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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 117 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
61.2.e.a	$61$	$2$	61.e	61.e	$5$	$12$	$3$	$0.487$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$-2$	$-1$	$-5$	$-10$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{5}q^{2}+(\beta _{8}+\beta _{10})q^{3}+(1-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
75.2.g.c	$75$	$2$	75.g	25.d	$5$	$12$	$3$	$0.599$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$0$	$3$	$-6$	$-12$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{2}q^{2}+\beta _{8}q^{3}+(-1+\beta _{1}-\beta _{5}+\cdots)q^{4}+\cdots$
100.2.g.a	$100$	$2$	100.g	25.d	$5$	$12$	$3$	$0.799$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$0$	$2$	$-4$	$-2$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{4}q^{3}+(-1-\beta _{4}+\beta _{5}-\beta _{6}-\beta _{7}+\cdots)q^{5}+\cdots$
122.2.e.a	$122$	$2$	122.e	61.e	$5$	$12$	$3$	$0.974$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$3$	$-4$	$-6$	$10$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{7}q^{2}-\beta _{6}q^{3}+\beta _{4}q^{4}+(-1-\beta _{5}+\cdots)q^{5}+\cdots$
123.2.g.b	$123$	$2$	123.g	41.d	$5$	$12$	$3$	$0.982$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$4$	$-12$	$1$	$8$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{1}+\beta _{4}-\beta _{5})q^{2}-q^{3}+(-1+\cdots)q^{4}+\cdots$
142.2.c.c	$142$	$2$	142.c	71.c	$5$	$12$	$3$	$1.134$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$-3$	$-2$	$-2$	$-4$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{5}q^{2}-\beta _{1}q^{3}+\beta _{3}q^{4}+(-\beta _{4}+\beta _{6}+\cdots)q^{5}+\cdots$
151.2.d.a	$151$	$2$	151.d	151.d	$5$	$12$	$3$	$1.206$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$-8$	$-2$	$-3$	$7$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1-\beta _{5})q^{2}+(\beta _{6}+\beta _{8})q^{3}+(1+\beta _{4}+\cdots)q^{4}+\cdots$
225.2.h.d	$225$	$2$	225.h	25.d	$5$	$12$	$3$	$1.797$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$0$	$0$	$6$	$-12$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{2}q^{2}+(-1+\beta _{1}-\beta _{5}-2\beta _{8}+\beta _{9}+\cdots)q^{4}+\cdots$
33.4.e.c	$33$	$4$	33.e	11.c	$5$	$12$	$3$	$1.947$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$0$	$9$	$28$	$12$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1-\beta _{3}-\beta _{5}-\beta _{6}-\beta _{7})q^{2}-3\beta _{6}q^{3}+\cdots$
286.2.h.c	$286$	$2$	286.h	11.c	$5$	$12$	$3$	$2.284$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$-3$	$4$	$3$	$-8$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\beta _{1}+\beta _{3}+\beta _{9})q^{2}-\beta _{5}q^{3}+\cdots$
286.2.h.d	$286$	$2$	286.h	11.c	$5$	$12$	$3$	$2.284$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$3$	$0$	$3$	$-2$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{6}q^{2}+(\beta _{4}-\beta _{5}+\beta _{11})q^{3}-\beta _{10}q^{4}+\cdots$
286.2.h.e	$286$	$2$	286.h	11.c	$5$	$12$	$3$	$2.284$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$3$	$4$	$3$	$-6$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\beta _{5}-\beta _{6}-\beta _{8})q^{2}+(\beta _{1}-\beta _{7}+\cdots)q^{3}+\cdots$
308.2.j.c	$308$	$2$	308.j	11.c	$5$	$12$	$3$	$2.459$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$0$	$6$	$1$	$-3$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{1}+\beta _{3}-\beta _{4}+\beta _{5}+\beta _{8}-\beta _{9}+\beta _{11})q^{3}+\cdots$
44.4.e.a	$44$	$4$	44.e	11.c	$5$	$12$	$3$	$2.596$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$0$	$-4$	$-4$	$6$	$2^{4}$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{7}q^{3}+(1+\beta _{1}+3\beta _{2}+3\beta _{4}-\beta _{5}+\cdots)q^{5}+\cdots$
328.2.m.b	$328$	$2$	328.m	41.d	$5$	$12$	$3$	$2.619$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$0$	$0$	$-3$	$5$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\beta _{5}-\beta _{6}+\beta _{8})q^{3}+(-1+\beta _{1}+\cdots)q^{5}+\cdots$
350.2.h.b	$350$	$2$	350.h	25.d	$5$	$12$	$3$	$2.795$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$3$	$1$	$-5$	$-12$	$5$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{5}q^{2}+(\beta _{1}-\beta _{3}+\beta _{7})q^{3}-\beta _{3}q^{4}+\cdots$
