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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 141 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
77.2.f.b	$77$	$2$	77.f	11.c	$5$	$16$	$4$	$0.615$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$-3$	$-2$	$-5$	$-4$	$5$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{5}-\beta _{6})q^{2}+(\beta _{9}-\beta _{11}+\beta _{13}+\cdots)q^{3}+\cdots$
93.2.f.b	$93$	$2$	93.f	31.d	$5$	$16$	$4$	$0.743$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$-3$	$-4$	$6$	$-7$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{1}q^{2}+\beta _{8}q^{3}+(-1-\beta _{8}-\beta _{9}+\cdots)q^{4}+\cdots$
122.2.e.b	$122$	$2$	122.e	61.e	$5$	$16$	$4$	$0.974$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$-4$	$2$	$3$	$-2$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\beta _{5}-\beta _{6}-\beta _{8})q^{2}-\beta _{3}q^{3}+\cdots$
123.2.g.c	$123$	$2$	123.g	41.d	$5$	$16$	$4$	$0.982$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$-1$	$16$	$-1$	$-2$	$5$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{12}q^{2}+q^{3}+(-1+\beta _{1}+\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots$
125.2.d.b	$125$	$2$	125.d	25.d	$5$	$16$	$4$	$0.998$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$0$	$5^{2}$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{6}q^{2}+(\beta _{6}+\beta _{12}+\beta _{13}-\beta _{14}+\cdots)q^{3}+\cdots$
143.2.h.b	$143$	$2$	143.h	11.c	$5$	$16$	$4$	$1.142$	16.0.$\cdots$.1	None		$2$	$0$	$2$	$5$	$5$	$9$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{14}q^{2}+(\beta _{2}-\beta _{4}-\beta _{5}-\beta _{11})q^{3}+\cdots$
164.2.g.a	$164$	$2$	164.g	41.d	$5$	$16$	$4$	$1.310$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$0$	$-2$	$-4$	$0$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{2}q^{3}+(\beta _{3}+\beta _{4}-\beta _{6}+\beta _{7}-\beta _{9}+\cdots)q^{5}+\cdots$
200.2.m.c	$200$	$2$	200.m	25.d	$5$	$16$	$4$	$1.597$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$0$	$1$	$-1$	$-6$	$5$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{1}q^{3}+(-1+\beta _{2}-\beta _{4}+\beta _{5}+\beta _{14}+\cdots)q^{5}+\cdots$
202.2.d.a	$202$	$2$	202.d	101.d	$5$	$16$	$4$	$1.613$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$2$	$0$	$4$	$-2$	$1$	$-8$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{9}q^{2}+(-\beta _{6}+\beta _{13}-\beta _{15})q^{3}+\cdots$
11.6.c.a	$11$	$6$	11.c	11.c	$5$	$16$	$4$	$1.764$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$-1$	$-24$	$-10$	$196$	$2^{4}$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\beta _{7})q^{2}+\cdots$
225.2.h.e	$225$	$2$	225.h	25.d	$5$	$16$	$4$	$1.797$	16.0.$\cdots$.3	None		$4$	$0$	$0$	$0$	$0$	$0$	$5^{2}$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{3}-\beta _{10}+\beta _{12}-\beta _{14})q^{2}+(-\beta _{8}+\cdots)q^{4}+\cdots$
248.2.j.a	$248$	$2$	248.j	31.d	$5$	$16$	$4$	$1.980$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$0$	$-2$	$-2$	$-8$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1+\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\beta _{7})q^{3}+\cdots$
248.2.j.b	$248$	$2$	248.j	31.d	$5$	$16$	$4$	$1.980$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$2$	$0$	$0$	$0$	$2$	$-2$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{7}q^{3}-\beta _{14}q^{5}+(-\beta _{1}-\beta _{4}+\beta _{11}+\cdots)q^{7}+\cdots$
262.2.c.b	$262$	$2$	262.c	131.c	$5$	$16$	$4$	$2.092$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$4$	$-4$	$6$	$-5$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{11}q^{2}+(\beta _{5}+\beta _{9}-\beta _{11})q^{3}+(-1+\cdots)q^{4}+\cdots$
275.2.h.c	$275$	$2$	275.h	11.c	$5$	$16$	$4$	$2.196$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$0$	$-2$	$0$	$4$	$5$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{2}+\beta _{5}-\beta _{9})q^{2}-\beta _{14}q^{3}+(-1+\cdots)q^{4}+\cdots$
275.2.h.d	$275$	$2$	275.h	11.c	$5$	$16$	$4$	$2.196$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{1}+\beta _{12}+\beta _{13})q^{2}+(-\beta _{5}+\beta _{13}+\cdots)q^{3}+\cdots$
275.2.h.e	$275$	$2$	275.h	11.c	$5$	$16$	$4$	$2.196$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$0$	$2$	$0$	$-4$	$5$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{2}-\beta _{5}+\beta _{9})q^{2}+\beta _{14}q^{3}+(-1+\cdots)q^{4}+\cdots$
