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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 368 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
192.1.h.a	$192$	$1$	192.h	24.h	$2$	$2$	$2$	$0.096$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-2}) $	$\Q(\sqrt{6}) $		✓	✓	✓	192.1.h.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{3}-q^{9}+2 i q^{19}-q^{25}+i q^{27}+\cdots$
192.2.a.a	$192$	$2$	192.a	1.a	$1$	$1$	$1$	$1.533$	$\Q$	$_{}$	None	None	✓		✓	✓	96.2.a.a	$1$	$1$	$0$	$-1$	$-2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}-4q^{7}+q^{9}-4q^{11}+\cdots$
192.2.a.b	$192$	$2$	192.a	1.a	$1$	$1$	$1$	$1.533$	$\Q$	$_{}$	None	None	✓		✓	✓	24.2.a.a	$1$	$0$	$0$	$-1$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots$
192.2.a.c	$192$	$2$	192.a	1.a	$1$	$1$	$1$	$1.533$	$\Q$	$_{}$	None	None	✓				96.2.a.a	$1$	$0$	$0$	$1$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}+4q^{7}+q^{9}+4q^{11}+\cdots$
192.2.a.d	$192$	$2$	192.a	1.a	$1$	$1$	$1$	$1.533$	$\Q$	$_{}$	None	None	✓				24.2.a.a	$1$	$0$	$0$	$1$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots$
192.2.c.a	$192$	$2$	192.c	12.b	$2$	$2$	$2$	$1.533$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None					48.2.c.a	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q-\beta q^{3}-2\beta q^{7}-3 q^{9}+2 q^{13}+\cdots$
192.2.c.b	$192$	$2$	192.c	12.b	$2$	$4$	$4$	$1.533$	$\Q(\zeta_{8})$	$_{}$	None	None			✓		96.2.c.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_1 q^{3}-\beta_{3} q^{5}+(-\beta_{2}+\beta_1)q^{7}+\cdots$
192.2.d.a	$192$	$2$	192.d	8.b	$2$	$4$	$4$	$1.533$	$\Q(\zeta_{12})$	$_{}$	None	None		✓	✓	✓	192.2.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_1 q^{3}-\beta_{2} q^{5}+\beta_{3} q^{7}-q^{9}+\cdots$
192.2.f.a	$192$	$2$	192.f	24.f	$2$	$4$	$4$	$1.533$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-6}) $	None		✓			192.2.f.a	$8$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta_{2} q^{3}-\beta_{3} q^{5}+\beta_1 q^{7}-3 q^{9}+\cdots$
192.2.f.b	$192$	$2$	192.f	24.f	$2$	$4$	$4$	$1.533$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-3}) $	None		✓			192.2.f.b	$8$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta_1 q^{3}-\beta_{3} q^{7}+3 q^{9}-\beta_{2} q^{13}+\cdots$
192.2.j.a	$192$	$2$	192.j	16.e	$4$	$8$	$4$	$1.533$	8.0.18939904.2	$_{}$	None	None			✓	✓	48.2.j.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{2}q^{3}+(-\beta _{3}+\beta _{5})q^{5}+(\beta _{4}+\beta _{5}+\cdots)q^{7}+\cdots$
192.2.k.a	$192$	$2$	192.k	48.k	$4$	$12$	$6$	$1.533$	12.0.$\cdots$.2	$_{}$	None	None			✓	✓	48.2.k.a	$4$	$0$	$0$	$2$	$0$	$8$		$2^{7}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{10}q^{3}+\beta _{7}q^{5}+(1-\beta _{11})q^{7}+(\beta _{3}+\cdots)q^{9}+\cdots$
192.2.r.a	$192$	$2$	192.r	64.i	$16$	$128$	$16$	$1.533$		$_{}$	None	None		✓	✓	✓	192.2.r.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{16}]$
