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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 58 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				Fricke sign	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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
2541.1.h.a	$2541$	$1$	2541.h	231.h	$2$	$4$	$4$	$1.268$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-3}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}^{2}q^{3}-q^{4}-\zeta_{8}q^{7}-q^{9}-\zeta_{8}^{2}q^{12}+\cdots$
2541.1.k.a	$2541$	$1$	2541.k	231.k	$6$	$8$	$4$	$1.268$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{24}^{2}q^{3}-\zeta_{24}^{8}q^{4}-\zeta_{24}^{5}q^{7}+\cdots$
2541.1.q.a	$2541$	$1$	2541.q	21.h	$6$	$2$	$1$	$1.268$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-1$		$1$		$q-\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\cdots$
2541.1.q.b	$2541$	$1$	2541.q	21.h	$6$	$2$	$1$	$1.268$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$1$		$1$		$q-\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\cdots$
2541.1.q.c	$2541$	$1$	2541.q	21.h	$6$	$4$	$2$	$1.268$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-3}) $	None		$8$	$0$	$0$	$2$	$0$	$0$		$1$		$q-\zeta_{12}^{4}q^{3}+\zeta_{12}^{4}q^{4}-\zeta_{12}q^{7}-\zeta_{12}^{2}q^{9}+\cdots$
2541.1.r.a	$2541$	$1$	2541.r	231.r	$10$	$4$	$1$	$1.268$	$\Q(\zeta_{10})$	$D_{3}$	$\Q(\sqrt{-231}) $	None		$8$	$0$	$-1$	$-1$	$1$	$1$		$1$		$q-\zeta_{10}q^{2}-\zeta_{10}^{3}q^{3}-\zeta_{10}^{4}q^{5}+\zeta_{10}^{4}q^{6}+\cdots$
2541.1.r.b	$2541$	$1$	2541.r	231.r	$10$	$4$	$1$	$1.268$	$\Q(\zeta_{10})$	$D_{3}$	$\Q(\sqrt{-231}) $	None		$8$	$0$	$-1$	$1$	$-1$	$-1$		$1$		$q-\zeta_{10}q^{2}+\zeta_{10}^{3}q^{3}+\zeta_{10}^{4}q^{5}-\zeta_{10}^{4}q^{6}+\cdots$
2541.1.r.c	$2541$	$1$	2541.r	231.r	$10$	$4$	$1$	$1.268$	$\Q(\zeta_{10})$	$D_{3}$	$\Q(\sqrt{-231}) $	None		$8$	$0$	$1$	$-1$	$1$	$-1$		$1$		$q+\zeta_{10}q^{2}-\zeta_{10}^{3}q^{3}-\zeta_{10}^{4}q^{5}-\zeta_{10}^{4}q^{6}+\cdots$
2541.1.r.d	$2541$	$1$	2541.r	231.r	$10$	$4$	$1$	$1.268$	$\Q(\zeta_{10})$	$D_{3}$	$\Q(\sqrt{-231}) $	None		$8$	$0$	$1$	$1$	$-1$	$1$		$1$		$q+\zeta_{10}q^{2}+\zeta_{10}^{3}q^{3}+\zeta_{10}^{4}q^{5}+\zeta_{10}^{4}q^{6}+\cdots$
2541.1.r.e	$2541$	$1$	2541.r	231.r	$10$	$16$	$4$	$1.268$	$\Q(\zeta_{40})$	$D_{4}$	$\Q(\sqrt{-3}) $	None		$32$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{40}^{14}q^{3}-\zeta_{40}^{16}q^{4}-\zeta_{40}^{11}q^{7}+\cdots$
2541.1.bh.a	$2541$	$1$	2541.bh	231.z	$30$	$8$	$1$	$1.268$	$\Q(\zeta_{15})$	$D_{3}$	$\Q(\sqrt{-3}) $	None		$16$	$0$	$0$	$1$	$0$	$-1$		$1$		$q+\zeta_{30}^{8}q^{3}+\zeta_{30}^{2}q^{4}-\zeta_{30}^{2}q^{7}+\cdots$
2541.1.bh.b	$2541$	$1$	2541.bh	231.z	$30$	$8$	$1$	$1.268$	$\Q(\zeta_{15})$	$D_{3}$	$\Q(\sqrt{-3}) $	None		$16$	$0$	$0$	$1$	$0$	$1$		$1$		$q+\zeta_{30}^{8}q^{3}+\zeta_{30}^{2}q^{4}+\zeta_{30}^{2}q^{7}+\cdots$
2541.1.bh.c	$2541$	$1$	2541.bh	231.z	$30$	$16$	$2$	$1.268$	$\Q(\zeta_{60})$	$D_{6}$	$\Q(\sqrt{-3}) $	None		$32$	$0$	$0$	$-2$	$0$	$0$		$1$		$q-\zeta_{60}^{28}q^{3}-\zeta_{60}^{22}q^{4}-\zeta_{60}^{7}q^{7}+\cdots$
2541.1.bn.a	$2541$	$1$	2541.bn	231.af	$30$	$32$	$4$	$1.268$	$\Q(\zeta_{120})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		$32$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{120}^{22}q^{3}+\zeta_{120}^{28}q^{4}+\zeta_{120}^{43}q^{7}+\cdots$
2541.2.a.a	$2541$	$2$	2541.a	1.a	$1$	$1$	$1$	$20.290$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-2$	$-1$	$-3$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-q^{3}+2q^{4}-3q^{5}+2q^{6}+\cdots$
