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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 63 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
131.1.b.a	$131$	$1$	131.b	131.b	$2$	$2$	$2$	$0.065$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-131}) $	None	✓	$2$	$0$	$0$	$-1$	$-1$	$-1$	$1$		$q+(-1+\beta )q^{3}+q^{4}-\beta q^{5}-\beta q^{7}+\cdots$
524.1.d.a	$524$	$1$	524.d	131.b	$2$	$1$	$1$	$0.262$	$\Q$	$D_{3}$	$\Q(\sqrt{-131}) $	None	✓	$2$	$0$	$0$	$-1$	$2$	$-1$	$1$		$q-q^{3}+2q^{5}-q^{7}+2q^{11}-q^{13}+\cdots$
524.1.d.b	$524$	$1$	524.d	131.b	$2$	$4$	$4$	$0.262$	$\Q(\zeta_{15})^+$	$D_{15}$	$\Q(\sqrt{-131}) $	None	✓	$2$	$0$	$0$	$1$	$-2$	$1$	$1$		$q+\beta _{1}q^{3}+\beta _{3}q^{5}+(-\beta _{2}-\beta _{3})q^{7}+\cdots$
655.1.d.b	$655$	$1$	655.d	655.d	$2$	$1$	$1$	$0.327$	$\Q$	$D_{2}$	$\Q(\sqrt{-131}) $, $\Q(\sqrt{-655}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q-q^{4}-q^{5}+q^{9}+2q^{11}+q^{16}+q^{20}+\cdots$
655.1.d.e	$655$	$1$	655.d	655.d	$2$	$4$	$4$	$0.327$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-131}) $	None		$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q+(\zeta_{10}+\zeta_{10}^{4})q^{3}-q^{4}-\zeta_{10}^{2}q^{5}+\cdots$
917.1.h.a	$917$	$1$	917.h	917.h	$6$	$2$	$1$	$0.458$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-131}) $	None		$4$	$0$	$0$	$1$	$1$	$-1$	$1$		$q+\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{7}+\cdots$
917.1.h.b	$917$	$1$	917.h	917.h	$6$	$8$	$4$	$0.458$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-131}) $	None		$4$	$0$	$0$	$-1$	$-1$	$1$	$1$		$q+(\zeta_{30}^{8}+\zeta_{30}^{12})q^{3}+\zeta_{30}^{10}q^{4}+\cdots$
1179.1.c.a	$1179$	$1$	1179.c	131.b	$2$	$2$	$2$	$0.588$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-131}) $	None	✓	$2$	$0$	$0$	$0$	$1$	$-1$	$1$		$q+q^{4}+(1-\beta )q^{5}+(-1+\beta )q^{7}+\beta q^{11}+\cdots$
1179.1.h.a	$1179$	$1$	1179.h	1179.h	$6$	$2$	$1$	$0.588$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-131}) $	None		$4$	$0$	$0$	$-1$	$1$	$1$	$1$		$q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}-\zeta_{6}^{2}q^{7}+\cdots$
1179.1.h.c	$1179$	$1$	1179.h	1179.h	$6$	$8$	$4$	$0.588$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-131}) $	None		$4$	$0$	$0$	$1$	$-1$	$-1$	$1$		$q-\zeta_{30}^{11}q^{3}+\zeta_{30}^{10}q^{4}+(\zeta_{30}^{2}-\zeta_{30}^{3}+\cdots)q^{5}+\cdots$
1441.1.u.a	$1441$	$1$	1441.u	1441.u	$10$	$20$	$5$	$0.719$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-131}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{50}^{9}-\zeta_{50}^{21})q^{3}+\zeta_{50}^{10}q^{4}+\cdots$
1703.1.d.a	$1703$	$1$	1703.d	1703.d	$2$	$1$	$1$	$0.850$	$\Q$	$D_{2}$	$\Q(\sqrt{-131}) $, $\Q(\sqrt{-1703}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q+2q^{3}-q^{4}+3q^{9}-2q^{12}-q^{13}+\cdots$
