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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 138 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	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	CM	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
434.2.a.a	$434$	$2$	434.a	1.a	$1$	$1$	$1$	$3.466$	$\Q$	None	✓	✓	✓	✓	434.2.a.a	$1$	$1$	$-1$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{7}-q^{8}-3q^{9}-2q^{11}+\cdots$
434.2.a.b	$434$	$2$	434.a	1.a	$1$	$1$	$1$	$3.466$	$\Q$	None	✓	✓			434.2.a.b	$1$	$0$	$1$	$-3$	$-3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-3q^{3}+q^{4}-3q^{5}-3q^{6}-q^{7}+\cdots$
434.2.a.c	$434$	$2$	434.a	1.a	$1$	$1$	$1$	$3.466$	$\Q$	None	✓	✓	✓	✓	434.2.a.c	$1$	$1$	$1$	$-2$	$-2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}-2q^{5}-2q^{6}+q^{7}+\cdots$
434.2.a.d	$434$	$2$	434.a	1.a	$1$	$1$	$1$	$3.466$	$\Q$	None	✓	✓			434.2.a.d	$1$	$0$	$1$	$1$	$3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+3q^{5}+q^{6}+q^{7}+\cdots$
434.2.a.e	$434$	$2$	434.a	1.a	$1$	$1$	$1$	$3.466$	$\Q$	None	✓	✓			434.2.a.e	$1$	$0$	$1$	$2$	$2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}+q^{4}+2q^{5}+2q^{6}-q^{7}+\cdots$
434.2.a.f	$434$	$2$	434.a	1.a	$1$	$2$	$2$	$3.466$	$\Q(\sqrt{2}) $	None	✓	✓	✓	✓	434.2.a.f	$1$	$0$	$-2$	$2$	$-2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1+\beta )q^{3}+q^{4}+(-1+2\beta )q^{5}+\cdots$
434.2.a.g	$434$	$2$	434.a	1.a	$1$	$2$	$2$	$3.466$	$\Q(\sqrt{17}) $	None	✓	✓	✓		434.2.a.g	$1$	$0$	$2$	$1$	$3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta q^{3}+q^{4}+(2-\beta )q^{5}+\beta q^{6}+\cdots$
434.2.a.h	$434$	$2$	434.a	1.a	$1$	$3$	$3$	$3.466$	3.3.568.1	None	✓	✓	✓	✓	434.2.a.h	$1$	$0$	$-3$	$-2$	$-2$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-1-\beta _{2})q^{5}+\cdots$
434.2.a.i	$434$	$2$	434.a	1.a	$1$	$3$	$3$	$3.466$	3.3.568.1	None	✓	✓	✓		434.2.a.i	$1$	$0$	$3$	$1$	$-1$	$3$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{2}q^{3}+q^{4}+\beta _{2}q^{5}-\beta _{2}q^{6}+\cdots$
434.2.d.a	$434$	$2$	434.d	217.d	$2$	$2$	$2$	$3.466$	$\Q(\sqrt{-3}) $	None		✓			434.2.d.a	$2$	$0$	$-2$	$-4$	$0$	$4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}-2q^{3}+q^{4}+2q^{6}+(2+\zeta_{6})q^{7}+\cdots$
434.2.d.b	$434$	$2$	434.d	217.d	$2$	$2$	$2$	$3.466$	$\Q(\sqrt{-3}) $	None		✓			434.2.d.a	$2$	$0$	$-2$	$4$	$0$	$4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+2q^{3}+q^{4}-2q^{6}+(2+\zeta_{6})q^{7}+\cdots$
434.2.d.c	$434$	$2$	434.d	217.d	$2$	$2$	$2$	$3.466$	$\Q(\sqrt{-3}) $	None		✓			434.2.d.c	$2$	$0$	$2$	$-2$	$0$	$4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}-q^{3}+q^{4}+\zeta_{6}q^{5}-q^{6}+(2+\cdots)q^{7}+\cdots$
434.2.d.d	$434$	$2$	434.d	217.d	$2$	$2$	$2$	$3.466$	$\Q(\sqrt{-3}) $	None		✓			434.2.d.c	$2$	$0$	$2$	$2$	$0$	$4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{3}+q^{4}+\zeta_{6}q^{5}+q^{6}+(2+\cdots)q^{7}+\cdots$
