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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 196 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
196.1.c.a	$196$	$1$	196.c	4.b	$2$	$1$	$1$	$0.098$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-7}) $	$\Q(\sqrt{7}) $	✓	✓	✓	✓	196.1.c.a	$4$	$0$	$-1$	$0$	$0$	$0$		$1$		$q-q^{2}+q^{4}-q^{8}+q^{9}+q^{16}-q^{18}+\cdots$
196.1.g.a	$196$	$1$	196.g	28.g	$6$	$2$	$1$	$0.098$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-7}) $	$\Q(\sqrt{7}) $		✓	✓	✓	196.1.c.a	$8$	$0$	$1$	$0$	$0$	$0$		$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-q^{8}+\zeta_{6}^{2}q^{9}+\cdots$
196.2.a.a	$196$	$2$	196.a	1.a	$1$	$1$	$1$	$1.565$	$\Q$	$_{}$	None	None	✓		✓	✓	28.2.e.a	$1$	$1$	$0$	$-1$	$-3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{5}-2q^{9}-3q^{11}-2q^{13}+\cdots$
196.2.a.b	$196$	$2$	196.a	1.a	$1$	$1$	$1$	$1.565$	$\Q$	$_{}$	None	None	✓				28.2.e.a	$1$	$0$	$0$	$1$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{5}-2q^{9}-3q^{11}+2q^{13}+\cdots$
196.2.a.c	$196$	$2$	196.a	1.a	$1$	$2$	$2$	$1.565$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓	✓		196.2.a.c	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2\beta q^{3}-\beta q^{5}+5q^{9}+4q^{11}-3\beta q^{13}+\cdots$
196.2.d.a	$196$	$2$	196.d	28.d	$2$	$4$	$4$	$1.565$	4.0.2048.2	$_{}$	$\Q(\sqrt{-1}) $	None		✓			196.2.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$7$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{2}q^{2}+2q^{4}+\beta _{1}q^{5}-2\beta _{2}q^{8}+\cdots$
196.2.d.b	$196$	$2$	196.d	28.d	$2$	$4$	$4$	$1.565$	$\Q(\zeta_{12})$	$_{}$	None	None					28.2.f.a	$4$	$0$	$4$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta_1+1)q^{2}+\beta_{3} q^{3}+2\beta_1 q^{4}+\cdots$
196.2.d.c	$196$	$2$	196.d	28.d	$2$	$8$	$8$	$1.565$	8.0.$\cdots$.10	$_{}$	None	None		✓	✓		196.2.d.c	$4$	$0$	$-4$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta _{5})q^{2}+(-2\beta _{1}-\beta _{7})q^{3}+\cdots$
196.2.e.a	$196$	$2$	196.e	7.c	$3$	$2$	$1$	$1.565$	$\Q(\sqrt{-3}) $	$_{}$	None	None					28.2.e.a	$2$	$0$	$0$	$1$	$3$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}+3\zeta_{6}q^{5}+2\zeta_{6}q^{9}+(3+\cdots)q^{11}+\cdots$
196.2.e.b	$196$	$2$	196.e	7.c	$3$	$4$	$2$	$1.565$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		✓	✓		196.2.a.c	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+2\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{5}+5\beta _{2}q^{9}+\cdots$
196.2.f.a	$196$	$2$	196.f	28.f	$6$	$4$	$2$	$1.565$	$\Q(\zeta_{12})$	$_{}$	None	None					28.2.f.a	$4$	$0$	$-2$	$0$	$6$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\cdots)q^{3}+\cdots$
196.2.f.b	$196$	$2$	196.f	28.f	$6$	$4$	$2$	$1.565$	$\Q(\sqrt{-3}, \sqrt{-7})$	$_{}$	$\Q(\sqrt{-7}) $	None					28.2.d.a	$8$	$0$	$1$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+\beta _{3}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(3-\beta _{1}+\cdots)q^{8}+\cdots$
