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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 82 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
71.2.c.a	$71$	$2$	71.c	71.c	$5$	$20$	$5$	$0.567$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$-6$	$-1$	$-1$	$-1$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{14}q^{2}+\beta _{17}q^{3}+(-\beta _{2}-\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots$
183.2.h.a	$183$	$2$	183.h	61.e	$5$	$20$	$5$	$1.461$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$1$	$5$	$6$	$-8$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{4}q^{2}+\beta _{11}q^{3}+(-\beta _{1}+\beta _{2}-\beta _{8}+\cdots)q^{4}+\cdots$
202.2.d.b	$202$	$2$	202.d	101.d	$5$	$20$	$5$	$1.613$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$-5$	$2$	$-9$	$0$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1-\beta _{8}+\beta _{12}+\beta _{13})q^{2}+(\beta _{1}+\cdots)q^{3}+\cdots$
213.2.e.b	$213$	$2$	213.e	71.c	$5$	$20$	$5$	$1.701$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		$2$	$0$	$0$	$5$	$10$	$-3$	$5^{2}$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{2}q^{2}+(1-\beta _{5}+\beta _{11}-\beta _{14})q^{3}+\cdots$
231.2.j.g	$231$	$2$	231.j	11.c	$5$	$20$	$5$	$1.845$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		$2$	$0$	$0$	$-5$	$-5$	$5$	$2^{4}$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{7}q^{2}-\beta _{4}q^{3}+(\beta _{3}-\beta _{6}-\beta _{8}-2\beta _{9}+\cdots)q^{4}+\cdots$
244.2.h.a	$244$	$2$	244.h	61.e	$5$	$20$	$5$	$1.948$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		$2$	$0$	$0$	$0$	$3$	$-1$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{1}-\beta _{4}-\beta _{6}+\beta _{9})q^{3}+(1+\beta _{7}+\cdots)q^{5}+\cdots$
328.2.m.c	$328$	$2$	328.m	41.d	$5$	$20$	$5$	$2.619$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$0$	$2$	$2$	$0$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{11}q^{3}+\beta _{2}q^{5}+(\beta _{6}-\beta _{14})q^{7}+\cdots$
350.2.h.d	$350$	$2$	350.h	25.d	$5$	$20$	$5$	$2.795$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$5$	$3$	$-5$	$20$	$5^{2}$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{14}q^{2}+\beta _{1}q^{3}+\beta _{6}q^{4}+(\beta _{10}+\beta _{13}+\cdots)q^{5}+\cdots$
374.2.g.g	$374$	$2$	374.g	11.c	$5$	$20$	$5$	$2.986$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$5$	$-1$	$0$	$6$	$5$	$\mathrm{SU}(2)[C_{5}]$	$q+(1+\beta _{3}-\beta _{7}-\beta _{9})q^{2}-\beta _{5}q^{3}-\beta _{7}q^{4}+\cdots$
418.2.f.h	$418$	$2$	418.f	11.c	$5$	$20$	$5$	$3.338$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$5$	$-1$	$-1$	$13$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{9}q^{2}-\beta _{4}q^{3}+(-1+\beta _{8}+\beta _{9}+\cdots)q^{4}+\cdots$
422.2.d.b	$422$	$2$	422.d	211.d	$5$	$20$	$5$	$3.370$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$5$	$-3$	$-7$	$8$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{10}q^{2}+\beta _{6}q^{3}+(-1-\beta _{9}-\beta _{10}+\cdots)q^{4}+\cdots$
429.2.n.b	$429$	$2$	429.n	11.c	$5$	$20$	$5$	$3.426$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$1$	$5$	$4$	$-3$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{5}q^{2}-\beta _{9}q^{3}+(-\beta _{3}-\beta _{5}-\beta _{7}+\cdots)q^{4}+\cdots$
