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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 (1-50 of 401 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
400.1.b.a	$400$	$1$	400.b	4.b	$2$	$1$	$1$	$0.200$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-5}) $	$\Q(\sqrt{5}) $	✓		✓	✓	80.1.h.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{9}-2q^{29}-2q^{41}+q^{49}-2q^{61}+\cdots$
400.1.x.a	$400$	$1$	400.x	100.h	$10$	$4$	$1$	$0.200$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	400.1.x.a	$4$	$0$	$0$	$0$	$1$	$0$		$1$		$q+\zeta_{10}^{3}q^{5}-\zeta_{10}^{4}q^{9}+(\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{13}+\cdots$
400.2.a.a	$400$	$2$	400.a	1.a	$1$	$1$	$1$	$3.194$	$\Q$	$_{}$	None	None	✓				200.2.a.a	$1$	$1$	$0$	$-3$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+2q^{7}+6q^{9}-q^{11}-4q^{13}+\cdots$
400.2.a.b	$400$	$2$	400.a	1.a	$1$	$1$	$1$	$3.194$	$\Q$	$_{}$	None	None	✓				40.2.c.a	$1$	$0$	$0$	$-2$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-2q^{7}+q^{9}+4q^{11}+4q^{13}+\cdots$
400.2.a.c	$400$	$2$	400.a	1.a	$1$	$1$	$1$	$3.194$	$\Q$	$_{}$	None	None	✓				20.2.a.a	$1$	$0$	$0$	$-2$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+2q^{7}+q^{9}-2q^{13}+6q^{17}+\cdots$
400.2.a.d	$400$	$2$	400.a	1.a	$1$	$1$	$1$	$3.194$	$\Q$	$_{}$	None	None	✓		✓	✓	50.2.a.a	$1$	$1$	$0$	$-1$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{7}-2q^{9}+3q^{11}-4q^{13}+\cdots$
400.2.a.e	$400$	$2$	400.a	1.a	$1$	$1$	$1$	$3.194$	$\Q$	$_{}$	None	None	✓				40.2.a.a	$1$	$1$	$0$	$0$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{7}-3q^{9}-4q^{11}+2q^{13}-2q^{17}+\cdots$
400.2.a.f	$400$	$2$	400.a	1.a	$1$	$1$	$1$	$3.194$	$\Q$	$_{}$	None	None	✓				50.2.a.a	$1$	$0$	$0$	$1$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{7}-2q^{9}+3q^{11}+4q^{13}+\cdots$
400.2.a.g	$400$	$2$	400.a	1.a	$1$	$1$	$1$	$3.194$	$\Q$	$_{}$	None	None	✓				40.2.c.a	$1$	$0$	$0$	$2$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+2q^{7}+q^{9}+4q^{11}-4q^{13}+\cdots$
400.2.a.h	$400$	$2$	400.a	1.a	$1$	$1$	$1$	$3.194$	$\Q$	$_{}$	None	None	✓				200.2.a.a	$1$	$0$	$0$	$3$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-2q^{7}+6q^{9}-q^{11}+4q^{13}+\cdots$
400.2.c.a	$400$	$2$	400.c	5.b	$2$	$2$	$2$	$3.194$	$\Q(\sqrt{-1}) $	$_{}$	None	None					200.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3iq^{3}+2iq^{7}-6q^{9}-q^{11}+4iq^{13}+\cdots$
400.2.c.b	$400$	$2$	400.c	5.b	$2$	$2$	$2$	$3.194$	$\Q(\sqrt{-1}) $	$_{}$	None	None					20.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+iq^{7}-q^{9}+iq^{13}+3iq^{17}+\cdots$
400.2.c.c	$400$	$2$	400.c	5.b	$2$	$2$	$2$	$3.194$	$\Q(\sqrt{-1}) $	$_{}$	None	None					50.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}-2iq^{7}+2q^{9}+3q^{11}+4iq^{13}+\cdots$
400.2.c.d	$400$	$2$	400.c	5.b	$2$	$2$	$2$	$3.194$	$\Q(\sqrt{-1}) $	$_{}$	None	None					40.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+2iq^{7}+3q^{9}-4q^{11}+iq^{13}+iq^{17}+\cdots$