1703.1.d.d	$1703$	$1$	1703.d	1703.d	$2$	$4$	$4$	$0.850$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-131}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q+(\zeta_{10}^{2}-\zeta_{10}^{3})q^{3}-q^{4}+(\zeta_{10}+\zeta_{10}^{4}+\cdots)q^{5}+\cdots$
1703.1.i.a	$1703$	$1$	1703.i	1703.i	$6$	$2$	$1$	$0.850$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-131}) $	None		$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q-\zeta_{6}^{2}q^{3}+\zeta_{6}q^{4}+(-\zeta_{6}-\zeta_{6}^{2})q^{5}+\cdots$
1703.1.i.b	$1703$	$1$	1703.i	1703.i	$6$	$8$	$4$	$0.850$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-131}) $	None		$4$	$0$	$0$	$-1$	$0$	$0$	$1$		$q+(\zeta_{30}^{4}+\zeta_{30}^{6})q^{3}-\zeta_{30}^{10}q^{4}+(-\zeta_{30}^{7}+\cdots)q^{5}+\cdots$
1703.1.k.a	$1703$	$1$	1703.k	1703.k	$6$	$2$	$1$	$0.850$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-131}) $	None		$4$	$0$	$0$	$1$	$-2$	$-2$	$1$		$q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-q^{5}-\zeta_{6}q^{7}-\zeta_{6}^{2}q^{11}+\cdots$
1703.1.k.c	$1703$	$1$	1703.k	1703.k	$6$	$8$	$4$	$0.850$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-131}) $	None		$4$	$0$	$0$	$-1$	$2$	$2$	$1$		$q+(\zeta_{30}^{4}+\zeta_{30}^{6})q^{3}+\zeta_{30}^{10}q^{4}+(-\zeta_{30}^{7}+\cdots)q^{5}+\cdots$
1965.1.i.a	$1965$	$1$	1965.i	1965.i	$4$	$2$	$1$	$0.981$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-131}) $	None		$4$	$0$	$0$	$-2$	$0$	$-2$	$1$		$q-q^{3}+iq^{4}-iq^{5}+(-1+i)q^{7}+\cdots$
1965.1.i.b	$1965$	$1$	1965.i	1965.i	$4$	$2$	$1$	$0.981$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-131}) $	None		$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q-iq^{3}+iq^{4}+iq^{5}+(-1+i)q^{7}+\cdots$
1965.1.i.c	$1965$	$1$	1965.i	1965.i	$4$	$8$	$4$	$0.981$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-131}) $	None		$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q-\zeta_{20}q^{3}+\zeta_{20}^{5}q^{4}-\zeta_{20}^{7}q^{5}+(-\zeta_{20}^{7}+\cdots)q^{7}+\cdots$
1965.1.i.d	$1965$	$1$	1965.i	1965.i	$4$	$8$	$4$	$0.981$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-131}) $	None		$4$	$0$	$0$	$2$	$0$	$2$	$1$		$q-\zeta_{20}^{8}q^{3}+\zeta_{20}^{5}q^{4}-\zeta_{20}^{9}q^{5}+\cdots$
2096.1.h.a	$2096$	$1$	2096.h	131.b	$2$	$1$	$1$	$1.046$	$\Q$	$D_{3}$	$\Q(\sqrt{-131}) $	None	✓	$2$	$0$	$0$	$1$	$2$	$1$	$1$		$q+q^{3}+2q^{5}+q^{7}-2q^{11}-q^{13}+\cdots$
2096.1.h.b	$2096$	$1$	2096.h	131.b	$2$	$2$	$2$	$1.046$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-131}) $	None	✓	$2$	$0$	$0$	$1$	$-1$	$1$	$1$		$q+(1-\beta )q^{3}-\beta q^{5}+\beta q^{7}+(1-\beta )q^{9}+\cdots$
2096.1.h.d	$2096$	$1$	2096.h	131.b	$2$	$4$	$4$	$1.046$	$\Q(\zeta_{15})^+$	$D_{15}$	$\Q(\sqrt{-131}) $	None	✓	$2$	$0$	$0$	$-1$	$-2$	$-1$	$1$		$q-\beta _{1}q^{3}+\beta _{3}q^{5}+(\beta _{2}+\beta _{3})q^{7}+(1+\cdots)q^{9}+\cdots$
2620.1.e.a	$2620$	$1$	2620.e	655.d	$2$	$2$	$2$	$1.308$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-131}) $	None		$4$	$0$	$0$	$0$	$-2$	$0$	$2$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{3}-q^{5}+(\zeta_{6}+\zeta_{6}^{2})q^{7}+\cdots$