192.2.s.a	$192$	$2$	192.s	192.s	$16$	$240$	$30$	$1.533$		$_{}$	None	None		✓	✓	✓	192.2.s.a	$4$	$0$	$0$	$-8$	$0$	$-16$			$\mathrm{SU}(2)[C_{16}]$
192.3.b.a	$192$	$3$	192.b	8.d	$2$	$4$	$4$	$5.232$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			192.3.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_1 q^{3}-\beta_{2} q^{5}+\beta_{3} q^{7}+3 q^{9}+\cdots$
192.3.b.b	$192$	$3$	192.b	8.d	$2$	$4$	$4$	$5.232$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			192.3.b.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_1 q^{3}-\beta_{2} q^{5}+5\beta_{3} q^{7}+3 q^{9}+\cdots$
192.3.e.a	$192$	$3$	192.e	3.b	$2$	$1$	$1$	$5.232$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓				12.3.c.a	$2$	$0$	$0$	$-3$	$0$	$-2$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-3q^{3}-2q^{7}+9q^{9}+22q^{13}+26q^{19}+\cdots$
192.3.e.b	$192$	$3$	192.e	3.b	$2$	$1$	$1$	$5.232$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓				12.3.c.a	$2$	$0$	$0$	$3$	$0$	$2$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+3q^{3}+2q^{7}+9q^{9}+22q^{13}-26q^{19}+\cdots$
192.3.e.c	$192$	$3$	192.e	3.b	$2$	$2$	$2$	$5.232$	$\Q(\sqrt{-2}) $	$_{}$	None	None					24.3.e.a	$2$	$0$	$0$	$-2$	$0$	$-12$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta )q^{3}-2\beta q^{5}-6q^{7}+(-7+\cdots)q^{9}+\cdots$
192.3.e.d	$192$	$3$	192.e	3.b	$2$	$2$	$2$	$5.232$	$\Q(\sqrt{-2}) $	$_{}$	None	None					24.3.e.a	$2$	$0$	$0$	$2$	$0$	$12$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\beta )q^{3}+2\beta q^{5}+6q^{7}+(-7+2\beta )q^{9}+\cdots$
192.3.e.e	$192$	$3$	192.e	3.b	$2$	$4$	$4$	$5.232$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	None	None					96.3.e.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{3}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-\beta _{2}q^{5}+(-2\beta _{1}+\beta _{3})q^{7}+\cdots$
192.3.e.f	$192$	$3$	192.e	3.b	$2$	$4$	$4$	$5.232$	$\Q(\sqrt{-2}, \sqrt{7})$	$_{}$	None	None					96.3.e.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}+\beta _{3})q^{3}+\beta _{2}q^{5}+(\beta _{1}+2\beta _{3})q^{7}+\cdots$
192.3.g.a	$192$	$3$	192.g	4.b	$2$	$2$	$2$	$5.232$	$\Q(\sqrt{-3}) $	$_{}$	None	None					48.3.g.a	$2$	$0$	$0$	$0$	$-12$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{3}-6 q^{5}+4\beta q^{7}-3 q^{9}+12\beta q^{11}+\cdots$
192.3.g.b	$192$	$3$	192.g	4.b	$2$	$2$	$2$	$5.232$	$\Q(\sqrt{-3}) $	$_{}$	None	None					12.3.d.a	$2$	$0$	$0$	$0$	$4$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{3}+2 q^{5}-4\beta q^{7}-3 q^{9}-4\beta q^{11}+\cdots$
192.3.g.c	$192$	$3$	192.g	4.b	$2$	$4$	$4$	$5.232$	$\Q(\zeta_{12})$	$_{}$	None	None			✓		96.3.g.a	$2$	$0$	$0$	$0$	$8$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_{2} q^{3}+(-\beta_{3}+2)q^{5}+(4\beta_{2}-\beta_1)q^{7}+\cdots$
