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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 94 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	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	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
43.2.a.a	$43$	$2$	43.a	1.a	$1$	$1$	$1$	$0.343$	$\Q$	None	✓	$1$	$1$	$-2$	$-2$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-2q^{3}+2q^{4}-4q^{5}+4q^{6}+\cdots$
43.2.a.b	$43$	$2$	43.a	1.a	$1$	$2$	$2$	$0.343$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$0$	$0$	$4$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-\beta q^{3}+(2-\beta )q^{5}-2q^{6}+(-2+\cdots)q^{7}+\cdots$
43.2.c.a	$43$	$2$	43.c	43.c	$3$	$2$	$1$	$0.343$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$2$	$-1$	$1$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(-1+\zeta_{6})q^{3}-q^{4}+(1-\zeta_{6})q^{5}+\cdots$
43.2.c.b	$43$	$2$	43.c	43.c	$3$	$4$	$2$	$0.343$	$\Q(\sqrt{-3}, \sqrt{5})$	None		$2$	$0$	$-6$	$3$	$2$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2-\beta _{2})q^{2}+(1+\beta _{1}+\beta _{3})q^{3}+\cdots$
43.2.e.a	$43$	$2$	43.e	43.e	$7$	$6$	$1$	$0.343$	$\Q(\zeta_{14})$	None		$2$	$0$	$-5$	$2$	$-3$	$0$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(-\zeta_{14}+\zeta_{14}^{2}-\zeta_{14}^{3}+\zeta_{14}^{4}+\cdots)q^{2}+\cdots$
43.2.e.b	$43$	$2$	43.e	43.e	$7$	$6$	$1$	$0.343$	$\Q(\zeta_{14})$	None		$2$	$0$	$3$	$-3$	$2$	$-16$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(\zeta_{14}+\zeta_{14}^{3}+\zeta_{14}^{5})q^{2}+(-1+\zeta_{14}+\cdots)q^{3}+\cdots$
43.2.g.a	$43$	$2$	43.g	43.g	$21$	$36$	$3$	$0.343$		None		$2$	$0$	$-10$	$-16$	$-17$	$6$			$\mathrm{SU}(2)[C_{21}]$
43.3.b.a	$43$	$3$	43.b	43.b	$2$	$1$	$1$	$1.172$	$\Q$	$\Q(\sqrt{-43}) $	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+4q^{4}+9q^{9}-21q^{11}-17q^{13}+\cdots$
43.3.b.b	$43$	$3$	43.b	43.b	$2$	$6$	$6$	$1.172$	$\mathbb{Q}[x]/(x^{6} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{5}q^{3}+(-2+\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots$
43.3.d.a	$43$	$3$	43.d	43.d	$6$	$12$	$6$	$1.172$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$0$	$0$	$-3$	$9$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{1}-\beta _{2})q^{2}+\beta _{3}q^{3}+(-2+\beta _{1}+\cdots)q^{4}+\cdots$
43.3.f.a	$43$	$3$	43.f	43.f	$14$	$42$	$7$	$1.172$		None		$2$	$0$	$-7$	$-7$	$-7$	$0$			$\mathrm{SU}(2)[C_{14}]$
43.3.h.a	$43$	$3$	43.h	43.h	$42$	$72$	$6$	$1.172$		None		$2$	$0$	$-14$	$-14$	$-11$	$-30$			$\mathrm{SU}(2)[C_{42}]$
43.4.a.a	$43$	$4$	43.a	1.a	$1$	$4$	$4$	$2.537$	4.4.45868.1	None	✓	$1$	$1$	$-4$	$-11$	$-27$	$-20$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{3})q^{2}+(-3+\beta _{2}-\beta _{3})q^{3}+\cdots$
43.4.a.b	$43$	$4$	43.a	1.a	$1$	$6$	$6$	$2.537$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	$1$	$0$	$6$	$7$	$43$	$8$	$+$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1-\beta _{3})q^{3}+(4-\beta _{1}+\cdots)q^{4}+\cdots$
