}+2q^{6}+\cdots$
203.2.a.b	$203$	$2$	203.a	1.a	$1$	$1$	$1$	$1.621$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-1$	$-1$	$1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}+q^{7}+\cdots$
203.2.a.c	$203$	$2$	203.a	1.a	$1$	$1$	$1$	$1.621$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$2$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}-q^{4}+2q^{5}+2q^{6}+q^{7}+\cdots$
203.2.a.d	$203$	$2$	203.a	1.a	$1$	$2$	$2$	$1.621$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$0$	$-2$	$-1$	$3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta q^{3}-q^{4}+(2-\beta )q^{5}+\beta q^{6}+\cdots$
203.2.a.e	$203$	$2$	203.a	1.a	$1$	$2$	$2$	$1.621$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$4$	$2$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(1+\beta )q^{3}+2q^{4}-2\beta q^{5}+\cdots$
203.2.a.f	$203$	$2$	203.a	1.a	$1$	$3$	$3$	$1.621$	3.3.148.1	$_{}$	None	None	✓	$1$	$1$	$-1$	$-3$	$-5$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots$
203.2.a.g	$203$	$2$	203.a	1.a	$1$	$5$	$5$	$1.621$	5.5.2626356.1	$_{}$	None	None	✓	$1$	$0$	$2$	$-2$	$5$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{4}q^{3}+(2+\beta _{2})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots$
203.2.b.a	$203$	$2$	203.b	29.b	$2$	$2$	$2$	$1.621$	$\Q(\sqrt{-5}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$4$	$-2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}+2q^{4}+2q^{5}-q^{7}-2q^{9}+\cdots$
203.2.b.b	$203$	$2$	203.b	29.b	$2$	$6$	$6$	$1.621$	6.0.16516096.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$8$	$6$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{2}+\beta _{1}q^{3}+(-1+\beta _{3})q^{4}+(1+\cdots)q^{5}+\cdots$
203.2.b.c	$203$	$2$	203.b	29.b	$2$	$6$	$6$	$1.621$	6.0.25809920.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$-8$	$-6$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{5}q^{3}+(-1+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots$
203.2.e.a	$203$	$2$	203.e	7.c	$3$	$2$	$1$	$1.621$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$1$	$-2$	$-2$	$-1$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-2\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots$
203.2.e.b	$203$	$2$	203.e	7.c	$3$	$2$	$1$	$1.621$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$3$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+3\zeta_{6}q^{5}+\cdots$
203.2.e.c	$203$	$2$	203.e	7.c	$3$	$16$	$8$	$1.621$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$3$	$2$	$1$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}-\beta _{5})q^{2}+\beta _{12}q^{3}+(-1-\beta _{3}+\cdots)q^{4}+\cdots$
203.2.e.d	$203$	$2$	203.e	7.c	$3$	$16$	$8$	$1.621$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$2$	$0$	$2$	$-5$	$-2$	$1$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}-\beta _{4})q^{2}+(\beta _{3}+\beta _{8}-\beta _{10}+\cdots)q^{3}+\cdots$