279.2.i.c	$279$	$2$	279.i	31.d	$5$	$16$	$4$	$2.228$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$3$	$0$	$-6$	$-7$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{1}q^{2}+(-1-\beta _{8}-\beta _{9}-\beta _{11})q^{4}+\cdots$
297.2.f.a	$297$	$2$	297.f	11.c	$5$	$16$	$4$	$2.372$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$-2$	$0$	$-1$	$-2$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{6}+\beta _{12})q^{2}+(-1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
297.2.f.b	$297$	$2$	297.f	11.c	$5$	$16$	$4$	$2.372$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{12}q^{2}+(-\beta _{2}-\beta _{5}+\beta _{6}-\beta _{7}+\cdots)q^{4}+\cdots$
297.2.f.c	$297$	$2$	297.f	11.c	$5$	$16$	$4$	$2.372$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$8$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{4}q^{2}+(1+\beta _{2}-2\beta _{3}-\beta _{5}-\beta _{6}+\cdots)q^{4}+\cdots$
297.2.f.d	$297$	$2$	297.f	11.c	$5$	$16$	$4$	$2.372$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$2$	$0$	$1$	$-2$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{6}-\beta _{12})q^{2}+(-1-\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots$
350.2.h.c	$350$	$2$	350.h	25.d	$5$	$16$	$4$	$2.795$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$2$	$0$	$-4$	$1$	$-4$	$-16$	$5$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{6}q^{2}-\beta _{10}q^{3}-\beta _{1}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
363.2.e.n	$363$	$2$	363.e	11.c	$5$	$16$	$4$	$2.899$	16.0.$\cdots$.3	None		$8$	$0$	$0$	$-4$	$-2$	$0$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{12}q^{2}+\beta _{4}q^{3}+(\beta _{3}-\beta _{6}+\beta _{8}+\cdots)q^{4}+\cdots$
369.2.h.d	$369$	$2$	369.h	41.d	$5$	$16$	$4$	$2.946$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$1$	$0$	$1$	$-2$	$5$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{12}q^{2}+(-1+\beta _{1}+\beta _{4}+\beta _{5}+\beta _{7}+\cdots)q^{4}+\cdots$
50.4.d.b	$50$	$4$	50.d	25.d	$5$	$16$	$4$	$2.950$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$2$	$0$	$-8$	$7$	$15$	$-54$	$5^{4}$	$\mathrm{SU}(2)[C_{5}]$	$q+2\beta _{6}q^{2}+(1-\beta _{1}+\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots$
374.2.g.f	$374$	$2$	374.g	11.c	$5$	$16$	$4$	$2.986$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$-4$	$5$	$-1$	$2$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\beta _{3}-\beta _{6}-\beta _{8})q^{2}+(-\beta _{6}+\cdots)q^{3}+\cdots$
375.2.g.d	$375$	$2$	375.g	25.d	$5$	$16$	$4$	$2.994$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$2$	$0$	$-2$	$4$	$0$	$16$	$5^{2}$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{5}q^{2}+\beta _{3}q^{3}+(\beta _{8}-\beta _{11})q^{4}+(1+\cdots)q^{6}+\cdots$
375.2.g.e	$375$	$2$	375.g	25.d	$5$	$16$	$4$	$2.994$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$2$	$0$	$2$	$-4$	$0$	$-16$	$5^{2}$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{5}q^{2}-\beta _{3}q^{3}+(\beta _{8}-\beta _{11})q^{4}+(1+\cdots)q^{6}+\cdots$
385.2.n.d	$385$	$2$	385.n	11.c	$5$	$16$	$4$	$3.074$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$-4$	$4$	$4$	$4$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1-\beta _{4}+\beta _{7}-\beta _{8}-\beta _{9}-\beta _{10}+\cdots)q^{2}+\cdots$
400.2.u.g	$400$	$2$	400.u	25.d	$5$	$16$	$4$	$3.194$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$0$	$-1$	$-1$	$6$	$5$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{1}q^{3}+(-1+\beta _{2}-\beta _{4}+\beta _{5}+\beta _{14}+\cdots)q^{5}+\cdots$
410.2.k.b	$410$	$2$	410.k	41.d	$5$	$16$	$4$	$3.274$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$-4$	$2$	$4$	$1$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{11}q^{2}+(-\beta _{1}-\beta _{2}+\beta _{4}+\beta _{7}+\cdots)q^{3}+\cdots$
410.2.k.c	$410$	$2$	410.k	41.d	$5$	$16$	$4$	$3.274$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$4$	$-2$	$-4$	$-7$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\beta _{4}+\beta _{7}+\beta _{10})q^{2}+(-\beta _{1}-\beta _{3}+\cdots)q^{3}+\cdots$
410.2.k.d	$410$	$2$	410.k	41.d	$5$	$16$	$4$	$3.274$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$2$	$0$	$4$	$0$	$4$	$3$	$5$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\beta _{10}+\beta _{11}+\beta _{12})q^{2}+(\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots$