400.2.j.a	$400$	$2$	400.j	80.j	$4$	$2$	$1$	$3.194$	$\Q(\sqrt{-1}) $	$_{}$	None	None					80.2.j.a	$2$	$0$	$-2$	$0$	$0$	$6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+i)q^{2}-2iq^{3}-2iq^{4}+(2+\cdots)q^{6}+\cdots$
400.2.j.b	$400$	$2$	400.j	80.j	$4$	$8$	$4$	$3.194$	$\Q(\zeta_{24})$	$_{}$	None	None		✓			400.2.j.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-\zeta_{24}-\zeta_{24}^{5})q^{2}+(\zeta_{24}^{4}-\zeta_{24}^{5}+\cdots)q^{3}+\cdots$
400.2.j.c	$400$	$2$	400.j	80.j	$4$	$16$	$8$	$3.194$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			400.2.j.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{12}q^{2}-\beta _{8}q^{3}+\beta _{15}q^{4}+(-1+\cdots)q^{6}+\cdots$
400.2.j.d	$400$	$2$	400.j	80.j	$4$	$18$	$9$	$3.194$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	$_{}$	None	None					80.2.j.b	$2$	$0$	$4$	$0$	$0$	$-2$		$2^{7}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{7}q^{2}+\beta _{16}q^{3}+\beta _{14}q^{4}+(-1+\cdots)q^{6}+\cdots$
400.2.j.e	$400$	$2$	400.j	80.j	$4$	$24$	$12$	$3.194$		$_{}$	None	None		✓	✓		400.2.j.e	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
400.2.l.a	$400$	$2$	400.l	16.e	$4$	$2$	$1$	$3.194$	$\Q(\sqrt{-1}) $	$_{}$	None	None					80.2.q.a	$2$	$1$	$-2$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+i)q^{2}+(-1+i)q^{3}-2iq^{4}+\cdots$
400.2.l.b	$400$	$2$	400.l	16.e	$4$	$2$	$1$	$3.194$	$\Q(\sqrt{-1}) $	$_{}$	None	None					80.2.q.a	$2$	$0$	$2$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1-i)q^{2}+(1-i)q^{3}-2iq^{4}-2iq^{6}+\cdots$
400.2.l.c	$400$	$2$	400.l	16.e	$4$	$2$	$1$	$3.194$	$\Q(\sqrt{-1}) $	$_{}$	None	None					16.2.e.a	$2$	$0$	$2$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+i)q^{2}+(1-i)q^{3}+2iq^{4}+2q^{6}+\cdots$
400.2.l.d	$400$	$2$	400.l	16.e	$4$	$4$	$2$	$3.194$	$\Q(i, \sqrt{11})$	$_{}$	None	None		✓			400.2.l.d	$2$	$0$	$-4$	$-2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-\beta _{1})q^{2}+(-\beta _{1}+\beta _{2})q^{3}+2\beta _{1}q^{4}+\cdots$
400.2.l.e	$400$	$2$	400.l	16.e	$4$	$4$	$2$	$3.194$	$\Q(i, \sqrt{11})$	$_{}$	None	None		✓			400.2.l.d	$2$	$0$	$4$	$2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+\beta _{1})q^{2}+(\beta _{1}-\beta _{2})q^{3}+2\beta _{1}q^{4}+\cdots$
400.2.l.f	$400$	$2$	400.l	16.e	$4$	$12$	$6$	$3.194$	12.0.$\cdots$.1	$_{}$	None	None		✓			400.2.l.f	$2$	$0$	$-4$	$-2$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{1}q^{2}-\beta _{6}q^{3}+\beta _{2}q^{4}+(\beta _{1}-\beta _{2}+\cdots)q^{6}+\cdots$
400.2.l.g	$400$	$2$	400.l	16.e	$4$	$12$	$6$	$3.194$	12.0.$\cdots$.1	$_{}$	None	None		✓			400.2.l.f	$2$	$0$	$4$	$2$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+\beta _{6}q^{3}+\beta _{2}q^{4}+(\beta _{1}-\beta _{2}+\cdots)q^{6}+\cdots$