203.2.g.a	$203$	$2$	203.g	203.g	$4$	$4$	$2$	$1.621$	$\Q(i, \sqrt{7})$	$_{}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{4}]$	$q+(-1+\beta _{1}-\beta _{2})q^{2}+(1-\beta _{1}+2\beta _{2}+\cdots)q^{4}+\cdots$
203.2.g.b	$203$	$2$	203.g	203.g	$4$	$32$	$16$	$1.621$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{4}]$
203.2.j.a	$203$	$2$	203.j	203.j	$6$	$36$	$18$	$1.621$		$_{}$	None	None		$4$	$0$	$0$	$0$	$2$	$-8$			$\mathrm{SU}(2)[C_{6}]$
203.2.k.a	$203$	$2$	203.k	29.d	$7$	$42$	$7$	$1.621$		$_{}$	None	None		$2$	$0$	$-1$	$2$	$-5$	$7$			$\mathrm{SU}(2)[C_{7}]$
203.2.k.b	$203$	$2$	203.k	29.d	$7$	$54$	$9$	$1.621$		$_{}$	None	None		$2$	$0$	$-3$	$-2$	$-3$	$-9$			$\mathrm{SU}(2)[C_{7}]$
203.2.l.a	$203$	$2$	203.l	203.l	$12$	$4$	$1$	$1.621$	$\Q(\zeta_{12})$	$_{}$	None	None		$4$	$0$	$2$	$6$	$0$	$-10$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(-\zeta_{12}+\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(1-\zeta_{12}+\cdots)q^{3}+\cdots$
203.2.l.b	$203$	$2$	203.l	203.l	$12$	$68$	$17$	$1.621$		$_{}$	None	None		$4$	$0$	$-6$	$-12$	$0$	$2$			$\mathrm{SU}(2)[C_{12}]$
203.2.p.a	$203$	$2$	203.p	29.e	$14$	$36$	$6$	$1.621$		$_{}$	None	None		$2$	$0$	$0$	$0$	$-1$	$-6$			$\mathrm{SU}(2)[C_{14}]$
203.2.p.b	$203$	$2$	203.p	29.e	$14$	$48$	$8$	$1.621$		$_{}$	None	None		$2$	$0$	$0$	$0$	$-3$	$8$			$\mathrm{SU}(2)[C_{14}]$
203.2.q.a	$203$	$2$	203.q	203.q	$21$	$216$	$18$	$1.621$		$_{}$	None	None		$4$	$0$	$-7$	$-5$	$-9$	$-14$			$\mathrm{SU}(2)[C_{21}]$
203.2.r.a	$203$	$2$	203.r	203.r	$28$	$12$	$1$	$1.621$	$\Q(\zeta_{28})$	$_{}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-6$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{28}]$	$q+(-\zeta_{28}-\zeta_{28}^{2}+\zeta_{28}^{3}-\zeta_{28}^{6}+\cdots)q^{2}+\cdots$
203.2.r.b	$203$	$2$	203.r	203.r	$28$	$12$	$1$	$1.621$	$\Q(\zeta_{28})$	$_{}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$8$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{28}]$	$q+(\zeta_{28}^{2}-\zeta_{28}^{5}+\zeta_{28}^{6}-\zeta_{28}^{8}-\zeta_{28}^{9}+\cdots)q^{2}+\cdots$
203.2.r.c	$203$	$2$	203.r	203.r	$28$	$192$	$16$	$1.621$		$_{}$	None	None		$4$	$0$	$-28$	$0$	$0$	$-10$			$\mathrm{SU}(2)[C_{28}]$
203.2.t.a	$203$	$2$	203.t	203.t	$42$	$216$	$18$	$1.621$		$_{}$	None	None		$4$	$0$	$-7$	$-7$	$-9$	$-6$			$\mathrm{SU}(2)[C_{42}]$
203.2.x.a	$203$	$2$	203.x	203.x	$84$	$432$	$18$	$1.621$		$_{}$	None	None		$4$	$0$	$-10$	$-36$	$-42$	$-20$			$\mathrm{SU}(2)[C_{84}]$
203.3.c.a	$203$	$3$	203.c	203.c	$2$	$2$	$2$	$5.531$	$\Q(\sqrt{-7}) $	$_{}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$14$		$2$	$\mathrm{U}(1)[D_{2}]$	$q-\beta q^{2}-3q^{4}+7q^{7}-\beta q^{8}-9q^{9}+\cdots$
203.3.c.b	$203$	$3$	203.c	203.c	$2$	$2$	$2$	$5.531$	$\Q(\sqrt{29}) $	$_{}$	$\Q(\sqrt{-203}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$-14$		$2$	$\mathrm{U}(1)[D_{2}]$	$q-\beta q^{3}+4q^{4}-7q^{7}+20q^{9}-4\beta q^{12}+\cdots$