192.3.h.a	$192$	$3$	192.h	24.h	$2$	$4$	$4$	$5.232$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-3}) $	None		✓			192.3.h.a	$8$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{U}(1)[D_{2}]$	$q+3\beta_1 q^{3}-\beta_{3} q^{7}-9 q^{9}-\beta_{2} q^{13}+\cdots$
192.3.h.b	$192$	$3$	192.h	24.h	$2$	$4$	$4$	$5.232$	$\Q(\zeta_{8})$	$_{}$	$\Q(\sqrt{-2}) $	None		✓			192.3.h.b	$8$	$0$	$0$	$0$	$0$	$0$		$2^{5}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta_{2} q^{3}+(-\beta_{3}+7)q^{9}+(-6\beta_{2}-3\beta_1)q^{11}+\cdots$
192.3.h.c	$192$	$3$	192.h	24.h	$2$	$8$	$8$	$5.232$	8.0.12960000.1	$_{}$	None	None		✓	✓		192.3.h.c	$8$	$0$	$0$	$0$	$0$	$0$		$2^{18}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}-\beta _{4}q^{5}-\beta _{1}q^{7}+(1-\beta _{5}+\cdots)q^{9}+\cdots$
192.3.i.a	$192$	$3$	192.i	48.i	$4$	$8$	$4$	$5.232$	8.0.629407744.1	$_{}$	None	None					48.3.i.a	$4$	$0$	$0$	$-4$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-\beta _{1}-\beta _{2}-\beta _{3}-\beta _{6}-\beta _{7})q^{3}+\cdots$
192.3.i.b	$192$	$3$	192.i	48.i	$4$	$20$	$10$	$5.232$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None			✓		48.3.i.b	$4$	$0$	$0$	$6$	$0$	$0$		$2^{23}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{4}q^{3}+(\beta _{8}-\beta _{9}-\beta _{10})q^{5}-\beta _{6}q^{7}+\cdots$
192.3.l.a	$192$	$3$	192.l	16.f	$4$	$16$	$8$	$5.232$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None			✓	✓	48.3.l.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{24}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{2}q^{3}-\beta _{9}q^{5}+\beta _{5}q^{7}-3\beta _{4}q^{9}+\cdots$
192.3.q.a	$192$	$3$	192.q	192.q	$16$	$496$	$62$	$5.232$		$_{}$	None	None		✓	✓	✓	192.3.q.a	$4$	$0$	$0$	$-8$	$0$	$-16$			$\mathrm{SU}(2)[C_{16}]$
192.3.t.a	$192$	$3$	192.t	64.j	$16$	$256$	$32$	$5.232$		$_{}$	None	None		✓	✓	✓	192.3.t.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{16}]$
192.4.a.a	$192$	$4$	192.a	1.a	$1$	$1$	$1$	$11.328$	$\Q$	$_{}$	None	None	✓				24.4.a.a	$1$	$0$	$0$	$-3$	$-14$	$-24$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-14q^{5}-24q^{7}+9q^{9}+28q^{11}+\cdots$
192.4.a.b	$192$	$4$	192.a	1.a	$1$	$1$	$1$	$11.328$	$\Q$	$_{}$	None	None	✓				96.4.a.c	$1$	$0$	$0$	$-3$	$-10$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-10q^{5}+4q^{7}+9q^{9}+20q^{11}+\cdots$
192.4.a.c	$192$	$4$	192.a	1.a	$1$	$1$	$1$	$11.328$	$\Q$	$_{}$	None	None	✓				6.4.a.a	$1$	$1$	$0$	$-3$	$-6$	$16$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-6q^{5}+2^{4}q^{7}+9q^{9}+12q^{11}+\cdots$
192.4.a.d	$192$	$4$	192.a	1.a	$1$	$1$	$1$	$11.328$	$\Q$	$_{}$	None	None	✓				96.4.a.b	$1$	$1$	$0$	$-3$	$-2$	$12$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-2q^{5}+12q^{7}+9q^{9}-60q^{11}+\cdots$
192.4.a.e	$192$	$4$	192.a	1.a	$1$	$1$	$1$	$11.328$	$\Q$	$_{}$	None	None	✓				96.4.a.a	$1$	$1$	$0$	$-3$	$14$	$-36$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+14q^{5}-6^{2}q^{7}+9q^{9}+6^{2}q^{11}+\cdots$