352.2.m.e	$352$	$2$	352.m	11.c	$5$	$12$	$3$	$2.811$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$-6$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{5}-\beta _{8})q^{3}+\beta _{9}q^{5}+(-1+\beta _{4}+\cdots)q^{7}+\cdots$
352.2.m.f	$352$	$2$	352.m	11.c	$5$	$12$	$3$	$2.811$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$6$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{5}+\beta _{8})q^{3}+\beta _{9}q^{5}+(1-\beta _{4}+\cdots)q^{7}+\cdots$
366.2.h.d	$366$	$2$	366.h	61.e	$5$	$12$	$3$	$2.923$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$3$	$3$	$2$	$4$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1+\beta _{7}-\beta _{8}+\beta _{9})q^{2}+(1+\beta _{7}-\beta _{8}+\cdots)q^{3}+\cdots$
369.2.h.c	$369$	$2$	369.h	41.d	$5$	$12$	$3$	$2.946$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$-4$	$0$	$-1$	$8$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{1}-\beta _{4}+\beta _{5})q^{2}+(-1+\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots$
50.4.d.a	$50$	$4$	50.d	25.d	$5$	$12$	$3$	$2.950$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$6$	$1$	$20$	$58$	$5^{3}$	$\mathrm{SU}(2)[C_{5}]$	$q+2\beta _{5}q^{2}+(-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{3}+\cdots$
372.2.j.c	$372$	$2$	372.j	31.d	$5$	$12$	$3$	$2.970$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$0$	$-3$	$2$	$-3$	$5$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\beta _{6}+\beta _{7}+\beta _{8})q^{3}-\beta _{3}q^{5}+\cdots$
375.2.g.c	$375$	$2$	375.g	25.d	$5$	$12$	$3$	$2.994$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$0$	$-3$	$0$	$12$	$5$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{2}q^{2}+\beta _{8}q^{3}+(-1-\beta _{4}+\beta _{8}+\cdots)q^{4}+\cdots$
400.2.u.f	$400$	$2$	400.u	25.d	$5$	$12$	$3$	$3.194$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$0$	$-2$	$-4$	$2$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{3}q^{3}+(-\beta _{1}+\beta _{2}+\beta _{3}-2\beta _{5}+\cdots)q^{5}+\cdots$
426.2.e.e	$426$	$2$	426.e	71.c	$5$	$12$	$3$	$3.402$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$-3$	$-3$	$4$	$6$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{8}q^{2}-\beta _{8}q^{3}+(-1-\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots$
426.2.e.f	$426$	$2$	426.e	71.c	$5$	$12$	$3$	$3.402$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$3$	$3$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{3}q^{2}-\beta _{3}q^{3}+\beta _{5}q^{4}+\beta _{1}q^{5}+\cdots$
429.2.n.a	$429$	$2$	429.n	11.c	$5$	$12$	$3$	$3.426$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$3$	$-3$	$8$	$5$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{6}q^{2}+\beta _{4}q^{3}+(-\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots$
434.2.i.b	$434$	$2$	434.i	31.d	$5$	$12$	$3$	$3.466$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$3$	$-2$	$0$	$3$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\beta _{4}+\beta _{7}-\beta _{8})q^{2}+(-1-\beta _{1}+\cdots)q^{3}+\cdots$
440.2.y.b	$440$	$2$	440.y	11.c	$5$	$12$	$3$	$3.513$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$0$	$-1$	$3$	$-8$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{1}+\beta _{4})q^{3}+(1-\beta _{6}+\beta _{7}-\beta _{8}+\cdots)q^{5}+\cdots$
440.2.y.c	$440$	$2$	440.y	11.c	$5$	$12$	$3$	$3.513$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$0$	$-1$	$3$	$-1$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{3}+\beta _{8})q^{3}-\beta _{6}q^{5}+(1+\beta _{2}+\beta _{5}+\cdots)q^{7}+\cdots$
22.6.c.b	$22$	$6$	22.c	11.c	$5$	$12$	$3$	$3.528$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$-12$	$0$	$44$	$-326$	$2^{4}\cdot 11^{2}$	$\mathrm{SU}(2)[C_{5}]$	$q+(-4+4\beta _{1}+4\beta _{2}-4\beta _{3})q^{2}+(2\beta _{1}+\cdots)q^{3}+\cdots$
450.2.h.f	$450$	$2$	450.h	25.d	$5$	$12$	$3$	$3.593$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$-3$	$0$	$1$	$-2$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{7}q^{2}+(-1+\beta _{4}-\beta _{6}+\beta _{7})q^{4}+\cdots$
450.2.h.g	$450$	$2$	450.h	25.d	$5$	$12$	$3$	$3.593$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$3$	$0$	$-1$	$-2$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{7}q^{2}+(-1+\beta _{4}-\beta _{6}+\beta _{7})q^{4}+\cdots$
