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Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Results (1-50 of 187 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
338.2.a.a	$338$	$2$	338.a	1.a	$1$	$1$	$1$	$2.699$	$\Q$	None	✓	$1$	$1$	$-1$	$-3$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-3q^{3}+q^{4}+q^{5}+3q^{6}-q^{7}+\cdots$
338.2.a.b	$338$	$2$	338.a	1.a	$1$	$1$	$1$	$2.699$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$3$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+3q^{5}+q^{6}+3q^{7}+\cdots$
338.2.a.c	$338$	$2$	338.a	1.a	$1$	$1$	$1$	$2.699$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-4q^{7}-q^{8}-3q^{9}+\cdots$
338.2.a.d	$338$	$2$	338.a	1.a	$1$	$1$	$1$	$2.699$	$\Q$	None	✓	$1$	$1$	$1$	$-1$	$-3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-3q^{5}-q^{6}-3q^{7}+\cdots$
338.2.a.e	$338$	$2$	338.a	1.a	$1$	$1$	$1$	$2.699$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+4q^{7}+q^{8}-3q^{9}+\cdots$
338.2.a.f	$338$	$2$	338.a	1.a	$1$	$1$	$1$	$2.699$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+3q^{5}+q^{6}+q^{7}+\cdots$
338.2.a.g	$338$	$2$	338.a	1.a	$1$	$3$	$3$	$2.699$	$\Q(\zeta_{14})^+$	None	✓	$1$	$0$	$-3$	$3$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+q^{4}-2\beta _{1}q^{5}+\cdots$
338.2.a.h	$338$	$2$	338.a	1.a	$1$	$3$	$3$	$2.699$	$\Q(\zeta_{14})^+$	None	✓	$1$	$0$	$3$	$3$	$2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+q^{4}+2\beta _{1}q^{5}+\cdots$
338.2.b.a	$338$	$2$	338.b	13.b	$2$	$2$	$2$	$2.699$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$-6$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}-3q^{3}-q^{4}-iq^{5}-3iq^{6}+\cdots$
338.2.b.b	$338$	$2$	338.b	13.b	$2$	$2$	$2$	$2.699$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}-q^{4}-iq^{5}-4iq^{7}-iq^{8}+\cdots$
338.2.b.c	$338$	$2$	338.b	13.b	$2$	$2$	$2$	$2.699$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+q^{3}-q^{4}+3iq^{5}+iq^{6}+\cdots$
338.2.b.d	$338$	$2$	338.b	13.b	$2$	$6$	$6$	$2.699$	6.0.153664.1	None		$2$	$0$	$0$	$6$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{2}+(1+\beta _{2}-\beta _{4})q^{3}-q^{4}-2\beta _{1}q^{5}+\cdots$
338.2.c.a	$338$	$2$	338.c	13.c	$3$	$2$	$1$	$2.699$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$-1$	$6$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
338.2.c.b	$338$	$2$	338.c	13.c	$3$	$2$	$1$	$2.699$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$1$	$-6$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
338.2.c.c	$338$	$2$	338.c	13.c	$3$	$2$	$1$	$2.699$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$3$	$-2$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(3-3\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
338.2.c.d	$338$	$2$	338.c	13.c	$3$	$2$	$1$	$2.699$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$-1$	$-6$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
338.2.c.e	$338$	$2$	338.c	13.c	$3$	$2$	$1$	$2.699$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$0$	$2$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{5}+4\zeta_{6}q^{7}+\cdots$
338.2.c.f	$338$	$2$	338.c	13.c	$3$	$2$	$1$	$2.699$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$1$	$6$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
