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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 144 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	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	Image	CM	RM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
496.1.e.a	$496$	$1$	496.e	31.b	$2$	$1$	$1$	$0.248$	$\Q$	$D_{3}$	$\Q(\sqrt{-31}) $	None	✓	$2$	$0$	$0$	$0$	$-1$	$1$		$1$		$q-q^{5}+q^{7}+q^{9}+q^{19}-q^{31}-q^{35}+\cdots$
496.1.j.a	$496$	$1$	496.j	496.j	$4$	$2$	$1$	$0.248$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$-2$	$0$	$2$	$0$		$1$		$q-q^{2}+q^{4}+(1+i)q^{5}-iq^{7}-q^{8}+\cdots$
496.1.j.b	$496$	$1$	496.j	496.j	$4$	$4$	$2$	$0.248$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$2$	$0$	$-2$	$0$		$1$		$q+\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}+(\zeta_{12}^{4}-\zeta_{12}^{5}+\cdots)q^{5}+\cdots$
496.2.a.a	$496$	$2$	496.a	1.a	$1$	$1$	$1$	$3.961$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-3$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}+3q^{7}-3q^{9}-2q^{11}-4q^{13}+\cdots$
496.2.a.b	$496$	$2$	496.a	1.a	$1$	$1$	$1$	$3.961$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-3q^{9}+2q^{13}-6q^{17}-4q^{19}+\cdots$
496.2.a.c	$496$	$2$	496.a	1.a	$1$	$1$	$1$	$3.961$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-3q^{7}-3q^{9}-6q^{11}-4q^{13}+\cdots$
496.2.a.d	$496$	$2$	496.a	1.a	$1$	$1$	$1$	$3.961$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$-3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-3q^{5}+q^{7}+q^{9}+6q^{11}+\cdots$
496.2.a.e	$496$	$2$	496.a	1.a	$1$	$1$	$1$	$3.961$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{5}+3q^{7}+q^{9}+2q^{11}+\cdots$
496.2.a.f	$496$	$2$	496.a	1.a	$1$	$1$	$1$	$3.961$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+2q^{5}+q^{9}-2q^{11}+4q^{13}+\cdots$
496.2.a.g	$496$	$2$	496.a	1.a	$1$	$2$	$2$	$3.961$	$\Q(\sqrt{33}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-4$	$3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+(1+\beta )q^{5}+(-1+\beta )q^{7}+q^{9}+\cdots$
496.2.a.h	$496$	$2$	496.a	1.a	$1$	$2$	$2$	$3.961$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+2\beta q^{5}-2q^{7}+(1-2\beta )q^{9}+\cdots$
496.2.a.i	$496$	$2$	496.a	1.a	$1$	$2$	$2$	$3.961$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$2$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+q^{5}+(2-\beta )q^{7}+(3+2\beta )q^{9}+\cdots$
496.2.a.j	$496$	$2$	496.a	1.a	$1$	$3$	$3$	$3.961$	3.3.316.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$-3$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1}-\beta _{2})q^{3}+(-1+\beta _{2})q^{5}+\cdots$
496.2.h.a	$496$	$2$	496.h	124.d	$2$	$2$	$2$	$3.961$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-4$	$6$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-2q^{3}+3q^{5}+\zeta_{6}q^{7}+q^{9}+2\zeta_{6}q^{13}+\cdots$
496.2.h.b	$496$	$2$	496.h	124.d	$2$	$2$	$2$	$3.961$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$4$	$6$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+2q^{3}+3q^{5}+\zeta_{6}q^{7}+q^{9}-2\zeta_{6}q^{13}+\cdots$
496.2.h.c	$496$	$2$	496.h	124.d	$2$	$4$	$4$	$3.961$	$\Q(\sqrt{2}, \sqrt{-13})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$4$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+q^{5}-\beta _{3}q^{7}-q^{9}+2\beta _{1}q^{11}+\cdots$
