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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 273 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				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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
294.2.a.a	$294$	$2$	294.a	1.a	$1$	$1$	$1$	$2.348$	$\Q$	None	✓				42.2.e.b	$1$	$0$	$-1$	$-1$	$-3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-3q^{5}+q^{6}-q^{8}+\cdots$
294.2.a.b	$294$	$2$	294.a	1.a	$1$	$1$	$1$	$2.348$	$\Q$	None	✓	✓			294.2.a.b	$1$	$0$	$-1$	$-1$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+4q^{5}+q^{6}-q^{8}+\cdots$
294.2.a.c	$294$	$2$	294.a	1.a	$1$	$1$	$1$	$2.348$	$\Q$	None	✓	✓	✓	✓	294.2.a.b	$1$	$1$	$-1$	$1$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-4q^{5}-q^{6}-q^{8}+\cdots$
294.2.a.d	$294$	$2$	294.a	1.a	$1$	$1$	$1$	$2.348$	$\Q$	None	✓		✓	✓	42.2.e.b	$1$	$0$	$-1$	$1$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}-q^{8}+\cdots$
294.2.a.e	$294$	$2$	294.a	1.a	$1$	$1$	$1$	$2.348$	$\Q$	None	✓		✓	✓	42.2.e.a	$1$	$0$	$1$	$-1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots$
294.2.a.f	$294$	$2$	294.a	1.a	$1$	$1$	$1$	$2.348$	$\Q$	None	✓				42.2.e.a	$1$	$0$	$1$	$1$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots$
294.2.a.g	$294$	$2$	294.a	1.a	$1$	$1$	$1$	$2.348$	$\Q$	None	✓				42.2.a.a	$1$	$0$	$1$	$1$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+q^{8}+\cdots$
294.2.d.a	$294$	$2$	294.d	21.c	$2$	$4$	$4$	$2.348$	$\Q(\zeta_{12})$	None					42.2.f.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_1 q^{2}+\beta_{3} q^{3}-q^{4}+\beta_{3} q^{5}+\cdots$
294.2.d.b	$294$	$2$	294.d	21.c	$2$	$8$	$8$	$2.348$	$\Q(\zeta_{16})$	None		✓	✓		294.2.d.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{16}^{4}q^{2}+(\zeta_{16}+\zeta_{16}^{5}+\zeta_{16}^{7})q^{3}+\cdots$
294.2.e.a	$294$	$2$	294.e	7.c	$3$	$2$	$1$	$2.348$	$\Q(\sqrt{-3}) $	None					42.2.a.a	$2$	$0$	$-1$	$-1$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
294.2.e.b	$294$	$2$	294.e	7.c	$3$	$2$	$1$	$2.348$	$\Q(\sqrt{-3}) $	None					42.2.e.a	$2$	$0$	$-1$	$-1$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
294.2.e.c	$294$	$2$	294.e	7.c	$3$	$2$	$1$	$2.348$	$\Q(\sqrt{-3}) $	None					42.2.a.a	$2$	$0$	$-1$	$1$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
294.2.e.d	$294$	$2$	294.e	7.c	$3$	$2$	$1$	$2.348$	$\Q(\sqrt{-3}) $	None		✓			294.2.a.b	$2$	$0$	$1$	$-1$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
294.2.e.e	$294$	$2$	294.e	7.c	$3$	$2$	$1$	$2.348$	$\Q(\sqrt{-3}) $	None		✓			294.2.a.b	$2$	$0$	$1$	$1$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
294.2.e.f	$294$	$2$	294.e	7.c	$3$	$2$	$1$	$2.348$	$\Q(\sqrt{-3}) $	None					42.2.e.b	$2$	$0$	$1$	$1$	$3$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
294.2.f.a	$294$	$2$	294.f	21.g	$6$	$4$	$2$	$2.348$	$\Q(\zeta_{12})$	None					42.2.f.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$
294.2.f.b	$294$	$2$	294.f	21.g	$6$	$8$	$4$	$2.348$	$\Q(\zeta_{24})$	None					42.2.d.a	$8$	$0$	$0$	$0$	$0$	$0$		$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta_{4}-\beta_1)q^{2}-\beta_{6} q^{3}+(-\beta_{2}+1)q^{4}+\cdots$
294.2.f.c	$294$	$2$	294.f	21.g	$6$	$16$	$8$	$2.348$	$\Q(\zeta_{48})$	None		✓	✓		294.2.d.b	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(\zeta_{48}^{4}-\zeta_{48}^{12})q^{2}+(\zeta_{48}+\zeta_{48}^{3}+\cdots)q^{3}+\cdots$
