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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

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Results (47 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	2	13	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
5408.2.a.a	$5408$	$2$	5408.a	1.a	$1$	$1$	$1$	$43.183$	$\Q$	None	✓				416.2.f.a	$1$	$0$	$0$	$-3$	$-3$	$-1$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-3q^{5}-q^{7}+6q^{9}+4q^{11}+\cdots$
5408.2.a.b	$5408$	$2$	5408.a	1.a	$1$	$1$	$1$	$43.183$	$\Q$	None	✓				416.2.f.a	$1$	$1$	$0$	$-3$	$3$	$1$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+3q^{5}+q^{7}+6q^{9}-4q^{11}+\cdots$
5408.2.a.c	$5408$	$2$	5408.a	1.a	$1$	$1$	$1$	$43.183$	$\Q$	None	✓				416.2.i.a	$1$	$0$	$0$	$-2$	$-1$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{5}+q^{9}+4q^{11}+2q^{15}+\cdots$
5408.2.a.d	$5408$	$2$	5408.a	1.a	$1$	$1$	$1$	$43.183$	$\Q$	None	✓				416.2.i.a	$1$	$1$	$0$	$-2$	$1$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}+q^{9}-4q^{11}-2q^{15}+\cdots$
5408.2.a.e	$5408$	$2$	5408.a	1.a	$1$	$1$	$1$	$43.183$	$\Q$	None	✓				416.2.a.a	$1$	$1$	$0$	$-1$	$-1$	$3$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+3q^{7}-2q^{9}+2q^{11}+\cdots$
5408.2.a.f	$5408$	$2$	5408.a	1.a	$1$	$1$	$1$	$43.183$	$\Q$	$\Q(\sqrt{-1}) $	✓				416.2.f.b	$2$	$1$	$0$	$0$	$-4$	$0$	$-$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	$q-4q^{5}-3q^{9}+2q^{17}+11q^{25}+10q^{29}+\cdots$
5408.2.a.g	$5408$	$2$	5408.a	1.a	$1$	$1$	$1$	$43.183$	$\Q$	$\Q(\sqrt{-1}) $	✓				32.2.a.a	$2$	$1$	$0$	$0$	$2$	$0$	$+$	$+$	$+$	$1$	$N(\mathrm{U}(1))$	$q+2q^{5}-3q^{9}+2q^{17}-q^{25}-10q^{29}+\cdots$
5408.2.a.h	$5408$	$2$	5408.a	1.a	$1$	$1$	$1$	$43.183$	$\Q$	$\Q(\sqrt{-1}) $	✓				416.2.f.b	$2$	$0$	$0$	$0$	$4$	$0$	$+$	$-$	$-$	$1$	$N(\mathrm{U}(1))$	$q+4q^{5}-3q^{9}+2q^{17}+11q^{25}+10q^{29}+\cdots$
5408.2.a.i	$5408$	$2$	5408.a	1.a	$1$	$1$	$1$	$43.183$	$\Q$	None	✓				416.2.a.a	$1$	$0$	$0$	$1$	$-1$	$-3$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-3q^{7}-2q^{9}-2q^{11}+\cdots$
5408.2.a.j	$5408$	$2$	5408.a	1.a	$1$	$1$	$1$	$43.183$	$\Q$	None	✓				416.2.i.a	$1$	$1$	$0$	$2$	$-1$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-q^{5}+q^{9}-4q^{11}-2q^{15}+\cdots$
5408.2.a.k	$5408$	$2$	5408.a	1.a	$1$	$1$	$1$	$43.183$	$\Q$	None	✓				416.2.i.a	$1$	$0$	$0$	$2$	$1$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{5}+q^{9}+4q^{11}+2q^{15}+\cdots$
5408.2.a.l	$5408$	$2$	5408.a	1.a	$1$	$1$	$1$	$43.183$	$\Q$	None	✓				416.2.f.a	$1$	$1$	$0$	$3$	$-3$	$1$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-3q^{5}+q^{7}+6q^{9}-4q^{11}+\cdots$