434.2.d.e	$434$	$2$	434.d	217.d	$2$	$8$	$8$	$3.466$	8.0.$\cdots$.2	None		✓			434.2.d.e	$4$	$0$	$-8$	$0$	$0$	$-16$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}-\beta _{4}q^{3}+q^{4}+(-\beta _{2}-\beta _{6})q^{5}+\cdots$
434.2.d.f	$434$	$2$	434.d	217.d	$2$	$8$	$8$	$3.466$	8.0.1024000000.2	None		✓			434.2.d.f	$4$	$0$	$8$	$0$	$0$	$-12$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+\beta _{6}q^{3}+q^{4}+(-1-\beta _{5}-\beta _{7})q^{5}+\cdots$
434.2.e.a	$434$	$2$	434.e	31.c	$3$	$4$	$2$	$3.466$	$\Q(\sqrt{-3}, \sqrt{5})$	None		✓			434.2.e.a	$2$	$0$	$4$	$-1$	$3$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}-\beta _{1}q^{3}+q^{4}+(-\beta _{1}-\beta _{2}-\beta _{3})q^{5}+\cdots$
434.2.e.b	$434$	$2$	434.e	31.c	$3$	$4$	$2$	$3.466$	$\Q(\sqrt{-3}, \sqrt{13})$	None		✓			434.2.e.b	$2$	$0$	$4$	$1$	$-5$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+(1-\beta _{1}+3\beta _{2}+\cdots)q^{5}+\cdots$
434.2.e.c	$434$	$2$	434.e	31.c	$3$	$8$	$4$	$3.466$	8.0.$\cdots$.1	None		✓			434.2.e.c	$2$	$0$	$-8$	$2$	$-4$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}+(-\beta _{1}+\beta _{5})q^{3}+q^{4}+(-1+\cdots)q^{5}+\cdots$
434.2.e.d	$434$	$2$	434.e	31.c	$3$	$8$	$4$	$3.466$	8.0.207360000.1	None		✓			434.2.e.d	$2$	$0$	$-8$	$2$	$2$	$-4$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}+(1-\beta _{2}+\beta _{3})q^{3}+q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots$
434.2.e.e	$434$	$2$	434.e	31.c	$3$	$8$	$4$	$3.466$	8.0.$\cdots$.1	None		✓			434.2.e.e	$2$	$0$	$8$	$4$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(1+\beta _{1}+\beta _{3})q^{3}+q^{4}+(-\beta _{4}+\cdots)q^{5}+\cdots$
434.2.f.a	$434$	$2$	434.f	7.c	$3$	$2$	$1$	$3.466$	$\Q(\sqrt{-3}) $	None		✓			434.2.f.a	$2$	$1$	$-1$	$-3$	$0$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
434.2.f.b	$434$	$2$	434.f	7.c	$3$	$2$	$1$	$3.466$	$\Q(\sqrt{-3}) $	None		✓			434.2.f.b	$2$	$1$	$-1$	$-1$	$-4$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
434.2.f.c	$434$	$2$	434.f	7.c	$3$	$4$	$2$	$3.466$	$\Q(\sqrt{2}, \sqrt{-3})$	None		✓			434.2.f.c	$2$	$0$	$-2$	$2$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{2}q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots$
434.2.f.d	$434$	$2$	434.f	7.c	$3$	$6$	$3$	$3.466$	6.0.64827.1	None		✓			434.2.f.d	$2$	$0$	$-3$	$-1$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{5}q^{2}-\beta _{4}q^{3}+(-1+\beta _{5})q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots$
434.2.f.e	$434$	$2$	434.f	7.c	$3$	$6$	$3$	$3.466$	6.0.2958147.4	None		✓			434.2.f.e	$2$	$0$	$-3$	$1$	$5$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{3})q^{2}+\beta _{4}q^{3}-\beta _{3}q^{4}+(2+\cdots)q^{5}+\cdots$
434.2.f.f	$434$	$2$	434.f	7.c	$3$	$6$	$3$	$3.466$	6.0.1783323.2	None		✓			434.2.f.f	$2$	$0$	$3$	$1$	$-1$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{4})q^{2}+(-\beta _{1}-\beta _{2})q^{3}-\beta _{4}q^{4}+\cdots$
434.2.f.g	$434$	$2$	434.f	7.c	$3$	$14$	$7$	$3.466$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None		✓	✓		434.2.f.g	$2$	$0$	$7$	$1$	$-1$	$2$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{7})q^{2}+(-\beta _{1}-\beta _{5})q^{3}-\beta _{7}q^{4}+\cdots$