203.3.c.c	$203$	$3$	203.c	203.c	$2$	$2$	$2$	$5.531$	$\Q(\sqrt{7}) $	$_{}$	$\Q(\sqrt{-203}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$14$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{3}+4q^{4}+7q^{7}-2q^{9}+4\beta q^{12}+\cdots$
203.3.c.d	$203$	$3$	203.c	203.c	$2$	$32$	$32$	$5.531$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{2}]$
203.3.d.a	$203$	$3$	203.d	7.b	$2$	$36$	$36$	$5.531$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$4$			$\mathrm{SU}(2)[C_{2}]$
203.3.f.a	$203$	$3$	203.f	29.c	$4$	$60$	$30$	$5.531$		$_{}$	None	None		$2$	$0$	$-6$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
203.3.h.a	$203$	$3$	203.h	7.d	$6$	$76$	$38$	$5.531$		$_{}$	None	None		$2$	$0$	$0$	$-6$	$-6$	$4$			$\mathrm{SU}(2)[C_{6}]$
203.3.i.a	$203$	$3$	203.i	203.i	$6$	$76$	$38$	$5.531$		$_{}$	None	None		$4$	$0$	$0$	$0$	$-6$	$-12$			$\mathrm{SU}(2)[C_{6}]$
203.3.m.a	$203$	$3$	203.m	203.m	$12$	$152$	$38$	$5.531$		$_{}$	None	None		$4$	$0$	$-4$	$-2$	$0$	$-8$			$\mathrm{SU}(2)[C_{12}]$
203.3.n.a	$203$	$3$	203.n	203.n	$14$	$6$	$1$	$5.531$	$\Q(\zeta_{14})$	$_{}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$3$	$0$	$0$	$7$		$1$	$\mathrm{U}(1)[D_{14}]$	$q+(1+2\zeta_{14}^{2}+\zeta_{14}^{4})q^{2}+(-3+3\zeta_{14}+\cdots)q^{4}+\cdots$
203.3.n.b	$203$	$3$	203.n	203.n	$14$	$6$	$1$	$5.531$	$\Q(\zeta_{14})$	$_{}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$3$	$0$	$0$	$7$		$1$	$\mathrm{U}(1)[D_{14}]$	$q+(2-3\zeta_{14}+\zeta_{14}^{2}-3\zeta_{14}^{3}+2\zeta_{14}^{4}+\cdots)q^{2}+\cdots$
203.3.n.c	$203$	$3$	203.n	203.n	$14$	$216$	$36$	$5.531$		$_{}$	None	None		$4$	$0$	$-14$	$0$	$0$	$-11$			$\mathrm{SU}(2)[C_{14}]$
203.3.o.a	$203$	$3$	203.o	203.o	$14$	$6$	$1$	$5.531$	$\Q(\zeta_{14})$	$_{}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-7$	$0$	$0$	$-7$		$1$	$\mathrm{U}(1)[D_{14}]$	$q+(-3+2\zeta_{14}-\zeta_{14}^{2}+4\zeta_{14}^{3}-2\zeta_{14}^{4}+\cdots)q^{2}+\cdots$
203.3.o.b	$203$	$3$	203.o	203.o	$14$	$6$	$1$	$5.531$	$\Q(\zeta_{14})$	$_{}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$7$	$0$	$0$	$-7$		$1$	$\mathrm{U}(1)[D_{14}]$	$q+(\zeta_{14}-2\zeta_{14}^{2}+2\zeta_{14}^{3}-\zeta_{14}^{4}+\cdots)q^{2}+\cdots$
203.3.o.c	$203$	$3$	203.o	203.o	$14$	$216$	$36$	$5.531$		$_{}$	None	None		$4$	$0$	$-14$	$0$	$0$	$1$			$\mathrm{SU}(2)[C_{14}]$
203.3.s.a	$203$	$3$	203.s	29.f	$28$	$180$	$15$	$5.531$		$_{}$	None	None		$2$	$0$	$-4$	$-14$	$0$	$0$			$\mathrm{SU}(2)[C_{28}]$
203.3.s.b	$203$	$3$	203.s	29.f	$28$	$180$	$15$	$5.531$		$_{}$	None	None		$2$	$0$	$10$	$14$	$0$	$0$			$\mathrm{SU}(2)[C_{28}]$
203.3.u.a	$203$	$3$	203.u	203.u	$42$	$456$	$38$	$5.531$		$_{}$	None	None		$4$	$0$	$-7$	$-21$	$-15$	$-2$			$\mathrm{SU}(2)[C_{42}]$

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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.