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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 55 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
3249.1.b.a	$3249$	$1$	3249.b	3.b	$2$	$2$	$2$	$1.621$	$\Q(\sqrt{-2}) $	$D_{4}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{4}-\beta q^{5}+\beta q^{11}+q^{16}-\beta q^{17}+\cdots$
3249.1.c.a	$3249$	$1$	3249.c	19.b	$2$	$2$	$2$	$1.621$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$2$		$2$		$q+q^{4}+q^{7}+(\zeta_{6}+\zeta_{6}^{2})q^{13}+q^{16}+\cdots$
3249.1.i.a	$3249$	$1$	3249.i	171.i	$6$	$4$	$2$	$1.621$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$-2$	$-2$		$1$		$q-\zeta_{12}^{3}q^{2}-\zeta_{12}^{5}q^{3}+\zeta_{12}^{4}q^{5}+\cdots$
3249.1.p.a	$3249$	$1$	3249.p	19.d	$6$	$2$	$1$	$1.621$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-19}) $	$\Q(\sqrt{57}) $		$8$	$0$	$0$	$0$	$0$	$-4$		$1$		$q-\zeta_{6}q^{4}-q^{7}+\zeta_{6}^{2}q^{16}+\zeta_{6}q^{25}+\cdots$
3249.1.p.b	$3249$	$1$	3249.p	19.d	$6$	$2$	$1$	$1.621$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q-\zeta_{6}q^{4}+q^{7}+(1-\zeta_{6}^{2})q^{13}+\zeta_{6}^{2}q^{16}+\cdots$
3249.1.r.a	$3249$	$1$	3249.r	57.h	$6$	$4$	$2$	$1.621$	$\Q(\sqrt{-2}, \sqrt{-3})$	$D_{4}$	$\Q(\sqrt{-19}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-1+\beta _{2})q^{4}+(\beta _{1}-\beta _{3})q^{5}-\beta _{3}q^{11}+\cdots$
3249.1.s.a	$3249$	$1$	3249.s	171.s	$6$	$4$	$2$	$1.621$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$4$	$-2$		$1$		$q+\zeta_{12}^{5}q^{2}-\zeta_{12}q^{3}+q^{5}+q^{6}+\zeta_{12}^{4}q^{7}+\cdots$
3249.1.ba.a	$3249$	$1$	3249.ba	19.f	$18$	$6$	$1$	$1.621$	$\Q(\zeta_{18})$	$D_{6}$	$\Q(\sqrt{-3}) $	None		$12$	$0$	$0$	$0$	$0$	$-3$		$1$		$q-\zeta_{18}^{7}q^{4}-\zeta_{18}^{3}q^{7}+(\zeta_{18}-\zeta_{18}^{7}+\cdots)q^{13}+\cdots$
3249.1.ba.b	$3249$	$1$	3249.ba	19.f	$18$	$6$	$1$	$1.621$	$\Q(\zeta_{18})$	$D_{6}$	$\Q(\sqrt{-3}) $	None		$12$	$0$	$0$	$0$	$0$	$-3$		$1$		$q-\zeta_{18}^{7}q^{4}-\zeta_{18}^{3}q^{7}+(-\zeta_{18}+\zeta_{18}^{7}+\cdots)q^{13}+\cdots$
3249.1.ba.c	$3249$	$1$	3249.ba	19.f	$18$	$6$	$1$	$1.621$	$\Q(\zeta_{18})$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-19}) $	$\Q(\sqrt{57}) $		$24$	$0$	$0$	$0$	$0$	$6$		$1$		$q-\zeta_{18}^{7}q^{4}+\zeta_{18}^{3}q^{7}-\zeta_{18}^{5}q^{16}+\cdots$
3249.1.bb.a	$3249$	$1$	3249.bb	57.l	$18$	$12$	$2$	$1.621$	12.0.$\cdots$.1	$D_{4}$	$\Q(\sqrt{-19}) $	None		$24$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\beta _{2}-\beta _{8})q^{4}+(\beta _{1}-\beta _{7})q^{5}-\beta _{3}q^{11}+\cdots$
3249.1.bc.a	$3249$	$1$	3249.bc	171.ac	$18$	$12$	$2$	$1.621$	$\Q(\zeta_{36})$	$A_{4}$	None	None		$12$	$0$	$0$	$0$	$0$	$-6$		$1$		$q+\zeta_{36}^{11}q^{2}+\zeta_{36}^{5}q^{3}+\zeta_{36}^{8}q^{5}+\cdots$
3249.1.be.a	$3249$	$1$	3249.be	171.ae	$18$	$12$	$2$	$1.621$	$\Q(\zeta_{36})$	$A_{4}$	None	None		$12$	$0$	$0$	$0$	$0$	$12$		$1$		$q-\zeta_{36}q^{2}+\zeta_{36}q^{3}-\zeta_{36}^{10}q^{5}-\zeta_{36}^{2}q^{6}+\cdots$
3249.1.bi.a	$3249$	$1$	3249.bi	361.h	$38$	$18$	$1$	$1.621$	$\Q(\zeta_{38})$	$D_{38}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q+\zeta_{38}^{4}q^{4}+(-\zeta_{38}^{12}-\zeta_{38}^{18})q^{7}+\cdots$
3249.1.bs.a	$3249$	$1$	3249.bs	361.j	$114$	$36$	$1$	$1.621$	$\Q(\zeta_{57})$	$D_{114}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q+\zeta_{114}^{50}q^{4}+(-\zeta_{114}^{16}+\zeta_{114}^{17}+\cdots)q^{7}+\cdots$
3249.2.a.a	$3249$	$2$	3249.a	1.a	$1$	$1$	$1$	$25.943$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-2$	$0$	$-1$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}-q^{5}+3q^{7}+2q^{10}+\cdots$