338.2.c.g	$338$	$2$	338.c	13.c	$3$	$2$	$1$	$2.699$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$3$	$2$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(3-3\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
338.2.c.h	$338$	$2$	338.c	13.c	$3$	$6$	$3$	$2.699$	6.0.64827.1	None		$2$	$0$	$-3$	$-3$	$4$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{5}q^{2}+(\beta _{1}-\beta _{2}-\beta _{3}-\beta _{4}-\beta _{5})q^{3}+\cdots$
338.2.c.i	$338$	$2$	338.c	13.c	$3$	$6$	$3$	$2.699$	6.0.64827.1	None		$2$	$0$	$3$	$-3$	$-4$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{5})q^{2}+(-1-\beta _{1}+\beta _{4}+\beta _{5})q^{3}+\cdots$
338.2.e.a	$338$	$2$	338.e	13.e	$6$	$4$	$2$	$2.699$	$\Q(\zeta_{12})$	None		$4$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}+(-1+\zeta_{12}^{2})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$
338.2.e.b	$338$	$2$	338.e	13.e	$6$	$4$	$2$	$2.699$	$\Q(\zeta_{12})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{3}q^{5}+(4\zeta_{12}+\cdots)q^{7}+\cdots$
338.2.e.c	$338$	$2$	338.e	13.e	$6$	$4$	$2$	$2.699$	$\Q(\zeta_{12})$	None		$4$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}+(1-\zeta_{12}^{2})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$
338.2.e.d	$338$	$2$	338.e	13.e	$6$	$4$	$2$	$2.699$	$\Q(\zeta_{12})$	None		$4$	$0$	$0$	$6$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}+(3-3\zeta_{12}^{2})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$
338.2.e.e	$338$	$2$	338.e	13.e	$6$	$12$	$6$	$2.699$	12.0.$\cdots$.1	None		$4$	$0$	$0$	$-6$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{6}q^{2}+(\beta _{4}+2\beta _{9})q^{3}+\beta _{7}q^{4}+(2\beta _{2}+\cdots)q^{5}+\cdots$
338.2.g.a	$338$	$2$	338.g	169.g	$13$	$96$	$8$	$2.699$		None		$2$	$0$	$8$	$-1$	$3$	$-13$			$\mathrm{SU}(2)[C_{13}]$
338.2.g.b	$338$	$2$	338.g	169.g	$13$	$108$	$9$	$2.699$		None		$2$	$0$	$-9$	$-1$	$-5$	$5$			$\mathrm{SU}(2)[C_{13}]$
338.2.h.a	$338$	$2$	338.h	169.h	$26$	$192$	$16$	$2.699$		None		$2$	$0$	$0$	$2$	$0$	$0$			$\mathrm{SU}(2)[C_{26}]$
338.2.i.a	$338$	$2$	338.i	169.i	$39$	$168$	$7$	$2.699$		None		$2$	$0$	$-7$	$0$	$0$	$14$			$\mathrm{SU}(2)[C_{39}]$
338.2.i.b	$338$	$2$	338.i	169.i	$39$	$192$	$8$	$2.699$		None		$2$	$0$	$8$	$0$	$2$	$-10$			$\mathrm{SU}(2)[C_{39}]$
338.2.k.a	$338$	$2$	338.k	169.k	$78$	$336$	$14$	$2.699$		None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{78}]$
338.3.d.a	$338$	$3$	338.d	13.d	$4$	$2$	$1$	$9.210$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$-2$	$0$	$6$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-i)q^{2}+2iq^{4}+(3+3i)q^{5}+\cdots$
338.3.d.b	$338$	$3$	338.d	13.d	$4$	$2$	$1$	$9.210$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$-2$	$8$	$-8$	$-10$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-i)q^{2}+4q^{3}+2iq^{4}+(-4+\cdots)q^{5}+\cdots$
338.3.d.c	$338$	$3$	338.d	13.d	$4$	$2$	$1$	$9.210$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$2$	$8$	$8$	$10$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+i)q^{2}+4q^{3}+2iq^{4}+(4+4i)q^{5}+\cdots$