5408.2.a.m	$5408$	$2$	5408.a	1.a	$1$	$1$	$1$	$43.183$	$\Q$	None	✓				416.2.f.a	$1$	$0$	$0$	$3$	$3$	$-1$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+3q^{5}-q^{7}+6q^{9}+4q^{11}+\cdots$
5408.2.a.n	$5408$	$2$	5408.a	1.a	$1$	$2$	$2$	$43.183$	$\Q(\sqrt{2}) $	None	✓				416.2.i.c	$1$	$1$	$0$	$-2$	$0$	$-6$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+2\beta q^{5}+(-3+\beta )q^{7}+\cdots$
5408.2.a.o	$5408$	$2$	5408.a	1.a	$1$	$2$	$2$	$43.183$	$\Q(\sqrt{2}) $	None	✓				416.2.i.c	$1$	$0$	$0$	$-2$	$0$	$6$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}-2\beta q^{5}+(3-\beta )q^{7}+\cdots$
5408.2.a.p	$5408$	$2$	5408.a	1.a	$1$	$2$	$2$	$43.183$	$\Q(\sqrt{17}) $	None	✓				416.2.a.c	$1$	$0$	$0$	$-1$	$3$	$3$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(2-\beta )q^{5}+(2-\beta )q^{7}+(1+\beta )q^{9}+\cdots$
5408.2.a.q	$5408$	$2$	5408.a	1.a	$1$	$2$	$2$	$43.183$	$\Q(\sqrt{5}) $	None	✓				416.2.a.d	$2$	$1$	$0$	$0$	$-6$	$0$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{3}-3q^{5}+\beta q^{7}+2q^{9}-2\beta q^{11}+\cdots$
5408.2.a.r	$5408$	$2$	5408.a	1.a	$1$	$2$	$2$	$43.183$	$\Q(\sqrt{3}) $	$\Q(\sqrt{-1}) $	✓				416.2.w.b	$2$	$0$	$0$	$0$	$-4$	$0$	$+$	$-$	$-$	$1$	$N(\mathrm{U}(1))$	$q+(-2-\beta )q^{5}-3q^{9}+(-1-4\beta )q^{17}+\cdots$
5408.2.a.s	$5408$	$2$	5408.a	1.a	$1$	$2$	$2$	$43.183$	$\Q(\sqrt{3}) $	$\Q(\sqrt{-1}) $	✓				416.2.i.e	$2$	$1$	$0$	$0$	$-2$	$0$	$+$	$+$	$+$	$2$	$N(\mathrm{U}(1))$	$q+(-1-\beta )q^{5}-3q^{9}+(-1+2\beta )q^{17}+\cdots$
5408.2.a.t	$5408$	$2$	5408.a	1.a	$1$	$2$	$2$	$43.183$	$\Q(\sqrt{5}) $	None	✓				416.2.f.e	$2$	$0$	$0$	$0$	$-2$	$0$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{3}-q^{5}-\beta q^{7}+2q^{9}+\beta q^{15}+\cdots$
5408.2.a.u	$5408$	$2$	5408.a	1.a	$1$	$2$	$2$	$43.183$	$\Q(\sqrt{3}) $	None	✓				416.2.w.a	$2$	$1$	$0$	$0$	$0$	$-6$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+2\beta q^{5}-3q^{7}-5q^{11}+6q^{15}+\cdots$
5408.2.a.v	$5408$	$2$	5408.a	1.a	$1$	$2$	$2$	$43.183$	$\Q(\sqrt{13}) $	$\Q(\sqrt{-13}) $	✓				416.2.f.d	$2$	$1$	$0$	$0$	$0$	$-2$	$-$	$-$	$+$	$2$	$N(\mathrm{U}(1))$	$q+(-1-\beta )q^{7}-3q^{9}+(3-\beta )q^{11}+\cdots$
5408.2.a.w	$5408$	$2$	5408.a	1.a	$1$	$2$	$2$	$43.183$	$\Q(\sqrt{11}) $	None	✓				416.2.i.d	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-\beta q^{7}+8q^{9}-\beta q^{11}-3q^{17}+\cdots$
5408.2.a.x	$5408$	$2$	5408.a	1.a	$1$	$2$	$2$	$43.183$	$\Q(\sqrt{11}) $	None	✓				416.2.i.d	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+\beta q^{7}+8q^{9}+\beta q^{11}-3q^{17}+\cdots$
5408.2.a.y	$5408$	$2$	5408.a	1.a	$1$	$2$	$2$	$43.183$	$\Q(\sqrt{13}) $	$\Q(\sqrt{-13}) $	✓				416.2.f.d	$2$	$0$	$0$	$0$	$0$	$2$	$+$	$-$	$-$	$2$	$N(\mathrm{U}(1))$	$q+(1+\beta )q^{7}-3q^{9}+(-3+\beta )q^{11}+\cdots$
