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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 240 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				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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
869.1.j.a	$869$	$1$	869.j	869.j	$10$	$20$	$5$	$0.434$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{50}^{9}-\zeta_{50}^{21})q^{2}+(-\zeta_{50}^{5}+\cdots)q^{4}+\cdots$
63.2.i.b	$63$	$2$	63.i	63.i	$6$	$10$	$5$	$0.503$	10.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$0$	$-3$	$0$	$-6$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{3}-\beta _{5})q^{2}+(\beta _{1}-\beta _{7})q^{3}+(-1+\cdots)q^{4}+\cdots$
63.2.s.b	$63$	$2$	63.s	63.s	$6$	$10$	$5$	$0.503$	10.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$3$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{4}+\beta _{7}+\beta _{8})q^{2}+(-\beta _{1}+\beta _{2}-\beta _{4}+\cdots)q^{3}+\cdots$
71.2.d.a	$71$	$2$	71.d	71.d	$7$	$30$	$5$	$0.567$		$_{}$	None	None		$2$	$0$	$-3$	$-10$	$-10$	$-3$		$\mathrm{SU}(2)[C_{7}]$
73.2.g.a	$73$	$2$	73.g	73.g	$9$	$30$	$5$	$0.583$		$_{}$	None	None		$2$	$0$	$-6$	$0$	$-12$	$3$		$\mathrm{SU}(2)[C_{9}]$
1331.1.d.a	$1331$	$1$	1331.d	11.d	$10$	$20$	$5$	$0.664$	20.0.$\cdots$.1	$D_{11}$	$\Q(\sqrt{-11}) $	None		$8$	$0$	$0$	$1$	$1$	$0$	$1$		$q-\beta _{13}q^{3}+\beta _{9}q^{4}+(\beta _{8}+\beta _{11}+\beta _{12}+\cdots)q^{5}+\cdots$
1397.1.l.a	$1397$	$1$	1397.l	1397.l	$10$	$20$	$5$	$0.697$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-127}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{50}^{16}-\zeta_{50}^{19})q^{2}+(-\zeta_{50}^{7}+\zeta_{50}^{10}+\cdots)q^{4}+\cdots$
1441.1.u.a	$1441$	$1$	1441.u	1441.u	$10$	$20$	$5$	$0.719$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-131}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{50}^{9}-\zeta_{50}^{21})q^{3}+\zeta_{50}^{10}q^{4}+\cdots$
31.3.f.a	$31$	$3$	31.f	31.f	$10$	$20$	$5$	$0.845$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		$2$	$0$	$-3$	$-5$	$-14$	$-1$	$1$	$\mathrm{SU}(2)[C_{10}]$	$q-\beta _{10}q^{2}-\beta _{13}q^{3}+(3\beta _{11}+\beta _{19})q^{4}+\cdots$
1975.1.l.a	$1975$	$1$	1975.l	1975.l	$10$	$20$	$5$	$0.986$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{50}^{9}-\zeta_{50}^{21})q^{2}+(-\zeta_{50}^{5}+\cdots)q^{4}+\cdots$
1975.1.m.a	$1975$	$1$	1975.m	1975.m	$10$	$20$	$5$	$0.986$	$\Q(\zeta_{50})$	$D_{50}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{50}^{18}+\zeta_{50}^{22})q^{2}+(-\zeta_{50}^{11}+\cdots)q^{4}+\cdots$
129.2.i.c	$129$	$2$	129.i	43.e	$7$	$30$	$5$	$1.030$		$_{}$	None	None		$2$	$0$	$-2$	$-5$	$-4$	$2$		$\mathrm{SU}(2)[C_{7}]$
133.2.v.a	$133$	$2$	133.v	19.e	$9$	$30$	$5$	$1.062$		$_{}$	None	None		$2$	$0$	$0$	$-3$	$-3$	$-15$		$\mathrm{SU}(2)[C_{9}]$