192.4.a.f	$192$	$4$	192.a	1.a	$1$	$1$	$1$	$11.328$	$\Q$	$_{}$	None	None	✓				12.4.a.a	$1$	$0$	$0$	$-3$	$18$	$8$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+18q^{5}+8q^{7}+9q^{9}-6^{2}q^{11}+\cdots$
192.4.a.g	$192$	$4$	192.a	1.a	$1$	$1$	$1$	$11.328$	$\Q$	$_{}$	None	None	✓				24.4.a.a	$1$	$0$	$0$	$3$	$-14$	$24$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-14q^{5}+24q^{7}+9q^{9}-28q^{11}+\cdots$
192.4.a.h	$192$	$4$	192.a	1.a	$1$	$1$	$1$	$11.328$	$\Q$	$_{}$	None	None	✓				96.4.a.c	$1$	$1$	$0$	$3$	$-10$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-10q^{5}-4q^{7}+9q^{9}-20q^{11}+\cdots$
192.4.a.i	$192$	$4$	192.a	1.a	$1$	$1$	$1$	$11.328$	$\Q$	$_{}$	None	None	✓				6.4.a.a	$1$	$1$	$0$	$3$	$-6$	$-16$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-6q^{5}-2^{4}q^{7}+9q^{9}-12q^{11}+\cdots$
192.4.a.j	$192$	$4$	192.a	1.a	$1$	$1$	$1$	$11.328$	$\Q$	$_{}$	None	None	✓				96.4.a.b	$1$	$0$	$0$	$3$	$-2$	$-12$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-2q^{5}-12q^{7}+9q^{9}+60q^{11}+\cdots$
192.4.a.k	$192$	$4$	192.a	1.a	$1$	$1$	$1$	$11.328$	$\Q$	$_{}$	None	None	✓				96.4.a.a	$1$	$0$	$0$	$3$	$14$	$36$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+14q^{5}+6^{2}q^{7}+9q^{9}-6^{2}q^{11}+\cdots$
192.4.a.l	$192$	$4$	192.a	1.a	$1$	$1$	$1$	$11.328$	$\Q$	$_{}$	None	None	✓				12.4.a.a	$1$	$0$	$0$	$3$	$18$	$-8$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+18q^{5}-8q^{7}+9q^{9}+6^{2}q^{11}+\cdots$
192.4.c.a	$192$	$4$	192.c	12.b	$2$	$2$	$2$	$11.328$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None					48.4.c.a	$4$	$0$	$0$	$0$	$0$	$0$		$2\cdot 3$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{3}-6\beta q^{7}-27 q^{9}-70 q^{13}+\cdots$
192.4.c.b	$192$	$4$	192.c	12.b	$2$	$4$	$4$	$11.328$	$\Q(\sqrt{3}, \sqrt{-5})$	$_{}$	None	None					12.4.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{3}+\beta _{2}q^{5}+(\beta _{1}-\beta _{3})q^{7}+(-3+\cdots)q^{9}+\cdots$
192.4.c.c	$192$	$4$	192.c	12.b	$2$	$4$	$4$	$11.328$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	None	None					48.4.c.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{6}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}+\beta _{3}q^{5}-5\beta _{1}q^{7}+(21-\beta _{3})q^{9}+\cdots$
192.4.c.d	$192$	$4$	192.c	12.b	$2$	$12$	$12$	$11.328$	12.0.$\cdots$.1	$_{}$	None	None			✓		96.4.c.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{44}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{3}+\beta _{8}q^{5}+\beta _{1}q^{7}+(-2+\beta _{5}+\cdots)q^{9}+\cdots$
192.4.d.a	$192$	$4$	192.d	8.b	$2$	$4$	$4$	$11.328$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			192.4.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-3\beta_1 q^{3}-3\beta_{2} q^{5}-\beta_{3} q^{7}-9 q^{9}+\cdots$

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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.