294.2.i.a	$294$	$2$	294.i	49.e	$7$	$6$	$1$	$2.348$	$\Q(\zeta_{14})$	None		✓			294.2.i.a	$2$	$0$	$-1$	$-1$	$5$	$7$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(-1+\zeta_{14}-\zeta_{14}^{2}+\zeta_{14}^{3}-\zeta_{14}^{4}+\cdots)q^{2}+\cdots$
294.2.i.b	$294$	$2$	294.i	49.e	$7$	$12$	$2$	$2.348$	12.0.$\cdots$.1	None		✓			294.2.i.b	$2$	$0$	$2$	$-2$	$1$	$0$		$7$	$\mathrm{SU}(2)[C_{7}]$	$q-\beta _{1}q^{2}+\beta _{9}q^{3}-\beta _{4}q^{4}+(-\beta _{5}+\beta _{6}+\cdots)q^{5}+\cdots$
294.2.i.c	$294$	$2$	294.i	49.e	$7$	$12$	$2$	$2.348$	12.0.$\cdots$.1	None		✓			294.2.i.c	$2$	$0$	$2$	$2$	$-1$	$0$		$7$	$\mathrm{SU}(2)[C_{7}]$	$q+(1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{9})q^{2}+\cdots$
294.2.i.d	$294$	$2$	294.i	49.e	$7$	$18$	$3$	$2.348$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None		✓	✓		294.2.i.d	$2$	$0$	$-3$	$3$	$3$	$1$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q-\beta _{4}q^{2}+(1-\beta _{4}-\beta _{7}-\beta _{10}-\beta _{11}+\cdots)q^{3}+\cdots$
294.2.j.a	$294$	$2$	294.j	147.k	$14$	$120$	$20$	$2.348$		None		✓	✓	✓	294.2.j.a	$4$	$0$	$0$	$0$	$0$	$4$			$\mathrm{SU}(2)[C_{14}]$
294.2.m.a	$294$	$2$	294.m	49.g	$21$	$24$	$2$	$2.348$		None		✓			294.2.m.a	$2$	$0$	$-2$	$-2$	$1$	$0$			$\mathrm{SU}(2)[C_{21}]$
294.2.m.b	$294$	$2$	294.m	49.g	$21$	$24$	$2$	$2.348$		None		✓			294.2.m.b	$2$	$0$	$2$	$2$	$1$	$0$			$\mathrm{SU}(2)[C_{21}]$
294.2.m.c	$294$	$2$	294.m	49.g	$21$	$36$	$3$	$2.348$		None		✓			294.2.m.c	$2$	$0$	$-3$	$3$	$2$	$-5$			$\mathrm{SU}(2)[C_{21}]$
294.2.m.d	$294$	$2$	294.m	49.g	$21$	$36$	$3$	$2.348$		None		✓			294.2.m.d	$2$	$0$	$3$	$-3$	$0$	$-1$			$\mathrm{SU}(2)[C_{21}]$
294.2.p.a	$294$	$2$	294.p	147.o	$42$	$216$	$18$	$2.348$		None		✓	✓	✓	294.2.p.a	$4$	$0$	$0$	$0$	$0$	$10$			$\mathrm{SU}(2)[C_{42}]$
294.3.b.a	$294$	$3$	294.b	3.b	$2$	$2$	$2$	$8.011$	$\Q(\sqrt{-2}) $	None		✓			294.3.b.a	$2$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}+(-1-2\beta )q^{3}-2q^{4}+\beta q^{5}+\cdots$
294.3.b.b	$294$	$3$	294.b	3.b	$2$	$2$	$2$	$8.011$	$\Q(\sqrt{-2}) $	None					42.3.h.a	$2$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}+(-1-2\beta )q^{3}-2q^{4}-6\beta q^{5}+\cdots$
294.3.b.c	$294$	$3$	294.b	3.b	$2$	$2$	$2$	$8.011$	$\Q(\sqrt{-2}) $	None					42.3.h.a	$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}+(1+2\beta )q^{3}-2q^{4}+6\beta q^{5}+\cdots$
294.3.b.d	$294$	$3$	294.b	3.b	$2$	$2$	$2$	$8.011$	$\Q(\sqrt{-2}) $	None		✓			294.3.b.a	$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}+(1+2\beta )q^{3}-2q^{4}-\beta q^{5}+\cdots$
294.3.b.e	$294$	$3$	294.b	3.b	$2$	$4$	$4$	$8.011$	$\Q(\sqrt{-2}, \sqrt{-11})$	None					42.3.h.b	$2$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+(-\beta _{1}-\beta _{2}-\beta _{3})q^{3}-2q^{4}+\cdots$
294.3.b.f	$294$	$3$	294.b	3.b	$2$	$4$	$4$	$8.011$	$\Q(\zeta_{8})$	None		✓			294.3.b.f	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_{2} q^{2}+3\beta_1 q^{3}-2 q^{4}-8\beta_1 q^{5}+\cdots$
294.3.b.g	$294$	$3$	294.b	3.b	$2$	$4$	$4$	$8.011$	$\Q(\zeta_{8})$	None		✓			294.3.b.g	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_{2} q^{2}+(2\beta_{3}+\beta_1)q^{3}-2 q^{4}+\cdots$