465.2.n.e	$465$	$2$	465.n	31.d	$5$	$20$	$5$	$3.713$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$-1$	$5$	$-20$	$3$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{3}q^{2}+\beta _{13}q^{3}+(-\beta _{5}-\beta _{9})q^{4}+\cdots$
506.2.e.h	$506$	$2$	506.e	11.c	$5$	$20$	$5$	$4.040$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$-5$	$-3$	$-1$	$3$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{11}q^{2}+(\beta _{4}+\beta _{8})q^{3}+(-1-\beta _{6}+\cdots)q^{4}+\cdots$
525.2.n.b	$525$	$2$	525.n	25.d	$5$	$20$	$5$	$4.192$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$-2$	$5$	$5$	$-20$	$5^{2}$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{10}q^{2}+\beta _{4}q^{3}+(\beta _{1}-2\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots$
539.2.f.g	$539$	$2$	539.f	11.c	$5$	$20$	$5$	$4.304$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$3$	$-4$	$4$	$0$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{6}q^{2}+(-\beta _{1}-\beta _{7}-\beta _{18}+\beta _{19})q^{3}+\cdots$
539.2.f.h	$539$	$2$	539.f	11.c	$5$	$20$	$5$	$4.304$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$3$	$4$	$-4$	$0$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{6}q^{2}+(\beta _{1}+\beta _{7}+\beta _{18}-\beta _{19})q^{3}+\cdots$
549.2.k.b	$549$	$2$	549.k	61.e	$5$	$20$	$5$	$4.384$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$-1$	$0$	$-6$	$-8$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{4}q^{2}+(-\beta _{1}+\beta _{2}-\beta _{8}+\beta _{11}+\cdots)q^{4}+\cdots$
550.2.k.b	$550$	$2$	550.k	25.d	$5$	$20$	$5$	$4.392$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		$2$	$0$	$-5$	$4$	$-6$	$-16$	$5$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{3}q^{2}-\beta _{17}q^{3}+(-1-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots$
550.2.k.c	$550$	$2$	550.k	25.d	$5$	$20$	$5$	$4.392$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$5$	$6$	$-14$	$8$	$5$	$\mathrm{SU}(2)[C_{5}]$	$q+(1+\beta _{6}-\beta _{7}+\beta _{9})q^{2}+(2-\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots$
572.2.n.a	$572$	$2$	572.n	11.c	$5$	$20$	$5$	$4.567$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$0$	$1$	$1$	$3$	$5$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{5}q^{3}+(-\beta _{9}-\beta _{10})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots$
574.2.h.k	$574$	$2$	574.h	41.d	$5$	$20$	$5$	$4.583$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$5$	$-6$	$-1$	$5$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{4}q^{2}-\beta _{6}q^{3}+\beta _{3}q^{4}+\beta _{18}q^{5}+\cdots$
82.4.d.a	$82$	$4$	82.d	41.d	$5$	$20$	$5$	$4.838$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$-10$	$-4$	$6$	$-24$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+2\beta _{8}q^{2}+(-\beta _{4}+\beta _{5}+\beta _{8})q^{3}+4\beta _{2}q^{4}+\cdots$
82.4.d.b	$82$	$4$	82.d	41.d	$5$	$20$	$5$	$4.838$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$10$	$2$	$-6$	$24$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-2\beta _{6}q^{2}+(1+\beta _{2}-\beta _{3}+\beta _{5})q^{3}+\cdots$
606.2.g.e	$606$	$2$	606.g	101.d	$5$	$20$	$5$	$4.839$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$5$	$-5$	$-1$	$9$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{11}q^{2}-\beta _{8}q^{3}-\beta _{10}q^{4}-\beta _{6}q^{5}+\cdots$