496.2.h.d	$496$	$2$	496.h	124.d	$2$	$8$	$8$	$3.961$	8.0.796594176.1	$_{}$	None	None		$4$	$0$	$0$	$0$	$-16$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}-2q^{5}+(-\beta _{2}+\beta _{4})q^{7}+(2+\cdots)q^{9}+\cdots$
496.2.i.a	$496$	$2$	496.i	31.c	$3$	$2$	$1$	$3.961$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-1$	$-3$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+\cdots$
496.2.i.b	$496$	$2$	496.i	31.c	$3$	$2$	$1$	$3.961$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-1$	$3$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(5-5\zeta_{6})q^{7}+\cdots$
496.2.i.c	$496$	$2$	496.i	31.c	$3$	$2$	$1$	$3.961$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$1$	$-1$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+\cdots$
496.2.i.d	$496$	$2$	496.i	31.c	$3$	$2$	$1$	$3.961$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$1$	$1$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+\cdots$
496.2.i.e	$496$	$2$	496.i	31.c	$3$	$2$	$1$	$3.961$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$1$	$3$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+\cdots$
496.2.i.f	$496$	$2$	496.i	31.c	$3$	$2$	$1$	$3.961$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$3$	$-3$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(3-3\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+\cdots$
496.2.i.g	$496$	$2$	496.i	31.c	$3$	$2$	$1$	$3.961$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$3$	$-1$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(3-3\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+\cdots$
496.2.i.h	$496$	$2$	496.i	31.c	$3$	$4$	$2$	$3.961$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		$2$	$0$	$0$	$-2$	$-2$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{1}-\beta _{2})q^{3}+\beta _{2}q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots$
496.2.i.i	$496$	$2$	496.i	31.c	$3$	$6$	$3$	$3.961$	6.0.954288.1	$_{}$	None	None		$2$	$0$	$0$	$-1$	$-1$	$1$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{4}-\beta _{5})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
496.2.i.j	$496$	$2$	496.i	31.c	$3$	$6$	$3$	$3.961$	6.0.591408.1	$_{}$	None	None		$2$	$0$	$0$	$-1$	$3$	$-1$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{4}q^{3}+(1-\beta _{2}-\beta _{3}+\beta _{4}-\beta _{5})q^{5}+\cdots$
496.2.k.a	$496$	$2$	496.k	16.e	$4$	$2$	$1$	$3.961$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$-2$	$2$	$6$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-i)q^{2}+(1-i)q^{3}+2iq^{4}+\cdots$
496.2.k.b	$496$	$2$	496.k	16.e	$4$	$4$	$2$	$3.961$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$1$	$-2$	$-4$	$-6$	$0$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}+(-1-\zeta_{12}^{2}+\cdots)q^{3}+\cdots$
496.2.k.c	$496$	$2$	496.k	16.e	$4$	$48$	$24$	$3.961$		$_{}$	None	None		$2$	$0$	$4$	$2$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
496.2.k.d	$496$	$2$	496.k	16.e	$4$	$66$	$33$	$3.961$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
496.2.m.a	$496$	$2$	496.m	496.m	$4$	$12$	$6$	$3.961$	12.0.$\cdots$.1	$_{}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{4}]$	$q+\beta _{5}q^{2}-\beta _{2}q^{4}+(\beta _{1}+\beta _{2}-\beta _{8})q^{5}+\cdots$
496.2.m.b	$496$	$2$	496.m	496.m	$4$	$112$	$56$	$3.961$		$_{}$	None	None		$4$	$0$	$-4$	$0$	$-4$	$-8$			$\mathrm{SU}(2)[C_{4}]$
496.2.n.a	$496$	$2$	496.n	31.d	$5$	$4$	$1$	$3.961$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$1$	$0$	$-5$	$-6$	$-7$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1-\zeta_{10}+\zeta_{10}^{2}+\zeta_{10}^{3})q^{3}+\cdots$