338.3.d.d	$338$	$3$	338.d	13.d	$4$	$4$	$2$	$9.210$	$\Q(\zeta_{12})$	None		$2$	$0$	$-4$	$0$	$0$	$2$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-\zeta_{12}^{2})q^{2}+(\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots$
338.3.d.e	$338$	$3$	338.d	13.d	$4$	$4$	$2$	$9.210$	$\Q(\zeta_{12})$	None		$2$	$0$	$4$	$0$	$0$	$-2$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+\zeta_{12}^{2})q^{2}+(\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots$
338.3.d.f	$338$	$3$	338.d	13.d	$4$	$8$	$4$	$9.210$	8.0.$\cdots$.1	None		$2$	$0$	$-8$	$0$	$-6$	$-10$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+\beta _{5})q^{2}+(-1+\beta _{1}+\beta _{3}+\beta _{5}+\cdots)q^{3}+\cdots$
338.3.d.g	$338$	$3$	338.d	13.d	$4$	$8$	$4$	$9.210$	8.0.$\cdots$.1	None		$2$	$0$	$8$	$0$	$6$	$10$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(1-\beta _{5})q^{2}+(-1+\beta _{1}+\beta _{3}+\beta _{5}+\cdots)q^{3}+\cdots$
338.3.d.h	$338$	$3$	338.d	13.d	$4$	$12$	$6$	$9.210$	12.0.$\cdots$.2	None		$2$	$0$	$-12$	$-8$	$8$	$24$		$13^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+\beta _{1})q^{2}+(-1+\beta _{4}+\beta _{7}-\beta _{9}+\cdots)q^{3}+\cdots$
338.3.d.i	$338$	$3$	338.d	13.d	$4$	$12$	$6$	$9.210$	12.0.$\cdots$.2	None		$2$	$0$	$12$	$-8$	$-8$	$-24$		$13^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(1-\beta _{1})q^{2}+(-1+\beta _{4}+\beta _{7}-\beta _{9}+\cdots)q^{3}+\cdots$
338.3.f.a	$338$	$3$	338.f	13.f	$12$	$4$	$1$	$9.210$	$\Q(\zeta_{12})$	None		$4$	$0$	$-2$	$-8$	$16$	$-10$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}-4\zeta_{12}^{2}q^{3}+\cdots$
338.3.f.b	$338$	$3$	338.f	13.f	$12$	$4$	$1$	$9.210$	$\Q(\zeta_{12})$	None		$4$	$0$	$-2$	$0$	$-12$	$-4$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+2\zeta_{12}q^{4}+\cdots$
338.3.f.c	$338$	$3$	338.f	13.f	$12$	$4$	$1$	$9.210$	$\Q(\zeta_{12})$	None		$2$	$0$	$-2$	$0$	$0$	$-20$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(\zeta_{12}+\cdots)q^{3}+\cdots$
338.3.f.d	$338$	$3$	338.f	13.f	$12$	$4$	$1$	$9.210$	$\Q(\zeta_{12})$	None		$2$	$0$	$-2$	$0$	$0$	$22$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\cdots)q^{3}+\cdots$
338.3.f.e	$338$	$3$	338.f	13.f	$12$	$4$	$1$	$9.210$	$\Q(\zeta_{12})$	None		$4$	$0$	$2$	$-8$	$-16$	$10$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}-4\zeta_{12}^{2}q^{3}+\cdots$
338.3.f.f	$338$	$3$	338.f	13.f	$12$	$4$	$1$	$9.210$	$\Q(\zeta_{12})$	None		$2$	$0$	$2$	$0$	$0$	$20$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots$
338.3.f.g	$338$	$3$	338.f	13.f	$12$	$4$	$1$	$9.210$	$\Q(\zeta_{12})$	None		$4$	$0$	$2$	$0$	$12$	$4$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+2\zeta_{12}q^{4}+\cdots$
338.3.f.h	$338$	$3$	338.f	13.f	$12$	$8$	$2$	$9.210$	8.0.$\cdots$.1	None		$2$	$0$	$-4$	$0$	$6$	$-8$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(-\beta _{3}+\beta _{4})q^{2}+(\beta _{2}-\beta _{5})q^{3}-2\beta _{5}q^{4}+\cdots$
338.3.f.i	$338$	$3$	338.f	13.f	$12$	$8$	$2$	$9.210$	8.0.$\cdots$.1	None		$2$	$0$	$4$	$0$	$-6$	$2$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(\beta _{3}+\beta _{4})q^{2}+(\beta _{2}-\beta _{5})q^{3}+2\beta _{5}q^{4}+\cdots$

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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.