610.2.l.d	$610$	$2$	610.l	61.e	$5$	$20$	$5$	$4.871$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		$2$	$0$	$-5$	$1$	$5$	$-7$	$5^{2}$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\beta _{3}+\beta _{4}-\beta _{7})q^{2}+\beta _{12}q^{3}+\cdots$
610.2.l.e	$610$	$2$	610.l	61.e	$5$	$20$	$5$	$4.871$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$5$	$1$	$5$	$-5$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{3}q^{2}+\beta _{1}q^{3}-\beta _{10}q^{4}+\beta _{10}q^{5}+\cdots$
616.2.r.f	$616$	$2$	616.r	11.c	$5$	$20$	$5$	$4.919$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$0$	$-1$	$0$	$5$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{3}q^{3}+(-1-\beta _{2}-\beta _{4}-\beta _{6}-\beta _{11}+\cdots)q^{5}+\cdots$
620.2.n.b	$620$	$2$	620.n	31.d	$5$	$20$	$5$	$4.951$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$0$	$1$	$-20$	$-14$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{2}q^{3}-q^{5}+(-1+\beta _{4}+\beta _{15})q^{7}+\cdots$
638.2.g.d	$638$	$2$	638.g	11.c	$5$	$20$	$5$	$5.094$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$5$	$-2$	$0$	$0$	$5$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{8}q^{2}-\beta _{7}q^{3}-\beta _{5}q^{4}-\beta _{19}q^{5}+\cdots$
639.2.f.b	$639$	$2$	639.f	71.c	$5$	$20$	$5$	$5.102$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		$2$	$0$	$0$	$0$	$-10$	$-3$	$5^{2}$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{2}q^{2}+(-\beta _{1}-\beta _{4}-\beta _{13}+\beta _{15}+\cdots)q^{4}+\cdots$
639.2.f.c	$639$	$2$	639.f	71.c	$5$	$20$	$5$	$5.102$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$6$	$0$	$1$	$-1$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{14}q^{2}+(-\beta _{2}-\beta _{4}-\beta _{5}+\beta _{7}+\cdots)q^{4}+\cdots$
650.2.l.b	$650$	$2$	650.l	25.d	$5$	$20$	$5$	$5.190$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$5$	$-4$	$-10$	$8$	$5^{2}$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{10}q^{2}-\beta _{2}q^{3}-\beta _{13}q^{4}+(-1+\cdots)q^{5}+\cdots$
88.4.i.b	$88$	$4$	88.i	11.c	$5$	$20$	$5$	$5.192$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$0$	$3$	$1$	$1$	$2^{16}\cdot 5$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\beta _{6}+\beta _{7}+\beta _{9})q^{3}+(1+\beta _{3}+\beta _{7}+\cdots)q^{5}+\cdots$
656.2.u.h	$656$	$2$	656.u	41.d	$5$	$20$	$5$	$5.238$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$0$	$-2$	$2$	$0$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{11}q^{3}+\beta _{2}q^{5}+(-\beta _{6}+\beta _{14})q^{7}+\cdots$
33.6.e.a	$33$	$6$	33.e	11.c	$5$	$20$	$5$	$5.293$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$-2$	$-45$	$-33$	$-335$	$2^{4}\cdot 11^{2}$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{1}+\beta _{7})q^{2}-9\beta _{9}q^{3}+(-\beta _{6}+\cdots)q^{4}+\cdots$
33.6.e.b	$33$	$6$	33.e	11.c	$5$	$20$	$5$	$5.293$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$6$	$45$	$-11$	$-139$	$2^{4}\cdot 11^{2}$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{5}+\beta _{6})q^{2}+9\beta _{7}q^{3}+(-12+\cdots)q^{4}+\cdots$