500.2.g.a	$500$	$2$	500.g	25.d	$5$	$12$	$3$	$3.993$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$0$	$-2$	$0$	$2$	$5$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{4}q^{3}+(1+\beta _{3}+\beta _{6}+\beta _{7})q^{7}+(1+\cdots)q^{9}+\cdots$
549.2.k.a	$549$	$2$	549.k	61.e	$5$	$12$	$3$	$4.384$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$2$	$0$	$5$	$-10$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{5}q^{2}+(1-\beta _{1}-\beta _{2}+\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots$
550.2.g.a	$550$	$2$	550.g	275.g	$5$	$12$	$3$	$4.392$	12.0.$\cdots$.1	None		$2$	$0$	$3$	$-2$	$-5$	$-7$	$5$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{8}q^{2}+(\beta _{5}-\beta _{8}-\beta _{10})q^{3}-\beta _{6}q^{4}+\cdots$
550.2.j.a	$550$	$2$	550.j	275.j	$5$	$12$	$3$	$4.392$	12.0.$\cdots$.1	None		$2$	$0$	$3$	$-2$	$0$	$-7$	$5$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{3}q^{2}+(-\beta _{6}-\beta _{9})q^{3}-\beta _{8}q^{4}+\cdots$
574.2.h.j	$574$	$2$	574.h	41.d	$5$	$12$	$3$	$4.583$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$3$	$6$	$-4$	$-3$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{1}q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+\beta _{6}q^{4}+\cdots$
594.2.f.k	$594$	$2$	594.f	11.c	$5$	$12$	$3$	$4.743$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$-3$	$0$	$-1$	$3$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\beta _{2}+\beta _{3}-\beta _{7})q^{2}-\beta _{2}q^{4}+\cdots$
594.2.f.l	$594$	$2$	594.f	11.c	$5$	$12$	$3$	$4.743$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$3$	$0$	$1$	$3$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{7}q^{2}-\beta _{3}q^{4}+\beta _{9}q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots$
600.2.y.c	$600$	$2$	600.y	25.d	$5$	$12$	$3$	$4.791$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$0$	$-3$	$4$	$-8$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{5}q^{3}-\beta _{4}q^{5}+(-2+\beta _{1}-\beta _{4}+\cdots)q^{7}+\cdots$
600.2.y.d	$600$	$2$	600.y	25.d	$5$	$12$	$3$	$4.791$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$0$	$3$	$0$	$-4$	$5$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{5}q^{3}+(\beta _{1}+\beta _{2}-\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{5}+\cdots$
605.2.g.o	$605$	$2$	605.g	11.c	$5$	$12$	$3$	$4.831$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$4$	$0$	$-1$	$-1$	$3$	$1$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{11}q^{2}+\beta _{8}q^{3}+(-\beta _{1}-3\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots$
605.2.g.p	$605$	$2$	605.g	11.c	$5$	$12$	$3$	$4.831$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$4$	$0$	$1$	$-1$	$3$	$-1$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{9}q^{2}-\beta _{1}q^{3}+(-3+\beta _{3}+3\beta _{4}+\cdots)q^{4}+\cdots$
616.2.r.c	$616$	$2$	616.r	11.c	$5$	$12$	$3$	$4.919$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$0$	$-6$	$1$	$-3$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{4}-\beta _{5})q^{3}-\beta _{8}q^{5}-\beta _{5}q^{7}+\cdots$
656.2.u.f	$656$	$2$	656.u	41.d	$5$	$12$	$3$	$5.238$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$0$	$0$	$-3$	$-5$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\beta _{5}+\beta _{6}-\beta _{8})q^{3}+(-1+\beta _{1}+\cdots)q^{5}+\cdots$
704.2.m.m	$704$	$2$	704.m	11.c	$5$	$12$	$3$	$5.621$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$-6$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{5}+\beta _{8})q^{3}-\beta _{9}q^{5}+(-1+\beta _{4}+\cdots)q^{7}+\cdots$
704.2.m.n	$704$	$2$	704.m	11.c	$5$	$12$	$3$	$5.621$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$6$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{5}-\beta _{8})q^{3}-\beta _{9}q^{5}+(1-\beta _{4}-\beta _{6}+\cdots)q^{7}+\cdots$
99.4.f.d	$99$	$4$	99.f	11.c	$5$	$12$	$3$	$5.841$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$0$	$0$	$-28$	$12$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1+\beta _{3}+\beta _{5}+\beta _{6}+\beta _{7})q^{2}+(-1+\cdots)q^{4}+\cdots$
744.2.r.c	$744$	$2$	744.r	31.d	$5$	$12$	$3$	$5.941$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$0$	$-3$	$-6$	$5$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1-\beta _{2}-\beta _{7}-\beta _{9})q^{3}+(-1+\beta _{4}+\cdots)q^{5}+\cdots$

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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.