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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 (26 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
664.1.l.a	$664$	$1$	664.l	664.l	$82$	$40$	$1$	$0.331$	$\Q(\zeta_{82})$	$D_{41}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$-2$	$0$	$0$	$1$		$q+\zeta_{82}^{32}q^{2}+(\zeta_{82}^{28}-\zeta_{82}^{29})q^{3}+\cdots$
1151.1.b.a	$1151$	$1$	1151.b	1151.b	$2$	$20$	$20$	$0.574$	$\Q(\zeta_{82})^+$	$D_{41}$	$\Q(\sqrt{-1151}) $	None	✓	$2$	$0$	$-1$	$-1$	$-1$	$-1$	$1$		$q+\beta _{10}q^{2}+\beta _{16}q^{3}+(\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$
1245.1.p.a	$1245$	$1$	1245.p	1245.p	$82$	$40$	$1$	$0.621$	$\Q(\zeta_{82})$	$D_{41}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$-2$	$-1$	$-1$	$0$	$1$		$q+(\zeta_{82}^{8}+\zeta_{82}^{14})q^{2}-\zeta_{82}^{13}q^{3}+\cdots$
1245.1.p.b	$1245$	$1$	1245.p	1245.p	$82$	$40$	$1$	$0.621$	$\Q(\zeta_{82})$	$D_{41}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$2$	$1$	$1$	$0$	$1$		$q+(-\zeta_{82}^{8}-\zeta_{82}^{14})q^{2}+\zeta_{82}^{13}q^{3}+\cdots$
1577.1.p.a	$1577$	$1$	1577.p	1577.p	$82$	$40$	$1$	$0.787$	$\Q(\zeta_{82})$	$D_{41}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-2$	$-2$	$1$		$q+\zeta_{82}^{6}q^{4}+(-\zeta_{82}+\zeta_{82}^{38})q^{5}+\cdots$
1660.1.p.a	$1660$	$1$	1660.p	1660.p	$82$	$40$	$1$	$0.828$	$\Q(\zeta_{82})$	$D_{41}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$-1$	$-2$	$-1$	$-2$	$1$		$q-\zeta_{82}^{7}q^{2}+(-\zeta_{82}^{11}-\zeta_{82}^{13})q^{3}+\cdots$
1660.1.p.b	$1660$	$1$	1660.p	1660.p	$82$	$40$	$1$	$0.828$	$\Q(\zeta_{82})$	$D_{41}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$1$	$2$	$-1$	$2$	$1$		$q+\zeta_{82}^{7}q^{2}+(\zeta_{82}^{11}+\zeta_{82}^{13})q^{3}+\cdots$
1992.1.r.a	$1992$	$1$	1992.r	1992.r	$82$	$40$	$1$	$0.994$	$\Q(\zeta_{82})$	$D_{41}$	$\Q(\sqrt{-6}) $	None		$4$	$0$	$-1$	$-1$	$-2$	$-2$	$1$		$q+\zeta_{82}^{4}q^{2}-\zeta_{82}q^{3}+\zeta_{82}^{8}q^{4}+(\zeta_{82}^{16}+\cdots)q^{5}+\cdots$
1992.1.r.b	$1992$	$1$	1992.r	1992.r	$82$	$40$	$1$	$0.994$	$\Q(\zeta_{82})$	$D_{41}$	$\Q(\sqrt{-6}) $	None		$4$	$0$	$1$	$1$	$2$	$-2$	$1$		$q-\zeta_{82}^{4}q^{2}+\zeta_{82}q^{3}+\zeta_{82}^{8}q^{4}+(-\zeta_{82}^{16}+\cdots)q^{5}+\cdots$
2217.1.p.a	$2217$	$1$	2217.p	2217.p	$82$	$40$	$1$	$1.106$	$\Q(\zeta_{82})$	$D_{41}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q+\zeta_{82}^{30}q^{3}+\zeta_{82}^{10}q^{4}+(-\zeta_{82}^{23}+\cdots)q^{7}+\cdots$
2551.1.b.a	$2551$	$1$	2551.b	2551.b	$2$	$20$	$20$	$1.273$	$\Q(\zeta_{82})^+$	$D_{41}$	$\Q(\sqrt{-2551}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$-1$	$1$		$q+\beta _{10}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots$
2656.1.t.a	$2656$	$1$	2656.t	664.l	$82$	$40$	$1$	$1.326$	$\Q(\zeta_{82})$	$D_{41}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q+(-\zeta_{82}^{26}+\zeta_{82}^{35})q^{3}+(-\zeta_{82}^{11}+\cdots)q^{9}+\cdots$
2719.1.b.a	$2719$	$1$	2719.b	2719.b	$2$	$20$	$20$	$1.357$	$\Q(\zeta_{82})^+$	$D_{41}$	$\Q(\sqrt{-2719}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$-1$	$1$		$q+\beta _{10}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots$