133.2.v.b	$133$	$2$	133.v	19.e	$9$	$30$	$5$	$1.062$		$_{}$	None	None		$2$	$0$	$0$	$-3$	$3$	$15$		$\mathrm{SU}(2)[C_{9}]$
135.2.k.a	$135$	$2$	135.k	27.e	$9$	$30$	$5$	$1.078$		$_{}$	None	None		$2$	$0$	$0$	$3$	$0$	$0$		$\mathrm{SU}(2)[C_{9}]$
41.3.e.b	$41$	$3$	41.e	41.e	$8$	$20$	$5$	$1.117$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		$2$	$0$	$-8$	$4$	$-12$	$-4$	$2^{3}$	$\mathrm{SU}(2)[C_{8}]$	$q-\beta _{12}q^{2}-\beta _{8}q^{3}+(-\beta _{1}+\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots$
2449.1.x.a	$2449$	$1$	2449.x	2449.x	$10$	$20$	$5$	$1.222$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{50}^{9}-\zeta_{50}^{21})q^{2}+(-\zeta_{50}^{5}+\cdots)q^{4}+\cdots$
2497.1.h.a	$2497$	$1$	2497.h	2497.h	$10$	$20$	$5$	$1.246$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-227}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{50}^{16}-\zeta_{50}^{19})q^{3}+\zeta_{50}^{20}q^{4}+\cdots$
2629.1.g.a	$2629$	$1$	2629.g	2629.g	$10$	$20$	$5$	$1.312$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-239}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{50}^{16}-\zeta_{50}^{19})q^{2}+(-\zeta_{50}^{9}-\zeta_{50}^{21}+\cdots)q^{3}+\cdots$
170.2.n.a	$170$	$2$	170.n	85.m	$8$	$20$	$5$	$1.357$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$0$	$2$	$\mathrm{SU}(2)[C_{8}]$	$q+\beta _{7}q^{2}-\beta _{6}q^{3}-\beta _{10}q^{4}+\beta _{14}q^{5}+\cdots$
170.2.n.b	$170$	$2$	170.n	85.m	$8$	$20$	$5$	$1.357$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$0$	$2$	$\mathrm{SU}(2)[C_{8}]$	$q+\beta _{8}q^{2}+\beta _{5}q^{3}+\beta _{10}q^{4}-\beta _{16}q^{5}+\cdots$
2867.1.l.a	$2867$	$1$	2867.l	2867.l	$10$	$20$	$5$	$1.431$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-47}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{50}^{16}-\zeta_{50}^{19})q^{2}+(-\zeta_{50}^{17}+\cdots)q^{3}+\cdots$
2867.1.n.a	$2867$	$1$	2867.n	2867.n	$10$	$20$	$5$	$1.431$	$\Q(\zeta_{50})$	$D_{50}$	$\Q(\sqrt{-47}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{50}^{11}-\zeta_{50}^{24})q^{2}+(\zeta_{50}^{3}+\zeta_{50}^{7}+\cdots)q^{3}+\cdots$
2975.1.bl.a	$2975$	$1$	2975.bl	2975.al	$10$	$20$	$5$	$1.485$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-119}) $	None		$4$	$0$	$0$	$0$	$0$	$-20$	$1$		$q+(\zeta_{50}^{16}+\zeta_{50}^{24})q^{2}+(\zeta_{50}^{9}+\zeta_{50}^{21}+\cdots)q^{3}+\cdots$
2975.1.bl.b	$2975$	$1$	2975.bl	2975.al	$10$	$20$	$5$	$1.485$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-119}) $	None		$4$	$0$	$0$	$0$	$0$	$20$	$1$		$q+(\zeta_{50}^{16}+\zeta_{50}^{24})q^{2}+(-\zeta_{50}^{9}-\zeta_{50}^{21}+\cdots)q^{3}+\cdots$
189.2.i.b	$189$	$2$	189.i	63.i	$6$	$10$	$5$	$1.509$	10.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-6$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{3}-\beta _{5})q^{2}+(-1-2\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots$