43.4.c.a	$43$	$4$	43.c	43.c	$3$	$20$	$10$	$2.537$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$-2$	$-5$	$-19$	$-51$		$2^{6}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{5}q^{2}+(-\beta _{4}-\beta _{6})q^{3}+(4+\beta _{2}+\cdots)q^{4}+\cdots$
43.4.e.a	$43$	$4$	43.e	43.e	$7$	$60$	$10$	$2.537$		None		$2$	$0$	$-9$	$-3$	$-23$	$96$			$\mathrm{SU}(2)[C_{7}]$
43.4.g.a	$43$	$4$	43.g	43.g	$21$	$120$	$10$	$2.537$		None		$2$	$0$	$-12$	$-9$	$5$	$-54$			$\mathrm{SU}(2)[C_{21}]$
43.5.b.a	$43$	$5$	43.b	43.b	$2$	$1$	$1$	$4.445$	$\Q$	$\Q(\sqrt{-43}) $	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{4}q^{4}+3^{4}q^{9}+199q^{11}-7^{2}q^{13}+\cdots$
43.5.b.b	$43$	$5$	43.b	43.b	$2$	$12$	$12$	$4.445$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{4}q^{3}+(-8+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
43.5.d.a	$43$	$5$	43.d	43.d	$6$	$28$	$14$	$4.445$		None		$2$	$0$	$0$	$6$	$-3$	$129$			$\mathrm{SU}(2)[C_{6}]$
43.5.f.a	$43$	$5$	43.f	43.f	$14$	$78$	$13$	$4.445$		None		$2$	$0$	$-7$	$-7$	$-7$	$0$			$\mathrm{SU}(2)[C_{14}]$
43.5.h.a	$43$	$5$	43.h	43.h	$42$	$168$	$14$	$4.445$		None		$2$	$0$	$-14$	$-20$	$-11$	$-150$			$\mathrm{SU}(2)[C_{42}]$
43.6.a.a	$43$	$6$	43.a	1.a	$1$	$8$	$8$	$6.897$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$-12$	$-26$	$-212$	$-136$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-2+\beta _{1})q^{2}+(-2-\beta _{1}+\beta _{4}-\beta _{7})q^{3}+\cdots$
43.6.a.b	$43$	$6$	43.a	1.a	$1$	$10$	$10$	$6.897$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$8$	$28$	$138$	$60$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(3+\beta _{6})q^{3}+(21-\beta _{1}+\cdots)q^{4}+\cdots$
43.6.c.a	$43$	$6$	43.c	43.c	$3$	$34$	$17$	$6.897$		None		$2$	$0$	$-14$	$-14$	$71$	$225$			$\mathrm{SU}(2)[C_{3}]$
43.6.e.a	$43$	$6$	43.e	43.e	$7$	$108$	$18$	$6.897$		None		$2$	$0$	$-3$	$-9$	$67$	$-624$			$\mathrm{SU}(2)[C_{7}]$
43.6.g.a	$43$	$6$	43.g	43.g	$21$	$204$	$17$	$6.897$		None		$2$	$0$	$0$	$0$	$-85$	$454$			$\mathrm{SU}(2)[C_{21}]$
43.7.b.a	$43$	$7$	43.b	43.b	$2$	$1$	$1$	$9.892$	$\Q$	$\Q(\sqrt{-43}) $	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{6}q^{4}+3^{6}q^{9}-1638q^{11}+3706q^{13}+\cdots$
43.7.b.b	$43$	$7$	43.b	43.b	$2$	$20$	$20$	$9.892$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{15}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-40+\beta _{2})q^{4}+\cdots$
43.7.d.a	$43$	$7$	43.d	43.d	$6$	$42$	$21$	$9.892$		None		$2$	$0$	$0$	$-3$	$-3$	$-147$			$\mathrm{SU}(2)[C_{6}]$
43.7.f.a	$43$	$7$	43.f	43.f	$14$	$126$	$21$	$9.892$		None		$2$	$0$	$-7$	$-7$	$-7$	$0$			$\mathrm{SU}(2)[C_{14}]$
43.7.h.a	$43$	$7$	43.h	43.h	$42$	$252$	$21$	$9.892$		None		$2$	$0$	$-14$	$-11$	$-11$	$126$			$\mathrm{SU}(2)[C_{42}]$