496.2.n.b	$496$	$2$	496.n	31.d	$5$	$4$	$1$	$3.961$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$0$	$-1$	$-6$	$3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{3}+\cdots$
496.2.n.c	$496$	$2$	496.n	31.d	$5$	$4$	$1$	$3.961$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$0$	$3$	$8$	$-1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}^{3})q^{3}+2q^{5}+(-\zeta_{10}-\zeta_{10}^{2}+\cdots)q^{7}+\cdots$
496.2.n.d	$496$	$2$	496.n	31.d	$5$	$8$	$2$	$3.961$	8.0.1903140625.1	$_{}$	None	None		$2$	$0$	$0$	$2$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{7}q^{3}+(-\beta _{2}+\beta _{5}+\beta _{6})q^{5}+(\beta _{3}+\cdots)q^{7}+\cdots$
496.2.n.e	$496$	$2$	496.n	31.d	$5$	$8$	$2$	$3.961$	8.0.511890625.1	$_{}$	None	None		$2$	$0$	$0$	$4$	$-4$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{2}-\beta _{3})q^{3}+(-\beta _{1}+\beta _{5}-\beta _{6})q^{5}+\cdots$
496.2.n.f	$496$	$2$	496.n	31.d	$5$	$16$	$4$	$3.961$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{7}q^{3}-\beta _{14}q^{5}+(\beta _{1}+\beta _{4}-\beta _{11}+\cdots)q^{7}+\cdots$
496.2.n.g	$496$	$2$	496.n	31.d	$5$	$16$	$4$	$3.961$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$2$	$-2$	$8$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1-\beta _{1}+\beta _{2}-\beta _{3}-\beta _{4}-\beta _{7}+\cdots)q^{3}+\cdots$
496.2.o.a	$496$	$2$	496.o	124.g	$6$	$2$	$1$	$3.961$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-1$	$3$	$3$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(1+\zeta_{6})q^{7}+\cdots$
496.2.o.b	$496$	$2$	496.o	124.g	$6$	$2$	$1$	$3.961$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$1$	$3$	$-3$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1-\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(-1-\zeta_{6})q^{7}+\cdots$
496.2.o.c	$496$	$2$	496.o	124.g	$6$	$8$	$4$	$3.961$	8.0.6672275856.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$-6$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{3}-\beta _{4})q^{3}+\beta _{1}q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots$
496.2.o.d	$496$	$2$	496.o	124.g	$6$	$8$	$4$	$3.961$	8.0.6672275856.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$6$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{3}+\beta _{4})q^{3}+\beta _{1}q^{5}+(1+\beta _{2}-\beta _{6}+\cdots)q^{7}+\cdots$
496.2.o.e	$496$	$2$	496.o	124.g	$6$	$12$	$6$	$3.961$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{3}+(-\beta _{3}-\beta _{8}+\beta _{10})q^{5}+(\beta _{2}+\cdots)q^{7}+\cdots$
496.2.x.a	$496$	$2$	496.x	124.j	$10$	$16$	$4$	$3.961$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(-\beta _{1}-\beta _{4}-\beta _{8}+\beta _{14})q^{3}+(-\beta _{5}+\cdots)q^{5}+\cdots$
496.2.x.b	$496$	$2$	496.x	124.j	$10$	$48$	$12$	$3.961$		$_{}$	None	None		$4$	$0$	$0$	$0$	$4$	$0$			$\mathrm{SU}(2)[C_{10}]$
496.2.bd.a	$496$	$2$	496.bd	496.ad	$12$	$248$	$62$	$3.961$		$_{}$	None	None		$4$	$0$	$-8$	$-6$	$-2$	$-4$			$\mathrm{SU}(2)[C_{12}]$
496.2.bf.a	$496$	$2$	496.bf	496.af	$12$	$248$	$62$	$3.961$		$_{}$	None	None		$4$	$0$	$-8$	$-2$	$-2$	$0$			$\mathrm{SU}(2)[C_{12}]$
496.2.bg.a	$496$	$2$	496.bg	31.g	$15$	$8$	$1$	$3.961$	$\Q(\zeta_{15})$	$_{}$	None	None		$2$	$0$	$0$	$-3$	$1$	$-2$		$1$	$\mathrm{SU}(2)[C_{15}]$	$q+(-1+\zeta_{15}^{4}-\zeta_{15}^{5})q^{3}+(1-\zeta_{15}+\cdots)q^{5}+\cdots$

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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.