2541.2.a.b	$2541$	$2$	2541.a	1.a	$1$	$1$	$1$	$20.290$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-2$	$-1$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-q^{3}+2q^{4}+q^{5}+2q^{6}-q^{7}+\cdots$
2541.2.a.c	$2541$	$2$	2541.a	1.a	$1$	$1$	$1$	$20.290$	$\Q$	$_{}$	None	None	✓	$1$	$2$	$-1$	$-1$	$-3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}-3q^{5}+q^{6}-q^{7}+\cdots$
2541.2.a.d	$2541$	$2$	2541.a	1.a	$1$	$1$	$1$	$20.290$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-1$	$-1$	$1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}+q^{7}+\cdots$
2541.2.a.e	$2541$	$2$	2541.a	1.a	$1$	$1$	$1$	$20.290$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-3$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}-3q^{5}-q^{7}+q^{9}-2q^{12}+\cdots$
2541.2.a.f	$2541$	$2$	2541.a	1.a	$1$	$1$	$1$	$20.290$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$-3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}-3q^{5}+q^{7}+q^{9}-2q^{12}+\cdots$
2541.2.a.g	$2541$	$2$	2541.a	1.a	$1$	$1$	$1$	$20.290$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$1$	$-1$	$-3$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}-3q^{5}-q^{6}+q^{7}+\cdots$
2541.2.a.h	$2541$	$2$	2541.a	1.a	$1$	$1$	$1$	$20.290$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$-1$	$-2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}-2q^{5}-q^{6}-q^{7}+\cdots$
2541.2.a.i	$2541$	$2$	2541.a	1.a	$1$	$1$	$1$	$20.290$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$-1$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}+q^{5}-q^{6}-q^{7}+\cdots$
2541.2.a.j	$2541$	$2$	2541.a	1.a	$1$	$1$	$1$	$20.290$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$1$	$-2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}-2q^{5}+q^{6}+q^{7}+\cdots$
2541.2.a.k	$2541$	$2$	2541.a	1.a	$1$	$1$	$1$	$20.290$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$2$	$-1$	$-3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-q^{3}+2q^{4}-3q^{5}-2q^{6}+\cdots$
2541.2.a.l	$2541$	$2$	2541.a	1.a	$1$	$1$	$1$	$20.290$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$2$	$-1$	$1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-q^{3}+2q^{4}+q^{5}-2q^{6}+q^{7}+\cdots$
2541.2.a.m	$2541$	$2$	2541.a	1.a	$1$	$2$	$2$	$20.290$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$-3$	$-2$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{2}-q^{3}+3\beta q^{4}+\beta q^{5}+\cdots$
2541.2.a.n	$2541$	$2$	2541.a	1.a	$1$	$2$	$2$	$20.290$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$-2$	$-2$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+(2-3\beta )q^{5}+q^{6}+\cdots$
2541.2.a.o	$2541$	$2$	2541.a	1.a	$1$	$2$	$2$	$20.290$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$1$	$-2$	$-2$	$-4$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}-q^{3}+(2-2\beta )q^{4}+(-2+\cdots)q^{5}+\cdots$
2541.2.a.p	$2541$	$2$	2541.a	1.a	$1$	$2$	$2$	$20.290$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$-1$	$-2$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(-1+\beta )q^{5}+\cdots$
2541.2.a.q	$2541$	$2$	2541.a	1.a	$1$	$2$	$2$	$20.290$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$-1$	$-2$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(1-2\beta )q^{5}+\cdots$
2541.2.a.r	$2541$	$2$	2541.a	1.a	$1$	$2$	$2$	$20.290$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$-1$	$2$	$-4$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(-1-2\beta )q^{5}+\cdots$