3249.2.a.b	$3249$	$2$	3249.a	1.a	$1$	$1$	$1$	$25.943$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-2$	$0$	$3$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}+3q^{5}-5q^{7}-6q^{10}+\cdots$
3249.2.a.c	$3249$	$2$	3249.a	1.a	$1$	$1$	$1$	$25.943$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$0$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+q^{7}+3q^{8}+2q^{11}+5q^{13}+\cdots$
3249.2.a.d	$3249$	$2$	3249.a	1.a	$1$	$1$	$1$	$25.943$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-3$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-3q^{5}-q^{7}-3q^{11}+4q^{13}+\cdots$
3249.2.a.e	$3249$	$2$	3249.a	1.a	$1$	$1$	$1$	$25.943$	$\Q$	$_{}$	$\Q(\sqrt{-19}) $	None	✓	$2$	$0$	$0$	$0$	$1$	$3$	$-$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}+q^{5}+3q^{7}+5q^{11}+4q^{16}+\cdots$
3249.2.a.f	$3249$	$2$	3249.a	1.a	$1$	$1$	$1$	$25.943$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$1$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+q^{7}-3q^{8}+2q^{11}-5q^{13}+\cdots$
3249.2.a.g	$3249$	$2$	3249.a	1.a	$1$	$1$	$1$	$25.943$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$1$	$0$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+2q^{5}-3q^{8}+2q^{10}+\cdots$
3249.2.a.h	$3249$	$2$	3249.a	1.a	$1$	$2$	$2$	$25.943$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$-3$	$0$	$-1$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{2}+3\beta q^{4}-\beta q^{5}+(-2+\cdots)q^{7}+\cdots$
3249.2.a.i	$3249$	$2$	3249.a	1.a	$1$	$2$	$2$	$25.943$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$-1$	$0$	$-2$	$6$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+\beta )q^{4}-2\beta q^{5}+3q^{7}+\cdots$
3249.2.a.j	$3249$	$2$	3249.a	1.a	$1$	$2$	$2$	$25.943$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$-1$	$0$	$1$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+\beta )q^{4}+(-1+3\beta )q^{5}+\cdots$
3249.2.a.k	$3249$	$2$	3249.a	1.a	$1$	$2$	$2$	$25.943$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$0$	$-1$	$0$	$3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(2+\beta )q^{4}+(1+\beta )q^{5}+(-1+\cdots)q^{7}+\cdots$
3249.2.a.l	$3249$	$2$	3249.a	1.a	$1$	$2$	$2$	$25.943$	$\Q(\sqrt{19}) $	$_{}$	$\Q(\sqrt{-19}) $	None	✓	$4$	$1$	$0$	$0$	$0$	$-6$	$+$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}+\beta q^{5}-3q^{7}-\beta q^{11}+4q^{16}+\cdots$
3249.2.a.m	$3249$	$2$	3249.a	1.a	$1$	$2$	$2$	$25.943$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-2\beta )q^{2}+3q^{4}+(-1+\beta )q^{5}+\cdots$
3249.2.a.n	$3249$	$2$	3249.a	1.a	$1$	$2$	$2$	$25.943$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-2\beta )q^{2}+3q^{4}-\beta q^{5}+(-2+2\beta )q^{7}+\cdots$
3249.2.a.o	$3249$	$2$	3249.a	1.a	$1$	$2$	$2$	$25.943$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$1$	$0$	$-2$	$6$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{4}-2\beta q^{5}+3q^{7}+\cdots$
3249.2.a.p	$3249$	$2$	3249.a	1.a	$1$	$2$	$2$	$25.943$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$1$	$0$	$1$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{4}+(-1+3\beta )q^{5}+\cdots$
3249.2.a.q	$3249$	$2$	3249.a	1.a	$1$	$2$	$2$	$25.943$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$0$	$1$	$0$	$3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(2+\beta )q^{4}+(1+\beta )q^{5}+(-1+\cdots)q^{7}+\cdots$
3249.2.a.r	$3249$	$2$	3249.a	1.a	$1$	$2$	$2$	$25.943$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$3$	$0$	$-1$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+3\beta q^{4}-\beta q^{5}+(-2-\beta )q^{7}+\cdots$