2620.1.e.b	$2620$	$1$	2620.e	655.d	$2$	$8$	$8$	$1.308$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-131}) $	None		$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q+(\zeta_{30}^{4}+\zeta_{30}^{11})q^{3}-\zeta_{30}^{12}q^{5}+\cdots$
2751.1.h.a	$2751$	$1$	2751.h	2751.h	$2$	$1$	$1$	$1.373$	$\Q$	$D_{2}$	$\Q(\sqrt{-131}) $, $\Q(\sqrt{-2751}) $	$\Q(\sqrt{21}) $	✓	$4$	$0$	$0$	$-1$	$2$	$-1$	$1$		$q-q^{3}-q^{4}+2q^{5}-q^{7}+q^{9}+q^{12}+\cdots$
2751.1.h.b	$2751$	$1$	2751.h	2751.h	$2$	$1$	$1$	$1.373$	$\Q$	$D_{2}$	$\Q(\sqrt{-131}) $, $\Q(\sqrt{-2751}) $	$\Q(\sqrt{21}) $	✓	$4$	$0$	$0$	$1$	$-2$	$-1$	$1$		$q+q^{3}-q^{4}-2q^{5}-q^{7}+q^{9}-q^{12}+\cdots$
2751.1.h.h	$2751$	$1$	2751.h	2751.h	$2$	$4$	$4$	$1.373$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-131}) $	None		$4$	$0$	$0$	$-1$	$2$	$1$	$1$		$q-\zeta_{10}^{3}q^{3}-q^{4}+(\zeta_{10}-\zeta_{10}^{4})q^{5}+\cdots$
2751.1.h.i	$2751$	$1$	2751.h	2751.h	$2$	$4$	$4$	$1.373$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-131}) $	None		$4$	$0$	$0$	$1$	$-2$	$1$	$1$		$q+\zeta_{10}q^{3}-q^{4}+(\zeta_{10}^{2}-\zeta_{10}^{3})q^{5}+\cdots$
2751.1.k.a	$2751$	$1$	2751.k	2751.k	$6$	$2$	$1$	$1.373$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-131}) $	None		$4$	$0$	$0$	$1$	$1$	$1$	$1$		$q-\zeta_{6}^{2}q^{3}+\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}-\zeta_{6}^{2}q^{7}+\cdots$
2751.1.k.b	$2751$	$1$	2751.k	2751.k	$6$	$2$	$1$	$1.373$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-131}) $	None		$4$	$0$	$0$	$2$	$-1$	$1$	$1$		$q+q^{3}+\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}-\zeta_{6}^{2}q^{7}+\cdots$
2751.1.k.c	$2751$	$1$	2751.k	2751.k	$6$	$8$	$4$	$1.373$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-131}) $	None		$4$	$0$	$0$	$-2$	$1$	$-1$	$1$		$q+\zeta_{30}^{12}q^{3}-\zeta_{30}^{10}q^{4}+(\zeta_{30}+\zeta_{30}^{9}+\cdots)q^{5}+\cdots$
2751.1.k.d	$2751$	$1$	2751.k	2751.k	$6$	$8$	$4$	$1.373$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-131}) $	None		$4$	$0$	$0$	$-1$	$-1$	$-1$	$1$		$q-\zeta_{30}^{8}q^{3}-\zeta_{30}^{10}q^{4}+(-\zeta_{30}-\zeta_{30}^{9}+\cdots)q^{5}+\cdots$
3275.1.c.a	$3275$	$1$	3275.c	131.b	$2$	$1$	$1$	$1.634$	$\Q$	$D_{2}$	$\Q(\sqrt{-131}) $, $\Q(\sqrt{-655}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{4}-q^{9}+2q^{11}+q^{16}-q^{36}+\cdots$
3275.1.c.d	$3275$	$1$	3275.c	131.b	$2$	$2$	$2$	$1.634$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-131}) $	None	✓	$2$	$0$	$0$	$1$	$0$	$1$	$1$		$q+(1-\beta )q^{3}+q^{4}+\beta q^{7}+(1-\beta )q^{9}+\cdots$
3275.1.c.e	$3275$	$1$	3275.c	131.b	$2$	$4$	$4$	$1.634$	$\Q(\zeta_{20})^+$	$D_{10}$	$\Q(\sqrt{-131}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{3}+q^{4}+\beta _{3}q^{7}+(2+\beta _{2})q^{9}+\cdots$