5408.2.a.z	$5408$	$2$	5408.a	1.a	$1$	$2$	$2$	$43.183$	$\Q(\sqrt{3}) $	None	✓				416.2.w.a	$2$	$0$	$0$	$0$	$0$	$6$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-2\beta q^{5}+3q^{7}+5q^{11}-6q^{15}+\cdots$
5408.2.a.ba	$5408$	$2$	5408.a	1.a	$1$	$2$	$2$	$43.183$	$\Q(\sqrt{3}) $	$\Q(\sqrt{-1}) $	✓				416.2.i.e	$2$	$0$	$0$	$0$	$2$	$0$	$-$	$+$	$-$	$2$	$N(\mathrm{U}(1))$	$q+(1-\beta )q^{5}-3q^{9}+(-1-2\beta )q^{17}+\cdots$
5408.2.a.bb	$5408$	$2$	5408.a	1.a	$1$	$2$	$2$	$43.183$	$\Q(\sqrt{5}) $	None	✓				416.2.f.e	$2$	$1$	$0$	$0$	$2$	$0$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{3}+q^{5}+\beta q^{7}+2q^{9}-\beta q^{15}+\cdots$
5408.2.a.bc	$5408$	$2$	5408.a	1.a	$1$	$2$	$2$	$43.183$	$\Q(\sqrt{3}) $	$\Q(\sqrt{-1}) $	✓				416.2.w.b	$2$	$1$	$0$	$0$	$4$	$0$	$-$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	$q+(2-\beta )q^{5}-3q^{9}+(-1+4\beta )q^{17}+\cdots$
5408.2.a.bd	$5408$	$2$	5408.a	1.a	$1$	$2$	$2$	$43.183$	$\Q(\sqrt{17}) $	None	✓				416.2.a.c	$1$	$1$	$0$	$1$	$3$	$-3$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(2-\beta )q^{5}+(-2+\beta )q^{7}+(1+\cdots)q^{9}+\cdots$
5408.2.a.be	$5408$	$2$	5408.a	1.a	$1$	$2$	$2$	$43.183$	$\Q(\sqrt{2}) $	None	✓				416.2.i.c	$1$	$1$	$0$	$2$	$0$	$-6$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+2\beta q^{5}+(-3-\beta )q^{7}+\cdots$
5408.2.a.bf	$5408$	$2$	5408.a	1.a	$1$	$2$	$2$	$43.183$	$\Q(\sqrt{2}) $	None	✓				416.2.i.c	$1$	$0$	$0$	$2$	$0$	$6$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}-2\beta q^{5}+(3+\beta )q^{7}+2\beta q^{9}+\cdots$
5408.2.a.bg	$5408$	$2$	5408.a	1.a	$1$	$4$	$4$	$43.183$	4.4.7488.1	None	✓				416.2.w.c	$2$	$1$	$0$	$0$	$-8$	$0$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-2q^{5}+(\beta _{1}+\beta _{3})q^{7}+(2-2\beta _{2}+\cdots)q^{9}+\cdots$
5408.2.a.bh	$5408$	$2$	5408.a	1.a	$1$	$4$	$4$	$43.183$	4.4.9248.1	None	✓				416.2.i.g	$2$	$1$	$0$	$0$	$-2$	$0$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+\beta _{3}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots$
5408.2.a.bi	$5408$	$2$	5408.a	1.a	$1$	$4$	$4$	$43.183$	4.4.9248.1	None	✓				416.2.i.g	$2$	$0$	$0$	$0$	$2$	$0$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}-\beta _{3}q^{5}+(\beta _{1}-\beta _{2})q^{7}-\beta _{3}q^{9}+\cdots$
5408.2.a.bj	$5408$	$2$	5408.a	1.a	$1$	$4$	$4$	$43.183$	4.4.13448.1	None	✓				416.2.a.f	$2$	$0$	$0$	$0$	$2$	$0$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}-\beta _{3}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots$
5408.2.a.bk	$5408$	$2$	5408.a	1.a	$1$	$4$	$4$	$43.183$	4.4.7488.1	None	✓				416.2.w.c	$2$	$0$	$0$	$0$	$8$	$0$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+2q^{5}+(-\beta _{1}-\beta _{3})q^{7}+(2+\cdots)q^{9}+\cdots$