43.8.a.a	$43$	$8$	43.a	1.a	$1$	$11$	$11$	$13.433$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	$1$	$1$	$-24$	$-68$	$-752$	$-12$	$-$	$2^{6}\cdot 7$	$\mathrm{SU}(2)$	$q+(-2-\beta _{1})q^{2}+(-6-\beta _{5})q^{3}+(54+\cdots)q^{4}+\cdots$
43.8.a.b	$43$	$8$	43.a	1.a	$1$	$13$	$13$	$13.433$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓	$1$	$0$	$16$	$94$	$998$	$1360$	$+$	$2^{6}\cdot 3$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{2}+(7+\beta _{3})q^{3}+(71+2\beta _{1}+\cdots)q^{4}+\cdots$
43.8.c.a	$43$	$8$	43.c	43.c	$3$	$50$	$25$	$13.433$		None		$2$	$0$	$26$	$-2$	$-249$	$-687$			$\mathrm{SU}(2)[C_{3}]$
43.8.e.a	$43$	$8$	43.e	43.e	$7$	$144$	$24$	$13.433$		None		$2$	$0$	$1$	$-33$	$-253$	$3440$			$\mathrm{SU}(2)[C_{7}]$
43.8.g.a	$43$	$8$	43.g	43.g	$21$	$300$	$25$	$13.433$		None		$2$	$0$	$-40$	$-12$	$235$	$-4122$			$\mathrm{SU}(2)[C_{21}]$
43.9.b.a	$43$	$9$	43.b	43.b	$2$	$1$	$1$	$17.517$	$\Q$	$\Q(\sqrt{-43}) $	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{8}q^{4}+3^{8}q^{9}+10319q^{11}-54721q^{13}+\cdots$
43.9.b.b	$43$	$9$	43.b	43.b	$2$	$28$	$28$	$17.517$		None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
43.9.d.a	$43$	$9$	43.d	43.d	$6$	$56$	$28$	$17.517$		None		$2$	$0$	$0$	$-84$	$-3$	$-5031$			$\mathrm{SU}(2)[C_{6}]$
43.9.f.a	$43$	$9$	43.f	43.f	$14$	$174$	$29$	$17.517$		None		$2$	$0$	$-7$	$-7$	$-7$	$0$			$\mathrm{SU}(2)[C_{14}]$
43.9.h.a	$43$	$9$	43.h	43.h	$42$	$336$	$28$	$17.517$		None		$2$	$0$	$-14$	$70$	$-11$	$5010$			$\mathrm{SU}(2)[C_{42}]$
43.10.a.a	$43$	$10$	43.a	1.a	$1$	$15$	$15$	$22.147$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓	$1$	$1$	$-32$	$-317$	$-4717$	$-9680$	$+$	$2^{10}\cdot 3^{2}$	$\mathrm{SU}(2)$	$q+(-2-\beta _{1})q^{2}+(-21-\beta _{2})q^{3}+(6^{3}+\cdots)q^{4}+\cdots$
43.10.a.b	$43$	$10$	43.a	1.a	$1$	$17$	$17$	$22.147$	$\mathbb{Q}[x]/(x^{17} - \cdots)$	None	✓	$1$	$0$	$48$	$169$	$4033$	$-76$	$-$	$2^{13}\cdot 3^{5}$	$\mathrm{SU}(2)$	$q+(3-\beta _{1})q^{2}+(10-\beta _{3})q^{3}+(267-4\beta _{1}+\cdots)q^{4}+\cdots$
43.10.c.a	$43$	$10$	43.c	43.c	$3$	$64$	$32$	$22.147$		None		$2$	$0$	$-70$	$307$	$681$	$957$			$\mathrm{SU}(2)[C_{3}]$
43.10.e.a	$43$	$10$	43.e	43.e	$7$	$192$	$32$	$22.147$		None		$2$	$0$	$-23$	$141$	$677$	$-23872$			$\mathrm{SU}(2)[C_{7}]$
43.10.g.a	$43$	$10$	43.g	43.g	$21$	$384$	$32$	$22.147$		None		$2$	$0$	$56$	$-321$	$-695$	$32650$			$\mathrm{SU}(2)[C_{21}]$
43.11.b.a	$43$	$11$	43.b	43.b	$2$	$1$	$1$	$27.320$	$\Q$	$\Q(\sqrt{-43}) $	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{10}q^{4}+3^{10}q^{9}-18501q^{11}+\cdots$
43.11.b.b	$43$	$11$	43.b	43.b	$2$	$34$	$34$	$27.320$		None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
43.11.d.a	$43$	$11$	43.d	43.d	$6$	$72$	$36$	$27.320$		None		$2$	$0$	$0$	$-246$	$-3$	$31377$			$\mathrm{SU}(2)[C_{6}]$

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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.