3275.1.d.a	$3275$	$1$	3275.d	655.d	$2$	$4$	$4$	$1.634$	$\Q(i, \sqrt{5})$	$D_{5}$	$\Q(\sqrt{-131}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{3}-q^{4}+(-\beta _{1}-\beta _{3})q^{7}+\beta _{2}q^{9}+\cdots$
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		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{50}^{9}-\zeta_{50}^{21})q^{3}-\zeta_{50}^{15}q^{4}+\cdots$
3537.1.h.a	$3537$	$1$	3537.h	1179.h	$6$	$2$	$1$	$1.765$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-131}) $	None		$4$	$0$	$0$	$0$	$-1$	$1$	$1$		$q-\zeta_{6}q^{4}-\zeta_{6}q^{5}-\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{11}+\cdots$
3537.1.h.c	$3537$	$1$	3537.h	1179.h	$6$	$8$	$4$	$1.765$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-131}) $	None		$4$	$0$	$0$	$0$	$1$	$-1$	$3^{2}$		$q+\zeta_{30}^{10}q^{4}+(-\zeta_{30}^{6}-\zeta_{30}^{14})q^{5}+\cdots$
3537.1.r.a	$3537$	$1$	3537.r	3537.r	$18$	$6$	$1$	$1.765$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-131}) $	None		$4$	$0$	$0$	$0$	$6$	$-3$	$1$		$q-\zeta_{18}^{5}q^{3}-\zeta_{18}^{7}q^{4}+(1+\zeta_{18}^{8}+\cdots)q^{5}+\cdots$
3537.1.r.b	$3537$	$1$	3537.r	3537.r	$18$	$24$	$4$	$1.765$	$\Q(\zeta_{45})$	$D_{45}$	$\Q(\sqrt{-131}) $	None		$4$	$0$	$0$	$0$	$-6$	$3$	$1$		$q-\zeta_{90}^{29}q^{3}+\zeta_{90}^{10}q^{4}+(-\zeta_{90}^{23}+\cdots)q^{5}+\cdots$
3668.1.k.a	$3668$	$1$	3668.k	917.h	$6$	$2$	$1$	$1.831$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-131}) $	None		$4$	$0$	$0$	$-2$	$1$	$-1$	$1$		$q+\zeta_{6}^{2}q^{3}+\zeta_{6}q^{5}+\zeta_{6}^{2}q^{7}-3\zeta_{6}q^{9}+\cdots$
3668.1.k.b	$3668$	$1$	3668.k	917.h	$6$	$2$	$1$	$1.831$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-131}) $	None		$4$	$0$	$0$	$1$	$1$	$2$	$1$		$q-\zeta_{6}^{2}q^{3}+\zeta_{6}q^{5}+q^{7}+\zeta_{6}^{2}q^{11}+\cdots$
3668.1.k.d	$3668$	$1$	3668.k	917.h	$6$	$8$	$4$	$1.831$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-131}) $	None		$4$	$0$	$0$	$-1$	$-1$	$-2$	$1$		$q+(-\zeta_{30}^{9}-\zeta_{30}^{11})q^{3}+(\zeta_{30}^{12}-\zeta_{30}^{13}+\cdots)q^{5}+\cdots$
3668.1.k.e	$3668$	$1$	3668.k	917.h	$6$	$8$	$4$	$1.831$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-131}) $	None		$4$	$0$	$0$	$2$	$-1$	$1$	$1$		$q+(-\zeta_{30}^{11}+\zeta_{30}^{14})q^{3}+(\zeta_{30}^{8}+\zeta_{30}^{12}+\cdots)q^{5}+\cdots$
393.2.d.a	$393$	$2$	393.d	393.d	$2$	$10$	$10$	$3.138$	10.0.$\cdots$.1	$_{}$	$\Q(\sqrt{-131}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$3^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{1}q^{3}-2q^{4}+\beta _{6}q^{5}+(\beta _{4}-\beta _{7}+\cdots)q^{7}+\cdots$
131.3.b.a	$131$	$3$	131.b	131.b	$2$	$5$	$5$	$3.569$	5.5.53628125.1	$_{}$	$\Q(\sqrt{-131}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+(\beta _{2}-\beta _{3})q^{3}+4q^{4}+(-2\beta _{1}+\beta _{4})q^{5}+\cdots$

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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.