434.2.g.a	$434$	$2$	434.g	217.e	$3$	$2$	$1$	$3.466$	$\Q(\sqrt{-3}) $	None		✓			434.2.g.a	$2$	$0$	$-1$	$0$	$0$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+(-1+3\zeta_{6})q^{7}+\cdots$
434.2.g.b	$434$	$2$	434.g	217.e	$3$	$2$	$1$	$3.466$	$\Q(\sqrt{-3}) $	None		✓			434.2.g.b	$2$	$0$	$-1$	$2$	$0$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+2\zeta_{6}q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
434.2.g.c	$434$	$2$	434.g	217.e	$3$	$8$	$4$	$3.466$	8.0.$\cdots$.5	None		✓			434.2.g.c	$2$	$0$	$4$	$-2$	$-4$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{4}q^{2}+(\beta _{1}-\beta _{4})q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots$
434.2.g.d	$434$	$2$	434.g	217.e	$3$	$14$	$7$	$3.466$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None		✓			434.2.g.d	$2$	$0$	$7$	$3$	$2$	$4$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{5})q^{2}-\beta _{9}q^{3}+\beta _{5}q^{4}-\beta _{11}q^{5}+\cdots$
434.2.g.e	$434$	$2$	434.g	217.e	$3$	$18$	$9$	$3.466$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None		✓	✓		434.2.g.e	$2$	$0$	$-9$	$-5$	$2$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{11})q^{2}+(-1+\beta _{1}-\beta _{11}+\cdots)q^{3}+\cdots$
434.2.h.a	$434$	$2$	434.h	217.g	$3$	$2$	$1$	$3.466$	$\Q(\sqrt{-3}) $	None		✓			434.2.g.b	$2$	$1$	$-1$	$-4$	$0$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-2q^{3}-\zeta_{6}q^{4}+(2+\cdots)q^{6}+\cdots$
434.2.h.b	$434$	$2$	434.h	217.g	$3$	$2$	$1$	$3.466$	$\Q(\sqrt{-3}) $	None		✓			434.2.g.a	$2$	$1$	$-1$	$0$	$0$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-3+\zeta_{6})q^{7}+\cdots$
434.2.h.c	$434$	$2$	434.h	217.g	$3$	$8$	$4$	$3.466$	8.0.$\cdots$.5	None		✓			434.2.g.c	$2$	$0$	$4$	$4$	$8$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{4})q^{2}+(1+\beta _{3})q^{3}-\beta _{4}q^{4}+\cdots$
434.2.h.d	$434$	$2$	434.h	217.g	$3$	$14$	$7$	$3.466$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None		✓			434.2.g.d	$2$	$0$	$7$	$-6$	$-4$	$1$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{5}q^{2}+(\beta _{8}+\beta _{9})q^{3}+(-1-\beta _{5}+\cdots)q^{4}+\cdots$
434.2.h.e	$434$	$2$	434.h	217.g	$3$	$18$	$9$	$3.466$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None		✓	✓		434.2.g.e	$2$	$0$	$-9$	$10$	$-4$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{11}q^{2}+(1+\beta _{2})q^{3}+(-1-\beta _{11}+\cdots)q^{4}+\cdots$
434.2.i.a	$434$	$2$	434.i	31.d	$5$	$4$	$1$	$3.466$	$\Q(\zeta_{10})$	None		✓			434.2.i.a	$2$	$0$	$1$	$4$	$2$	$1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\zeta_{10}q^{2}+(2\zeta_{10}-2\zeta_{10}^{2})q^{3}+\zeta_{10}^{2}q^{4}+\cdots$
434.2.i.b	$434$	$2$	434.i	31.d	$5$	$12$	$3$	$3.466$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓			434.2.i.b	$2$	$0$	$3$	$-2$	$0$	$3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\beta _{4}+\beta _{7}-\beta _{8})q^{2}+(-1-\beta _{1}+\cdots)q^{3}+\cdots$