196.2.f.c	$196$	$2$	196.f	28.f	$6$	$8$	$4$	$1.565$	8.0.339738624.1	$_{}$	$\Q(\sqrt{-1}) $	None		✓			196.2.d.a	$8$	$0$	$0$	$0$	$0$	$0$		$7^{2}$	$\mathrm{U}(1)[D_{6}]$	$q+(-\beta _{2}-\beta _{5})q^{2}+2\beta _{4}q^{4}-\beta _{3}q^{5}+\cdots$
196.2.f.d	$196$	$2$	196.f	28.f	$6$	$16$	$8$	$1.565$	16.0.$\cdots$.2	$_{}$	None	None		✓	✓		196.2.d.c	$8$	$0$	$4$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{6}-\beta _{11})q^{2}+(2\beta _{1}+\beta _{3})q^{3}+\cdots$
196.2.i.a	$196$	$2$	196.i	49.e	$7$	$24$	$4$	$1.565$		$_{}$	None	None		✓	✓	✓	196.2.i.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{7}]$
196.2.j.a	$196$	$2$	196.j	196.j	$14$	$156$	$26$	$1.565$		$_{}$	None	None		✓	✓	✓	196.2.j.a	$4$	$0$	$-5$	$0$	$-14$	$0$			$\mathrm{SU}(2)[C_{14}]$
196.2.m.a	$196$	$2$	196.m	49.g	$21$	$60$	$5$	$1.565$		$_{}$	None	None		✓	✓	✓	196.2.m.a	$2$	$0$	$0$	$1$	$3$	$4$			$\mathrm{SU}(2)[C_{21}]$
196.2.p.a	$196$	$2$	196.p	196.p	$42$	$312$	$26$	$1.565$		$_{}$	None	None		✓	✓	✓	196.2.p.a	$4$	$0$	$-13$	$0$	$-22$	$0$			$\mathrm{SU}(2)[C_{42}]$
196.3.b.a	$196$	$3$	196.b	7.b	$2$	$2$	$2$	$5.341$	$\Q(\sqrt{-3}) $	$_{}$	None	None					28.3.h.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{3}+\beta q^{5}+6 q^{9}+15 q^{11}+\cdots$
196.3.b.b	$196$	$3$	196.b	7.b	$2$	$4$	$4$	$5.341$	4.0.2048.2	$_{}$	None	None		✓	✓		196.3.b.b	$2$	$0$	$0$	$0$	$0$	$0$		$7^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}+(\beta _{1}+2\beta _{2})q^{5}+(-1-\beta _{3})q^{9}+\cdots$
196.3.c.a	$196$	$3$	196.c	4.b	$2$	$2$	$2$	$5.341$	$\Q(\sqrt{2}) $	$_{}$	$\Q(\sqrt{-1}) $	None	✓	✓			196.3.c.a	$4$	$0$	$-4$	$0$	$0$	$0$		$7$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{2}+4q^{4}+\beta q^{5}-8q^{8}+9q^{9}+\cdots$
196.3.c.b	$196$	$3$	196.c	4.b	$2$	$2$	$2$	$5.341$	$\Q(\sqrt{-7}) $	$_{}$	$\Q(\sqrt{-7}) $	None		✓			196.3.c.b	$4$	$0$	$3$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(1+\beta )q^{2}+(-1+3\beta )q^{4}+(-7+5\beta )q^{8}+\cdots$
196.3.c.c	$196$	$3$	196.c	4.b	$2$	$2$	$2$	$5.341$	$\Q(\sqrt{2}) $	$_{}$	$\Q(\sqrt{-1}) $	None	✓	✓			196.3.c.c	$4$	$0$	$4$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{2}+4q^{4}+\beta q^{5}+8q^{8}+9q^{9}+\cdots$
196.3.c.d	$196$	$3$	196.c	4.b	$2$	$4$	$4$	$5.341$	$\Q(\sqrt{-3}, \sqrt{-5})$	$_{}$	None	None		✓			196.3.c.d	$4$	$0$	$-4$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta _{2})q^{2}+\beta _{1}q^{3}+(-2-2\beta _{2}+\cdots)q^{4}+\cdots$
196.3.c.e	$196$	$3$	196.c	4.b	$2$	$4$	$4$	$5.341$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		✓			196.3.c.e	$4$	$0$	$-4$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta _{2})q^{2}+\beta _{3}q^{3}+(-2-2\beta _{2}+\cdots)q^{4}+\cdots$
196.3.c.f	$196$	$3$	196.c	4.b	$2$	$4$	$4$	$5.341$	$\Q(\sqrt{2}, \sqrt{-15})$	$_{}$	None	None		✓			196.3.c.f	$4$	$0$	$2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(2\beta _{2}+\beta _{3})q^{3}+(-4+\beta _{1}+\cdots)q^{4}+\cdots$