189.2.s.b	$189$	$2$	189.s	63.s	$6$	$10$	$5$	$1.509$	10.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$3$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{3}-\beta _{4}-\beta _{5}-\beta _{7}-\beta _{8})q^{2}+\cdots$
194.2.f.a	$194$	$2$	194.f	97.f	$8$	$20$	$5$	$1.549$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-8$	$-8$	$2^{2}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{8}]$	$q-\beta _{7}q^{2}-\beta _{6}q^{3}-\beta _{4}q^{4}+\beta _{19}q^{5}+\cdots$
194.2.f.b	$194$	$2$	194.f	97.f	$8$	$20$	$5$	$1.549$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$4$	$4$	$-8$	$2^{2}$	$\mathrm{SU}(2)[C_{8}]$	$q-\beta _{10}q^{2}+\beta _{7}q^{3}+\beta _{6}q^{4}+(\beta _{3}-\beta _{5}+\cdots)q^{5}+\cdots$
3256.1.br.a	$3256$	$1$	3256.br	3256.ar	$10$	$20$	$5$	$1.625$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-74}) $	None		$4$	$0$	$-5$	$0$	$0$	$0$	$1$		$q-\zeta_{50}^{5}q^{2}+(-\zeta_{50}^{9}-\zeta_{50}^{21})q^{3}+\cdots$
3256.1.br.b	$3256$	$1$	3256.br	3256.ar	$10$	$20$	$5$	$1.625$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-74}) $	None		$4$	$0$	$5$	$0$	$0$	$0$	$1$		$q+\zeta_{50}^{5}q^{2}+(-\zeta_{50}^{9}-\zeta_{50}^{21})q^{3}+\cdots$
3275.1.o.a	$3275$	$1$	3275.o	3275.o	$10$	$20$	$5$	$1.634$	$\Q(\zeta_{50})$	$D_{50}$	$\Q(\sqrt{-131}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{50}^{18}-\zeta_{50}^{22})q^{3}-\zeta_{50}^{20}q^{4}+\cdots$
3275.1.x.a	$3275$	$1$	3275.x	3275.x	$10$	$20$	$5$	$1.634$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-131}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{50}^{9}-\zeta_{50}^{21})q^{3}-\zeta_{50}^{15}q^{4}+\cdots$
3333.1.be.a	$3333$	$1$	3333.be	3333.ae	$10$	$20$	$5$	$1.663$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-303}) $	None		$4$	$0$	$0$	$-5$	$0$	$0$	$1$		$q+(-\zeta_{50}^{9}-\zeta_{50}^{21})q^{2}+\zeta_{50}^{20}q^{3}+\cdots$
3333.1.be.b	$3333$	$1$	3333.be	3333.ae	$10$	$20$	$5$	$1.663$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-303}) $	None		$4$	$0$	$0$	$5$	$0$	$0$	$1$		$q+(\zeta_{50}^{9}+\zeta_{50}^{21})q^{2}-\zeta_{50}^{20}q^{3}+\cdots$
3337.1.h.a	$3337$	$1$	3337.h	3337.h	$10$	$20$	$5$	$1.665$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-47}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{50}^{16}-\zeta_{50}^{19})q^{2}+(\zeta_{50}^{2}+\zeta_{50}^{8}+\cdots)q^{3}+\cdots$
216.2.q.b	$216$	$2$	216.q	27.e	$9$	$30$	$5$	$1.725$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$3$		$\mathrm{SU}(2)[C_{9}]$
3476.1.s.a	$3476$	$1$	3476.s	3476.s	$10$	$20$	$5$	$1.735$	$\Q(\zeta_{50})$	$D_{50}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{50}^{19}q^{2}-\zeta_{50}^{13}q^{4}+(-\zeta_{50}^{8}+\cdots)q^{5}+\cdots$
3476.1.s.b	$3476$	$1$	3476.s	3476.s	$10$	$20$	$5$	$1.735$	$\Q(\zeta_{50})$	$D_{50}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{50}^{19}q^{2}-\zeta_{50}^{13}q^{4}+(\zeta_{50}^{7}+\zeta_{50}^{23}+\cdots)q^{5}+\cdots$