3249.2.a.s	$3249$	$2$	3249.a	1.a	$1$	$3$	$3$	$25.943$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓	$1$	$1$	$-3$	$0$	$3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+\cdots$
3249.2.a.t	$3249$	$2$	3249.a	1.a	$1$	$3$	$3$	$25.943$	3.3.564.1	$_{}$	None	None	✓	$1$	$1$	$-1$	$0$	$-2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1-\beta _{2})q^{5}+\cdots$
3249.2.a.u	$3249$	$2$	3249.a	1.a	$1$	$3$	$3$	$25.943$	$\Q(\zeta_{18})^+$	$_{}$	$\Q(\sqrt{-3}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}+(-3\beta _{1}+\beta _{2})q^{7}+(4\beta _{1}-\beta _{2})q^{13}+\cdots$
3249.2.a.v	$3249$	$2$	3249.a	1.a	$1$	$3$	$3$	$25.943$	$\Q(\zeta_{18})^+$	$_{}$	$\Q(\sqrt{-3}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}+(-3\beta _{1}+\beta _{2})q^{7}+(-4\beta _{1}+\cdots)q^{13}+\cdots$
3249.2.a.w	$3249$	$2$	3249.a	1.a	$1$	$3$	$3$	$25.943$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$3$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{2}q^{4}+(1-\beta _{1})q^{5}+(-1+\cdots)q^{7}+\cdots$
3249.2.a.x	$3249$	$2$	3249.a	1.a	$1$	$3$	$3$	$25.943$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(1-\beta _{1})q^{5}+(-1+\cdots)q^{7}+\cdots$
3249.2.a.y	$3249$	$2$	3249.a	1.a	$1$	$3$	$3$	$25.943$	3.3.564.1	$_{}$	None	None	✓	$1$	$0$	$1$	$0$	$-2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1-\beta _{2})q^{5}+\cdots$
3249.2.a.z	$3249$	$2$	3249.a	1.a	$1$	$3$	$3$	$25.943$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓	$1$	$0$	$3$	$0$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$
3249.2.a.ba	$3249$	$2$	3249.a	1.a	$1$	$4$	$4$	$25.943$	$\Q(\zeta_{20})^+$	$_{}$	None	None	✓	$2$	$1$	$0$	$0$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1-\beta _{2})q^{5}+\cdots$
3249.2.a.bb	$3249$	$2$	3249.a	1.a	$1$	$4$	$4$	$25.943$	$\Q(\zeta_{20})^+$	$_{}$	None	None	✓	$2$	$1$	$0$	$0$	$2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1+\beta _{2})q^{5}+\cdots$
3249.2.a.bc	$3249$	$2$	3249.a	1.a	$1$	$4$	$4$	$25.943$	$\Q(\zeta_{20})^+$	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$4$	$-8$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(2+2\beta _{2})q^{5}+\cdots$
3249.2.a.bd	$3249$	$2$	3249.a	1.a	$1$	$4$	$4$	$25.943$	4.4.27648.1	$_{}$	None	None	✓	$2$	$1$	$0$	$0$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}+(-1+\cdots)q^{7}+\cdots$
3249.2.a.be	$3249$	$2$	3249.a	1.a	$1$	$4$	$4$	$25.943$	4.4.27648.1	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+(-1+\cdots)q^{7}+\cdots$
3249.2.a.bf	$3249$	$2$	3249.a	1.a	$1$	$4$	$4$	$25.943$	4.4.13068.1	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{3})q^{4}+(-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$
3249.2.a.bg	$3249$	$2$	3249.a	1.a	$1$	$6$	$6$	$25.943$	6.6.6357609.1	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-9$	$9$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{3}+\beta _{4}+\beta _{5})q^{4}+(-2+\cdots)q^{5}+\cdots$
3249.2.a.bh	$3249$	$2$	3249.a	1.a	$1$	$6$	$6$	$25.943$	6.6.6357609.1	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-9$	$9$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{3}+\beta _{4}+\beta _{5})q^{4}+(-2+\cdots)q^{5}+\cdots$
3249.2.a.bi	$3249$	$2$	3249.a	1.a	$1$	$6$	$6$	$25.943$	6.6.21415104.1	$_{}$	None	None	✓	$2$	$1$	$0$	$0$	$0$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots$

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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.