418.2.f.f	$418$	$2$	418.f	11.c	$5$	$16$	$4$	$3.338$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$-4$	$0$	$4$	$6$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{4}q^{2}+(-1+\beta _{1}+\beta _{2}-\beta _{4}+\beta _{6}+\cdots)q^{3}+\cdots$
418.2.f.g	$418$	$2$	418.f	11.c	$5$	$16$	$4$	$3.338$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$4$	$1$	$1$	$-12$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1+\beta _{6}-\beta _{8}+\beta _{10})q^{2}+\beta _{1}q^{3}+\cdots$
422.2.d.a	$422$	$2$	422.d	211.d	$5$	$16$	$4$	$3.370$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$4$	$2$	$8$	$0$	$5$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{5}q^{2}+(-\beta _{4}-\beta _{5}+\beta _{7}+\beta _{8}+\beta _{11}+\cdots)q^{3}+\cdots$
434.2.i.c	$434$	$2$	434.i	31.d	$5$	$16$	$4$	$3.466$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$-4$	$0$	$-2$	$4$	$5$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{8}q^{2}+(\beta _{1}+\beta _{5}+\beta _{12})q^{3}+(-1+\cdots)q^{4}+\cdots$
434.2.i.d	$434$	$2$	434.i	31.d	$5$	$16$	$4$	$3.466$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$-4$	$4$	$6$	$-4$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{12}q^{2}+\beta _{4}q^{3}+(-1-\beta _{2}-\beta _{8}+\cdots)q^{4}+\cdots$
434.2.i.e	$434$	$2$	434.i	31.d	$5$	$16$	$4$	$3.466$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$4$	$2$	$2$	$-4$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{10}q^{2}+(-\beta _{1}-\beta _{2}-\beta _{3}-\beta _{5}+\cdots)q^{3}+\cdots$
440.2.y.d	$440$	$2$	440.y	11.c	$5$	$16$	$4$	$3.513$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$0$	$-3$	$-4$	$8$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{1}q^{3}+(-1+\beta _{4}-\beta _{10}+\beta _{12}+\cdots)q^{5}+\cdots$
62.4.d.a	$62$	$4$	62.d	31.d	$5$	$16$	$4$	$3.658$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$-8$	$4$	$-14$	$-26$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-2\beta _{8}q^{2}+(-\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{3}+\cdots$
62.4.d.b	$62$	$4$	62.d	31.d	$5$	$16$	$4$	$3.658$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$8$	$-2$	$-2$	$4$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-2\beta _{2}q^{2}+(-2+\beta _{1}-2\beta _{2}+2\beta _{3}+\cdots)q^{3}+\cdots$
465.2.n.d	$465$	$2$	465.n	31.d	$5$	$16$	$4$	$3.713$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$4$	$-4$	$-16$	$7$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{13}q^{2}-\beta _{5}q^{3}+(-\beta _{2}-\beta _{4}-\beta _{8}+\cdots)q^{4}+\cdots$
495.2.n.g	$495$	$2$	495.n	11.c	$5$	$16$	$4$	$3.953$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$-2$	$0$	$-4$	$-4$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\beta _{1}+\beta _{3}+\beta _{5}-\beta _{10}-\beta _{14}+\cdots)q^{2}+\cdots$
495.2.n.h	$495$	$2$	495.n	11.c	$5$	$16$	$4$	$3.953$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$2$	$0$	$4$	$-4$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\beta _{1}-\beta _{3}-\beta _{5}+\beta _{10}+\beta _{14}+\cdots)q^{2}+\cdots$
496.2.n.f	$496$	$2$	496.n	31.d	$5$	$16$	$4$	$3.961$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$2$	$0$	$0$	$0$	$2$	$2$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{7}q^{3}-\beta _{14}q^{5}+(\beta _{1}+\beta _{4}-\beta _{11}+\cdots)q^{7}+\cdots$
496.2.n.g	$496$	$2$	496.n	31.d	$5$	$16$	$4$	$3.961$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$0$	$2$	$-2$	$8$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1-\beta _{1}+\beta _{2}-\beta _{3}-\beta _{4}-\beta _{7}+\cdots)q^{3}+\cdots$
500.2.g.b	$500$	$2$	500.g	25.d	$5$	$16$	$4$	$3.993$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$0$	$5^{2}$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{1}-\beta _{11}-\beta _{13})q^{3}+(-\beta _{1}+\beta _{10}+\cdots)q^{7}+\cdots$
506.2.e.g	$506$	$2$	506.e	11.c	$5$	$16$	$4$	$4.040$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$-4$	$5$	$7$	$8$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{8}q^{2}+(\beta _{1}+\beta _{3}-\beta _{4}-\beta _{5})q^{3}+\cdots$

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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.