2905.1.bc.a	$2905$	$1$	2905.bc	2905.ac	$82$	$40$	$1$	$1.450$	$\Q(\zeta_{82})$	$D_{41}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$-2$	$-1$	$-1$	$1$		$q+(-\zeta_{82}^{3}-\zeta_{82}^{23})q^{3}+\zeta_{82}^{22}q^{4}+\cdots$
2905.1.bc.b	$2905$	$1$	2905.bc	2905.ac	$82$	$40$	$1$	$1.450$	$\Q(\zeta_{82})$	$D_{41}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$2$	$1$	$1$	$1$		$q+(\zeta_{82}^{3}+\zeta_{82}^{23})q^{3}+\zeta_{82}^{22}q^{4}+\cdots$
3079.1.b.a	$3079$	$1$	3079.b	3079.b	$2$	$20$	$20$	$1.537$	$\Q(\zeta_{82})^+$	$D_{41}$	$\Q(\sqrt{-3079}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$-1$	$1$		$q+\beta _{10}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots$
3237.1.ba.a	$3237$	$1$	3237.ba	3237.aa	$82$	$40$	$1$	$1.615$	$\Q(\zeta_{82})$	$D_{41}$	$\Q(\sqrt{-39}) $	None		$4$	$0$	$-2$	$-1$	$-2$	$0$	$1$		$q+(-\zeta_{82}-\zeta_{82}^{33})q^{2}-\zeta_{82}^{35}q^{3}+\cdots$
3237.1.ba.b	$3237$	$1$	3237.ba	3237.aa	$82$	$40$	$1$	$1.615$	$\Q(\zeta_{82})$	$D_{41}$	$\Q(\sqrt{-39}) $	None		$4$	$0$	$2$	$-1$	$2$	$0$	$1$		$q+(\zeta_{82}+\zeta_{82}^{33})q^{2}-\zeta_{82}^{35}q^{3}+(\zeta_{82}^{2}+\cdots)q^{4}+\cdots$
3284.1.p.a	$3284$	$1$	3284.p	3284.p	$82$	$40$	$1$	$1.639$	$\Q(\zeta_{82})$	$D_{41}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-2$	$0$	$1$		$q+\zeta_{82}^{22}q^{2}-\zeta_{82}^{3}q^{4}+(\zeta_{82}^{18}-\zeta_{82}^{35}+\cdots)q^{5}+\cdots$
3319.1.b.a	$3319$	$1$	3319.b	3319.b	$2$	$20$	$20$	$1.656$	$\Q(\zeta_{82})^+$	$D_{41}$	$\Q(\sqrt{-3319}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$0$	$1$		$q+\beta _{10}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots$
3511.1.b.a	$3511$	$1$	3511.b	3511.b	$2$	$20$	$20$	$1.752$	$\Q(\zeta_{82})^+$	$D_{41}$	$\Q(\sqrt{-3511}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$0$	$1$		$q+\beta _{10}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots$
3569.1.t.a	$3569$	$1$	3569.t	3569.t	$82$	$40$	$1$	$1.781$	$\Q(\zeta_{82})$	$D_{41}$	$\Q(\sqrt{-43}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{82}^{6}q^{4}+\zeta_{82}^{22}q^{9}+(-\zeta_{82}^{3}+\cdots)q^{11}+\cdots$
3693.1.t.a	$3693$	$1$	3693.t	3693.t	$82$	$40$	$1$	$1.843$	$\Q(\zeta_{82})$	$D_{41}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q+\zeta_{82}^{18}q^{3}+\zeta_{82}^{26}q^{4}+(\zeta_{82}^{26}+\cdots)q^{7}+\cdots$
3839.1.d.a	$3839$	$1$	3839.d	3839.d	$2$	$20$	$20$	$1.916$	$\Q(\zeta_{82})^+$	$D_{41}$	$\Q(\sqrt{-3839}) $	None	✓	$2$	$0$	$-1$	$-1$	$-1$	$-1$	$1$		$q+\beta _{10}q^{2}+\beta _{4}q^{3}+(\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$
3839.1.d.b	$3839$	$1$	3839.d	3839.d	$2$	$20$	$20$	$1.916$	$\Q(\zeta_{82})^+$	$D_{41}$	$\Q(\sqrt{-3839}) $	None	✓	$2$	$0$	$1$	$-1$	$-1$	$1$	$1$		$q-\beta _{10}q^{2}+\beta _{4}q^{3}+(\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$
3901.1.j.a	$3901$	$1$	3901.j	3901.j	$82$	$40$	$1$	$1.947$	$\Q(\zeta_{82})$	$D_{41}$	$\Q(\sqrt{-47}) $	None		$4$	$0$	$-2$	$-2$	$0$	$-2$	$1$		$q+(-\zeta_{82}^{17}-\zeta_{82}^{37})q^{2}+(\zeta_{82}^{16}+\cdots)q^{3}+\cdots$

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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.