2541.2.a.s	$2541$	$2$	2541.a	1.a	$1$	$2$	$2$	$20.290$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$-1$	$2$	$-3$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(-1-\beta )q^{5}+\cdots$
2541.2.a.t	$2541$	$2$	2541.a	1.a	$1$	$2$	$2$	$20.290$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$-1$	$2$	$2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}+q^{5}-\beta q^{6}+\cdots$
2541.2.a.u	$2541$	$2$	2541.a	1.a	$1$	$2$	$2$	$20.290$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$1$	$-1$	$2$	$2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+q^{3}+(2+\beta )q^{4}+q^{5}-\beta q^{6}+\cdots$
2541.2.a.v	$2541$	$2$	2541.a	1.a	$1$	$2$	$2$	$20.290$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-2\beta )q^{2}-q^{3}+3q^{4}+(1-\beta )q^{5}+\cdots$
2541.2.a.w	$2541$	$2$	2541.a	1.a	$1$	$2$	$2$	$20.290$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-2\beta )q^{2}-q^{3}+3q^{4}+\beta q^{5}+(-1+\cdots)q^{6}+\cdots$
2541.2.a.x	$2541$	$2$	2541.a	1.a	$1$	$2$	$2$	$20.290$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$1$	$-2$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(-1+\beta )q^{5}+\cdots$
2541.2.a.y	$2541$	$2$	2541.a	1.a	$1$	$2$	$2$	$20.290$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$1$	$-2$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(1-2\beta )q^{5}+\cdots$
2541.2.a.z	$2541$	$2$	2541.a	1.a	$1$	$2$	$2$	$20.290$	$\Q(\sqrt{21}) $	$_{}$	None	None	✓	$1$	$0$	$1$	$-2$	$6$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+(3+\beta )q^{4}+3q^{5}-\beta q^{6}+\cdots$
2541.2.a.ba	$2541$	$2$	2541.a	1.a	$1$	$2$	$2$	$20.290$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$1$	$2$	$-4$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(-1-2\beta )q^{5}+\cdots$
2541.2.a.bb	$2541$	$2$	2541.a	1.a	$1$	$2$	$2$	$20.290$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$1$	$2$	$-3$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(-1-\beta )q^{5}+\cdots$
2541.2.a.bc	$2541$	$2$	2541.a	1.a	$1$	$2$	$2$	$20.290$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$0$	$1$	$2$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+(2+\beta )q^{4}+q^{5}+\beta q^{6}+\cdots$
2541.2.a.bd	$2541$	$2$	2541.a	1.a	$1$	$2$	$2$	$20.290$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$2$	$-2$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}+(2-3\beta )q^{5}-q^{6}+\cdots$
2541.2.a.be	$2541$	$2$	2541.a	1.a	$1$	$2$	$2$	$20.290$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$0$	$2$	$-2$	$-4$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}-q^{3}+(2+2\beta )q^{4}+(-2+\cdots)q^{5}+\cdots$
2541.2.a.bf	$2541$	$2$	2541.a	1.a	$1$	$2$	$2$	$20.290$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$3$	$-2$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}-q^{3}+3\beta q^{4}+\beta q^{5}+(-1+\cdots)q^{6}+\cdots$
2541.2.a.bg	$2541$	$2$	2541.a	1.a	$1$	$3$	$3$	$20.290$	3.3.229.1	$_{}$	None	None	✓	$1$	$0$	$-2$	$3$	$4$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}+q^{3}+(2+\beta _{1})q^{4}+\cdots$
2541.2.a.bh	$2541$	$2$	2541.a	1.a	$1$	$3$	$3$	$20.290$	3.3.316.1	$_{}$	None	None	✓	$1$	$1$	$-1$	$3$	$1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots$
2541.2.a.bi	$2541$	$2$	2541.a	1.a	$1$	$3$	$3$	$20.290$	3.3.837.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$0$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots$
2541.2.a.bj	$2541$	$2$	2541.a	1.a	$1$	$3$	$3$	$20.290$	3.3.316.1	$_{}$	None	None	✓	$1$	$0$	$1$	$3$	$1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots$

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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.