294.3.b.h	$294$	$3$	294.b	3.b	$2$	$4$	$4$	$8.011$	$\Q(\sqrt{-2}, \sqrt{7})$	None					42.3.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{3})q^{3}-2q^{4}+(-2\beta _{1}+\cdots)q^{5}+\cdots$
294.3.b.i	$294$	$3$	294.b	3.b	$2$	$4$	$4$	$8.011$	$\Q(\sqrt{-2}, \sqrt{-11})$	None					42.3.h.b	$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+(\beta _{1}+\beta _{2}+\beta _{3})q^{3}-2q^{4}+\cdots$
294.3.c.a	$294$	$3$	294.c	7.b	$2$	$4$	$4$	$8.011$	$\Q(\sqrt{2}, \sqrt{-3})$	None					42.3.g.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{2}q^{3}+2q^{4}+(2\beta _{2}-2\beta _{3})q^{5}+\cdots$
294.3.c.b	$294$	$3$	294.c	7.b	$2$	$8$	$8$	$8.011$	8.0.339738624.1	None		✓	✓		294.3.c.b	$2$	$0$	$0$	$0$	$0$	$0$		$2^{4}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{2}q^{3}+2q^{4}+(\beta _{4}-2\beta _{7})q^{5}+\cdots$
294.3.g.a	$294$	$3$	294.g	7.d	$6$	$4$	$2$	$8.011$	$\Q(\sqrt{2}, \sqrt{-3})$	None					42.3.g.a	$2$	$0$	$0$	$-6$	$-12$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+(-2-\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots$
294.3.g.b	$294$	$3$	294.g	7.d	$6$	$4$	$2$	$8.011$	$\Q(\sqrt{2}, \sqrt{-3})$	None					42.3.c.a	$2$	$0$	$0$	$-6$	$12$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+(-2-\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots$
294.3.g.c	$294$	$3$	294.g	7.d	$6$	$4$	$2$	$8.011$	$\Q(\sqrt{2}, \sqrt{-3})$	None					42.3.c.a	$2$	$0$	$0$	$6$	$-12$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{3}+2\beta _{2}q^{4}+(-2+\cdots)q^{5}+\cdots$
294.3.g.d	$294$	$3$	294.g	7.d	$6$	$8$	$4$	$8.011$	8.0.339738624.1	None		✓			294.3.c.b	$2$	$0$	$0$	$-12$	$0$	$0$		$7^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{2}+\beta _{5})q^{2}+(-2-\beta _{4})q^{3}+2\beta _{4}q^{4}+\cdots$
294.3.g.e	$294$	$3$	294.g	7.d	$6$	$8$	$4$	$8.011$	8.0.339738624.1	None		✓			294.3.c.b	$2$	$0$	$0$	$12$	$0$	$0$		$7^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{2}+\beta _{5})q^{2}+(2+\beta _{4})q^{3}+2\beta _{4}q^{4}+\cdots$
294.3.h.a	$294$	$3$	294.h	21.h	$6$	$4$	$2$	$8.011$	$\Q(\sqrt{-2}, \sqrt{-3})$	None		✓			294.3.b.a	$4$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+(-2\beta _{1}-\beta _{2}+2\beta _{3})q^{3}+\cdots$
294.3.h.b	$294$	$3$	294.h	21.h	$6$	$4$	$2$	$8.011$	$\Q(\sqrt{-2}, \sqrt{-3})$	None					42.3.h.a	$4$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+(-2\beta _{1}-\beta _{2}+2\beta _{3})q^{3}+\cdots$
294.3.h.c	$294$	$3$	294.h	21.h	$6$	$4$	$2$	$8.011$	$\Q(\sqrt{-2}, \sqrt{-3})$	None		✓			294.3.b.a	$4$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+(2\beta _{1}+\beta _{2}-2\beta _{3})q^{3}+2\beta _{2}q^{4}+\cdots$
294.3.h.d	$294$	$3$	294.h	21.h	$6$	$8$	$4$	$8.011$	8.0.$\cdots$.5	None					42.3.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{4}q^{2}+(-\beta _{1}+\beta _{4}-\beta _{5}-\beta _{6})q^{3}+\cdots$
294.3.h.e	$294$	$3$	294.h	21.h	$6$	$8$	$4$	$8.011$	$\Q(\zeta_{24})$	None		✓			294.3.b.g	$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta_{5} q^{2}+(2\beta_{7}-2\beta_{4}+\beta_1)q^{3}+\cdots$
294.3.h.f	$294$	$3$	294.h	21.h	$6$	$8$	$4$	$8.011$	$\Q(\zeta_{24})$	None		✓			294.3.b.f	$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta_{5} q^{2}-3\beta_1 q^{3}+(-2\beta_{2}+2)q^{4}+\cdots$

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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.