434.2.i.c	$434$	$2$	434.i	31.d	$5$	$16$	$4$	$3.466$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓			434.2.i.c	$2$	$0$	$-4$	$0$	$-2$	$4$		$5$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{8}q^{2}+(\beta _{1}+\beta _{5}+\beta _{12})q^{3}+(-1+\cdots)q^{4}+\cdots$
434.2.i.d	$434$	$2$	434.i	31.d	$5$	$16$	$4$	$3.466$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓			434.2.i.d	$2$	$0$	$-4$	$4$	$6$	$-4$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{12}q^{2}+\beta _{4}q^{3}+(-1-\beta _{2}-\beta _{8}+\cdots)q^{4}+\cdots$
434.2.i.e	$434$	$2$	434.i	31.d	$5$	$16$	$4$	$3.466$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓			434.2.i.e	$2$	$0$	$4$	$2$	$2$	$-4$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{10}q^{2}+(-\beta _{1}-\beta _{2}-\beta _{3}-\beta _{5}+\cdots)q^{3}+\cdots$
434.2.l.a	$434$	$2$	434.l	217.l	$6$	$2$	$1$	$3.466$	$\Q(\sqrt{-3}) $	None		✓			434.2.l.a	$2$	$1$	$-1$	$-2$	$-6$	$-5$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\zeta_{6}q^{2}-2\zeta_{6}q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
434.2.l.b	$434$	$2$	434.l	217.l	$6$	$2$	$1$	$3.466$	$\Q(\sqrt{-3}) $	None		✓			434.2.l.b	$2$	$0$	$1$	$-2$	$0$	$-5$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{6}q^{2}-2\zeta_{6}q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
434.2.l.c	$434$	$2$	434.l	217.l	$6$	$10$	$5$	$3.466$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None		✓			434.2.l.c	$2$	$0$	$5$	$0$	$-6$	$9$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1-\beta _{6})q^{2}+\beta _{1}q^{3}-\beta _{6}q^{4}+(-1+\cdots)q^{5}+\cdots$
434.2.l.d	$434$	$2$	434.l	217.l	$6$	$10$	$5$	$3.466$	10.0.$\cdots$.1	None		✓			434.2.l.d	$2$	$0$	$5$	$3$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{6}q^{2}+(\beta _{1}+\beta _{4}-\beta _{6}+\beta _{8}-\beta _{9})q^{3}+\cdots$
434.2.l.e	$434$	$2$	434.l	217.l	$6$	$20$	$10$	$3.466$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		✓	✓		434.2.l.e	$2$	$0$	$-10$	$3$	$12$	$-1$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1-\beta _{8})q^{2}+\beta _{1}q^{3}+\beta _{8}q^{4}+(1+\cdots)q^{5}+\cdots$
434.2.m.a	$434$	$2$	434.m	217.s	$6$	$2$	$1$	$3.466$	$\Q(\sqrt{-3}) $	None		✓			434.2.m.a	$2$	$0$	$-2$	$-1$	$-3$	$4$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-q^{2}+(-1+\zeta_{6})q^{3}+q^{4}+(-2+\zeta_{6})q^{5}+\cdots$
434.2.m.b	$434$	$2$	434.m	217.s	$6$	$2$	$1$	$3.466$	$\Q(\sqrt{-3}) $	None		✓			434.2.m.a	$2$	$0$	$-2$	$1$	$3$	$1$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-q^{2}+(1-\zeta_{6})q^{3}+q^{4}+(2-\zeta_{6})q^{5}+\cdots$
434.2.m.c	$434$	$2$	434.m	217.s	$6$	$2$	$1$	$3.466$	$\Q(\sqrt{-3}) $	None		✓			434.2.m.c	$2$	$0$	$2$	$-1$	$3$	$-5$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+q^{2}+(-1+\zeta_{6})q^{3}+q^{4}+(2-\zeta_{6})q^{5}+\cdots$

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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.