5408.2.a.bl	$5408$	$2$	5408.a	1.a	$1$	$6$	$6$	$43.183$	6.6.1997632.1	None	✓	✓			5408.2.a.bl	$2$	$1$	$0$	$0$	$-4$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1+\beta _{4})q^{5}+(\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots$
5408.2.a.bm	$5408$	$2$	5408.a	1.a	$1$	$6$	$6$	$43.183$	6.6.134509248.1	None	✓				416.2.w.d	$2$	$1$	$0$	$0$	$0$	$-6$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{3})q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots$
5408.2.a.bn	$5408$	$2$	5408.a	1.a	$1$	$6$	$6$	$43.183$	6.6.134509248.1	None	✓				416.2.w.d	$2$	$0$	$0$	$0$	$0$	$6$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(\beta _{1}-\beta _{3})q^{5}+(1+\beta _{2})q^{7}+\cdots$
5408.2.a.bo	$5408$	$2$	5408.a	1.a	$1$	$6$	$6$	$43.183$	6.6.1997632.1	None	✓	✓			5408.2.a.bl	$2$	$1$	$0$	$0$	$4$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(1-\beta _{4})q^{5}+(-\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots$
5408.2.a.bp	$5408$	$2$	5408.a	1.a	$1$	$9$	$9$	$43.183$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	✓	✓		5408.2.a.bp	$1$	$1$	$0$	$-7$	$-6$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(-1-\beta _{3})q^{5}+(-\beta _{4}+\cdots)q^{7}+\cdots$
5408.2.a.bq	$5408$	$2$	5408.a	1.a	$1$	$9$	$9$	$43.183$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	✓	✓		5408.2.a.bp	$1$	$1$	$0$	$-7$	$6$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(1+\beta _{3})q^{5}+(\beta _{4}-\beta _{6}+\cdots)q^{7}+\cdots$
5408.2.a.br	$5408$	$2$	5408.a	1.a	$1$	$9$	$9$	$43.183$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	✓			5408.2.a.bp	$1$	$0$	$0$	$7$	$-6$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(-1-\beta _{3})q^{5}+(\beta _{4}-\beta _{6}+\cdots)q^{7}+\cdots$
5408.2.a.bs	$5408$	$2$	5408.a	1.a	$1$	$9$	$9$	$43.183$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	✓			5408.2.a.bp	$1$	$0$	$0$	$7$	$6$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(1+\beta _{3})q^{5}+(-\beta _{4}+\beta _{6}+\cdots)q^{7}+\cdots$
5408.2.a.bt	$5408$	$2$	5408.a	1.a	$1$	$12$	$12$	$43.183$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	✓	✓		5408.2.a.bt	$2$	$0$	$0$	$0$	$-8$	$0$	$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1+\beta _{4}+\beta _{5}+\beta _{7})q^{5}+\cdots$
5408.2.a.bu	$5408$	$2$	5408.a	1.a	$1$	$12$	$12$	$43.183$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	✓	✓		5408.2.a.bt	$2$	$0$	$0$	$0$	$8$	$0$	$+$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(1-\beta _{4}-\beta _{5}-\beta _{7})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$

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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.