693.2.m.j	$693$	$2$	693.m	11.c	$5$	$20$	$5$	$5.534$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		$2$	$0$	$0$	$0$	$5$	$5$	$2^{4}$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{7}q^{2}+(\beta _{3}-\beta _{6}-\beta _{8}-2\beta _{9}-\beta _{10}+\cdots)q^{4}+\cdots$
700.2.n.c	$700$	$2$	700.n	25.d	$5$	$20$	$5$	$5.590$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$0$	$0$	$4$	$20$	$5$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{2}-\beta _{8})q^{3}+(-\beta _{4}+\beta _{12}-\beta _{15}+\cdots)q^{5}+\cdots$
732.2.n.a	$732$	$2$	732.n	61.e	$5$	$20$	$5$	$5.845$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$0$	$-5$	$-5$	$1$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1-\beta _{5}+\beta _{6}-\beta _{8})q^{3}+\beta _{4}q^{5}+\cdots$
732.2.n.b	$732$	$2$	732.n	61.e	$5$	$20$	$5$	$5.845$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$0$	$5$	$-5$	$-5$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{9}q^{3}-\beta _{17}q^{5}+(\beta _{4}-\beta _{6}-\beta _{12}+\cdots)q^{7}+\cdots$
786.2.e.i	$786$	$2$	786.e	131.c	$5$	$20$	$5$	$6.276$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$-5$	$-5$	$8$	$-3$	$2^{4}$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{6}q^{2}+(-1-\beta _{4}-\beta _{5}-\beta _{6})q^{3}+\cdots$
806.2.k.b	$806$	$2$	806.k	31.d	$5$	$20$	$5$	$6.436$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$-5$	$-1$	$-4$	$-5$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{9}q^{2}+\beta _{8}q^{3}+(-1-\beta _{5}-\beta _{9}+\cdots)q^{4}+\cdots$
836.2.j.b	$836$	$2$	836.j	11.c	$5$	$20$	$5$	$6.675$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		$2$	$0$	$0$	$0$	$-4$	$15$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{1}-\beta _{6}+\beta _{9})q^{3}+(\beta _{3}-\beta _{17})q^{5}+\cdots$
852.2.i.b	$852$	$2$	852.i	71.c	$5$	$20$	$5$	$6.803$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$0$	$5$	$4$	$-3$	$5$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{3}q^{3}+(\beta _{8}+\beta _{14}+\beta _{15}+\beta _{17}+\cdots)q^{5}+\cdots$
44.6.e.a	$44$	$6$	44.e	11.c	$5$	$20$	$5$	$7.057$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$0$	$23$	$-7$	$253$	$2^{16}\cdot 11^{2}$	$\mathrm{SU}(2)[C_{5}]$	$q+(-2\beta _{2}+2\beta _{4}+\beta _{6})q^{3}+(2+\beta _{1}+\cdots)q^{5}+\cdots$
906.2.f.a	$906$	$2$	906.f	151.d	$5$	$20$	$5$	$7.234$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$20$	$-5$	$0$	$5$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+q^{2}-\beta _{5}q^{3}+q^{4}+\beta _{17}q^{5}-\beta _{5}q^{6}+\cdots$
976.2.v.d	$976$	$2$	976.v	61.e	$5$	$20$	$5$	$7.793$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		$2$	$0$	$0$	$0$	$3$	$1$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{1}+\beta _{4}+\beta _{6}-\beta _{9})q^{3}+(1+\beta _{7}+\cdots)q^{5}+\cdots$
984.2.y.e	$984$	$2$	984.y	41.d	$5$	$20$	$5$	$7.857$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$0$	$-20$	$-4$	$4$	$2^{4}$	$\mathrm{SU}(2)[C_{5}]$	$q-q^{3}-\beta _{1}q^{5}-\beta _{8}q^{7}+q^{9}+(1-\beta _{2}+\cdots)q^{11}+\cdots$
984.2.y.f	$984$	$2$	984.y	41.d	$5$	$20$	$5$	$7.857$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$0$	$20$	$3$	$-7$	$2^{4}$	$\mathrm{SU}(2)[C_{5}]$	$q+q^{3}+\beta _{10}q^{5}+(-\beta _{1}-\beta _{7}-\beta _{8}+\cdots)q^{7}+\cdots$

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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.