400.2.l.h	$400$	$2$	400.l	16.e	$4$	$16$	$8$	$3.194$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None					80.2.l.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{8}q^{2}+(\beta _{4}+\beta _{11})q^{3}+(\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots$
400.2.l.i	$400$	$2$	400.l	16.e	$4$	$16$	$8$	$3.194$	16.0.$\cdots$.1	$_{}$	None	None					80.2.q.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{10}q^{2}+(-\beta _{2}+\beta _{9}+\beta _{12}-\beta _{14}+\cdots)q^{3}+\cdots$
400.2.n.a	$400$	$2$	400.n	20.e	$4$	$2$	$1$	$3.194$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None					80.2.n.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q-3iq^{9}+(5-5i)q^{13}+(5+5i)q^{17}+\cdots$
400.2.n.b	$400$	$2$	400.n	20.e	$4$	$4$	$2$	$3.194$	$\Q(\zeta_{12})$	$_{}$	None	None					80.2.n.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	$q-\zeta_{12}^{2}q^{3}+\zeta_{12}^{3}q^{7}+3\zeta_{12}q^{9}+\cdots$
400.2.n.c	$400$	$2$	400.n	20.e	$4$	$4$	$2$	$3.194$	$\Q(i, \sqrt{5})$	$_{}$	$\Q(\sqrt{-5}) $	None		✓			400.2.n.c	$8$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{U}(1)[D_{4}]$	$q-\beta _{3}q^{3}+\beta _{2}q^{7}-7\beta _{1}q^{9}+10q^{21}+\cdots$
400.2.n.d	$400$	$2$	400.n	20.e	$4$	$8$	$4$	$3.194$	$\Q(\zeta_{24})$	$_{}$	None	None		✓	✓		400.2.n.d	$8$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{24}q^{3}+4\zeta_{24}^{5}q^{7}-2\zeta_{24}^{3}q^{9}+\cdots$
400.2.q.a	$400$	$2$	400.q	80.q	$4$	$2$	$1$	$3.194$	$\Q(\sqrt{-1}) $	$_{}$	None	None					16.2.e.a	$2$	$1$	$-2$	$-2$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+i)q^{2}+(-1-i)q^{3}-2iq^{4}+\cdots$
400.2.q.b	$400$	$2$	400.q	80.q	$4$	$2$	$1$	$3.194$	$\Q(\sqrt{-1}) $	$_{}$	None	None					16.2.e.a	$2$	$0$	$2$	$2$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1-i)q^{2}+(1+i)q^{3}-2iq^{4}+2q^{6}+\cdots$
400.2.q.c	$400$	$2$	400.q	80.q	$4$	$4$	$2$	$3.194$	$\Q(i, \sqrt{11})$	$_{}$	None	None		✓			400.2.l.d	$2$	$0$	$-4$	$2$	$0$	$-4$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-\beta _{1})q^{2}+(\beta _{1}-\beta _{2})q^{3}+2\beta _{1}q^{4}+\cdots$
400.2.q.d	$400$	$2$	400.q	80.q	$4$	$4$	$2$	$3.194$	$\Q(i, \sqrt{11})$	$_{}$	None	None		✓			400.2.l.d	$2$	$0$	$4$	$-2$	$0$	$4$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+\beta _{1})q^{2}+(-1-\beta _{2})q^{3}+2\beta _{1}q^{4}+\cdots$
400.2.q.e	$400$	$2$	400.q	80.q	$4$	$12$	$6$	$3.194$	12.0.$\cdots$.1	$_{}$	None	None		✓			400.2.l.f	$2$	$0$	$-2$	$2$	$0$	$-12$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{6}q^{2}-\beta _{7}q^{3}+\beta _{10}q^{4}+(-\beta _{3}+\cdots)q^{6}+\cdots$
400.2.q.f	$400$	$2$	400.q	80.q	$4$	$12$	$6$	$3.194$	12.0.$\cdots$.1	$_{}$	None	None		✓			400.2.l.f	$2$	$0$	$2$	$-2$	$0$	$12$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{6}q^{2}+\beta _{7}q^{3}+\beta _{10}q^{4}+(-\beta _{3}+\cdots)q^{6}+\cdots$
400.2.q.g	$400$	$2$	400.q	80.q	$4$	$16$	$8$	$3.194$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None					80.2.l.a	$2$	$0$	$-4$	$0$	$0$	$-8$		$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{2}q^{2}+(-\beta _{6}-\beta _{11})q^{3}+(-\beta _{2}+\cdots)q^{4}+\cdots$