196.3.c.g	$196$	$3$	196.c	4.b	$2$	$6$	$6$	$5.341$	6.0.1539727.2	$_{}$	None	None					28.3.c.a	$2$	$0$	$-1$	$0$	$4$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}-\beta _{3}q^{3}+\beta _{4}q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots$
196.3.c.h	$196$	$3$	196.c	4.b	$2$	$6$	$6$	$5.341$	6.0.15582448.1	$_{}$	None	None					28.3.g.a	$2$	$0$	$2$	$0$	$-2$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}-\beta _{2}q^{3}+(1-\beta _{4})q^{4}+(-1+\cdots)q^{5}+\cdots$
196.3.c.i	$196$	$3$	196.c	4.b	$2$	$6$	$6$	$5.341$	6.0.15582448.1	$_{}$	None	None					28.3.g.a	$2$	$0$	$2$	$0$	$2$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+\beta _{2}q^{3}+(1-\beta _{4})q^{4}+(1-\beta _{4}+\cdots)q^{5}+\cdots$
196.3.g.a	$196$	$3$	196.g	28.g	$6$	$4$	$2$	$5.341$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	$\Q(\sqrt{-1}) $	None		✓			196.3.c.c	$8$	$0$	$-4$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+2\beta _{2}q^{2}+(-4-4\beta _{2})q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots$
196.3.g.b	$196$	$3$	196.g	28.g	$6$	$4$	$2$	$5.341$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		✓			196.3.c.e	$4$	$0$	$-4$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+2\beta _{2}q^{2}+(\beta _{1}-\beta _{3})q^{3}+(-4-4\beta _{2}+\cdots)q^{4}+\cdots$
196.3.g.c	$196$	$3$	196.g	28.g	$6$	$4$	$2$	$5.341$	$\Q(\sqrt{-3}, \sqrt{-5})$	$_{}$	None	None		✓			196.3.c.d	$4$	$0$	$-4$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-2+2\beta _{2})q^{2}-\beta _{1}q^{3}-4\beta _{2}q^{4}+\cdots$
196.3.g.d	$196$	$3$	196.g	28.g	$6$	$4$	$2$	$5.341$	$\Q(\sqrt{-3}, \sqrt{-7})$	$_{}$	$\Q(\sqrt{-7}) $	None		✓			196.3.c.b	$8$	$0$	$-3$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(-2\beta _{2}+\beta _{3})q^{2}+(1-3\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
196.3.g.e	$196$	$3$	196.g	28.g	$6$	$4$	$2$	$5.341$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	$\Q(\sqrt{-1}) $	None		✓			196.3.c.a	$8$	$0$	$4$	$0$	$0$	$0$		$7^{2}$	$\mathrm{U}(1)[D_{6}]$	$q+(2+2\beta _{2})q^{2}+4\beta _{2}q^{4}+\beta _{1}q^{5}-8q^{8}+\cdots$
196.3.g.f	$196$	$3$	196.g	28.g	$6$	$4$	$2$	$5.341$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		✓			196.3.c.e	$4$	$0$	$8$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+2q^{2}+(\beta _{1}-\beta _{3})q^{3}+4q^{4}+4\beta _{1}q^{5}+\cdots$
196.3.g.g	$196$	$3$	196.g	28.g	$6$	$4$	$2$	$5.341$	$\Q(\sqrt{-3}, \sqrt{-5})$	$_{}$	None	None		✓			196.3.c.d	$4$	$0$	$8$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+2q^{2}+\beta _{1}q^{3}+4q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots$
196.3.g.h	$196$	$3$	196.g	28.g	$6$	$8$	$4$	$5.341$	8.0.207360000.1	$_{}$	None	None		✓			196.3.c.f	$8$	$0$	$-2$	$0$	$0$	$0$		$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{2}-\beta _{3})q^{2}+(\beta _{1}-2\beta _{4}-2\beta _{5}-2\beta _{7})q^{3}+\cdots$