226.2.e.b	$226$	$2$	226.e	113.e	$8$	$20$	$5$	$1.805$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$4$	$0$	$2^{6}$	$\mathrm{SU}(2)[C_{8}]$	$q+\beta _{6}q^{2}+\beta _{3}q^{3}-q^{4}-\beta _{14}q^{5}-\beta _{4}q^{6}+\cdots$
3689.1.bz.a	$3689$	$1$	3689.bz	3689.az	$10$	$20$	$5$	$1.841$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-119}) $	None		$4$	$0$	$0$	$0$	$0$	$-5$	$1$		$q+(\zeta_{50}^{4}-\zeta_{50}^{11})q^{2}+(\zeta_{50}^{16}-\zeta_{50}^{19}+\cdots)q^{3}+\cdots$
3689.1.bz.b	$3689$	$1$	3689.bz	3689.az	$10$	$20$	$5$	$1.841$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-119}) $	None		$4$	$0$	$0$	$0$	$0$	$5$	$1$		$q+(-\zeta_{50}^{11}+\zeta_{50}^{24})q^{2}+(\zeta_{50}^{19}+\cdots)q^{3}+\cdots$
3817.1.h.a	$3817$	$1$	3817.h	3817.h	$10$	$20$	$5$	$1.905$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-347}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{50}^{16}-\zeta_{50}^{19})q^{3}+\zeta_{50}^{20}q^{4}+\cdots$
244.2.k.a	$244$	$2$	244.k	61.f	$6$	$10$	$5$	$1.948$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$2$	$-1$	$-6$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{2}q^{3}+(-1-\beta _{4}+\beta _{5}+\beta _{6}+\beta _{7}+\cdots)q^{5}+\cdots$
19.5.d.a	$19$	$5$	19.d	19.d	$6$	$10$	$5$	$1.964$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None		$2$	$0$	$-3$	$9$	$8$	$-24$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{1}q^{2}+(\beta _{3}+\beta _{5})q^{3}+(6\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots$
3975.1.x.a	$3975$	$1$	3975.x	3975.x	$10$	$20$	$5$	$1.984$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-159}) $	None		$4$	$0$	$0$	$-5$	$0$	$0$	$1$		$q+(-\zeta_{50}^{9}-\zeta_{50}^{21})q^{2}-\zeta_{50}^{5}q^{3}+\cdots$
3975.1.x.b	$3975$	$1$	3975.x	3975.x	$10$	$20$	$5$	$1.984$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-159}) $	None		$4$	$0$	$0$	$5$	$0$	$0$	$1$		$q+(\zeta_{50}^{9}+\zeta_{50}^{21})q^{2}+\zeta_{50}^{5}q^{3}+(-\zeta_{50}^{5}+\cdots)q^{4}+\cdots$
254.2.f.d	$254$	$2$	254.f	127.f	$9$	$30$	$5$	$2.028$		$_{}$	None	None		$2$	$0$	$-30$	$0$	$0$	$3$		$\mathrm{SU}(2)[C_{9}]$
9.7.d.a	$9$	$7$	9.d	9.d	$6$	$10$	$5$	$2.070$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None		$2$	$0$	$-3$	$24$	$-219$	$-121$	$2^{2}\cdot 3^{10}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{1}q^{2}+(2+\beta _{1}-\beta _{2}+\beta _{3}+\beta _{6}+\cdots)q^{3}+\cdots$
13.6.e.a	$13$	$6$	13.e	13.e	$6$	$10$	$5$	$2.085$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None		$2$	$0$	$-3$	$-10$	$0$	$-276$	$2^{6}\cdot 3\cdot 13^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{3}q^{2}+(-2-2\beta _{2}-\beta _{5}-\beta _{6})q^{3}+\cdots$

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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.