400.2.q.h	$400$	$2$	400.q	80.q	$4$	$16$	$8$	$3.194$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None					80.2.l.a	$2$	$0$	$4$	$0$	$0$	$8$		$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{2}q^{2}+(\beta _{6}+\beta _{11})q^{3}+(-\beta _{2}-\beta _{12}+\cdots)q^{4}+\cdots$
400.2.s.a	$400$	$2$	400.s	80.s	$4$	$2$	$1$	$3.194$	$\Q(\sqrt{-1}) $	$_{}$	None	None					80.2.j.a	$2$	$0$	$2$	$4$	$0$	$6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1-i)q^{2}+2q^{3}-2iq^{4}+(2-2i)q^{6}+\cdots$
400.2.s.b	$400$	$2$	400.s	80.s	$4$	$8$	$4$	$3.194$	$\Q(\zeta_{24})$	$_{}$	None	None		✓			400.2.j.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(\zeta_{24}-\zeta_{24}^{5})q^{2}+\zeta_{24}^{7}q^{3}-2q^{4}+\cdots$
400.2.s.c	$400$	$2$	400.s	80.s	$4$	$16$	$8$	$3.194$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			400.2.j.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{6}q^{2}+\beta _{5}q^{3}-\beta _{15}q^{4}+(-1-\beta _{11}+\cdots)q^{6}+\cdots$
400.2.s.d	$400$	$2$	400.s	80.s	$4$	$18$	$9$	$3.194$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	$_{}$	None	None					80.2.j.b	$2$	$0$	$0$	$0$	$0$	$-2$		$2^{7}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{2}q^{2}+\beta _{4}q^{3}-\beta _{14}q^{4}+(-1-\beta _{3}+\cdots)q^{6}+\cdots$
400.2.s.e	$400$	$2$	400.s	80.s	$4$	$24$	$12$	$3.194$		$_{}$	None	None		✓	✓		400.2.j.e	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
400.2.u.a	$400$	$2$	400.u	25.d	$5$	$4$	$1$	$3.194$	$\Q(\zeta_{10})$	$_{}$	None	None					200.2.m.a	$2$	$1$	$0$	$-5$	$-5$	$-6$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-2+2\zeta_{10}+\zeta_{10}^{3})q^{3}+(-2+\zeta_{10}+\cdots)q^{5}+\cdots$
400.2.u.b	$400$	$2$	400.u	25.d	$5$	$4$	$1$	$3.194$	$\Q(\zeta_{10})$	$_{}$	None	None					25.2.d.a	$2$	$0$	$0$	$1$	$-5$	$2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\zeta_{10}^{3}q^{3}+(-2+\zeta_{10}-2\zeta_{10}^{2}+\cdots)q^{5}+\cdots$
400.2.u.c	$400$	$2$	400.u	25.d	$5$	$4$	$1$	$3.194$	$\Q(\zeta_{10})$	$_{}$	None	None					50.2.d.a	$2$	$0$	$0$	$1$	$5$	$12$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}-2\zeta_{10}^{3})q^{3}+(2-2\zeta_{10}+\cdots)q^{5}+\cdots$
400.2.u.d	$400$	$2$	400.u	25.d	$5$	$8$	$2$	$3.194$	8.0.58140625.2	$_{}$	None	None					50.2.d.b	$2$	$0$	$0$	$3$	$0$	$-4$		$5$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{2}+\beta _{3}+\beta _{5}+\beta _{6})q^{3}+(\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots$
400.2.u.e	$400$	$2$	400.u	25.d	$5$	$8$	$2$	$3.194$	8.0.58140625.2	$_{}$	None	None					200.2.m.b	$2$	$0$	$0$	$6$	$5$	$-4$		$5$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\beta _{3})q^{3}+(-\beta _{4}+\beta _{6})q^{5}+(-1+\cdots)q^{7}+\cdots$

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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.