196.3.g.i	$196$	$3$	196.g	28.g	$6$	$12$	$6$	$5.341$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None					28.3.g.a	$4$	$0$	$-2$	$0$	$2$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{6}q^{2}-\beta _{4}q^{3}+(-\beta _{1}+\beta _{5}+\beta _{9}+\cdots)q^{4}+\cdots$
196.3.g.j	$196$	$3$	196.g	28.g	$6$	$12$	$6$	$5.341$	12.0.$\cdots$.1	$_{}$	None	None					28.3.c.a	$4$	$0$	$1$	$0$	$-4$	$0$		$2^{12}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+\beta _{6}q^{3}-\beta _{4}q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots$
196.3.g.k	$196$	$3$	196.g	28.g	$6$	$12$	$6$	$5.341$	12.0.$\cdots$.1	$_{}$	None	None					28.3.c.a	$4$	$0$	$1$	$0$	$4$	$0$		$2^{12}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}-\beta _{6}q^{3}-\beta _{4}q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots$
196.3.h.a	$196$	$3$	196.h	7.d	$6$	$2$	$1$	$5.341$	$\Q(\sqrt{-3}) $	$_{}$	None	None					28.3.h.a	$2$	$0$	$0$	$-3$	$-3$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1-\zeta_{6})q^{3}+(-2+\zeta_{6})q^{5}-6\zeta_{6}q^{9}+\cdots$
196.3.h.b	$196$	$3$	196.h	7.d	$6$	$4$	$2$	$5.341$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None					28.3.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{3}q^{3}+(-\beta _{2}+\beta _{3})q^{5}+(15+15\beta _{1}+\cdots)q^{9}+\cdots$
196.3.h.c	$196$	$3$	196.h	7.d	$6$	$8$	$4$	$5.341$	8.0.339738624.1	$_{}$	None	None		✓	✓		196.3.b.b	$4$	$0$	$0$	$0$	$0$	$0$		$7^{4}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{3}q^{3}+(-\beta _{1}+\beta _{2}-2\beta _{6})q^{5}+(1+\cdots)q^{9}+\cdots$
196.3.k.a	$196$	$3$	196.k	196.k	$14$	$324$	$54$	$5.341$		$_{}$	None	None		✓	✓	✓	196.3.k.a	$4$	$0$	$-5$	$0$	$-10$	$0$			$\mathrm{SU}(2)[C_{14}]$
196.3.l.a	$196$	$3$	196.l	49.f	$14$	$60$	$10$	$5.341$		$_{}$	None	None		✓	✓	✓	196.3.l.a	$2$	$0$	$0$	$0$	$0$	$-10$			$\mathrm{SU}(2)[C_{14}]$
196.3.n.a	$196$	$3$	196.n	49.h	$42$	$108$	$9$	$5.341$		$_{}$	None	None		✓	✓	✓	196.3.n.a	$2$	$0$	$0$	$-3$	$-3$	$14$			$\mathrm{SU}(2)[C_{42}]$
196.3.o.a	$196$	$3$	196.o	196.o	$42$	$648$	$54$	$5.341$		$_{}$	None	None		✓	✓	✓	196.3.o.a	$4$	$0$	$-13$	$0$	$-26$	$0$			$\mathrm{SU}(2)[C_{42}]$
196.4.a.a	$196$	$4$	196.a	1.a	$1$	$1$	$1$	$11.564$	$\Q$	$_{}$	None	None	✓	✓			196.4.a.a	$1$	$0$	$0$	$-4$	$-20$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{3}-20q^{5}-11q^{9}+44q^{11}+\cdots$
196.4.a.b	$196$	$4$	196.a	1.a	$1$	$1$	$1$	$11.564$	$\Q$	$_{}$	None	None	✓				28.4.a.b	$1$	$0$	$0$	$-4$	$-6$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{3}-6q^{5}-11q^{9}-12q^{11}+82q^{13}+\cdots$
196.4.a.c	$196$	$4$	196.a	1.a	$1$	$1$	$1$	$11.564$	$\Q$	$_{}$	None	None	✓	✓			196.4.a.a	$1$	$0$	$0$	$4$	$20$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+4q^{3}+20q^{5}-11q^{9}+44q^{11}+\cdots$

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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.