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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 267 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
45.2.a.a	$45$	$2$	45.a	1.a	$1$	$1$	$1$	$0.359$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-q^{5}-3q^{8}-q^{10}+4q^{11}+\cdots$
45.2.b.a	$45$	$2$	45.b	5.b	$2$	$2$	$2$	$0.359$	$\Q(\sqrt{-5}) $	$\Q(\sqrt{-15}) $		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{2}-3q^{4}-\beta q^{5}-\beta q^{8}+5q^{10}+\cdots$
45.2.e.a	$45$	$2$	45.e	9.c	$3$	$2$	$1$	$0.359$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$-3$	$1$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$
45.2.e.b	$45$	$2$	45.e	9.c	$3$	$6$	$3$	$0.359$	6.0.954288.1	None		$2$	$0$	$-1$	$1$	$-3$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{2}-\beta _{4}-\beta _{5})q^{2}+\beta _{4}q^{3}+\cdots$
45.2.f.a	$45$	$2$	45.f	15.e	$4$	$4$	$2$	$0.359$	$\Q(\zeta_{8})$	None		$4$	$0$	$0$	$0$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}q^{2}-\zeta_{8}^{2}q^{4}+(-\zeta_{8}+2\zeta_{8}^{3})q^{5}+\cdots$
45.2.j.a	$45$	$2$	45.j	45.j	$6$	$8$	$4$	$0.359$	$\Q(\zeta_{24})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{24}^{6}q^{2}+(\zeta_{24}^{5}-\zeta_{24}^{7})q^{3}-\zeta_{24}^{3}q^{4}+\cdots$
45.2.l.a	$45$	$2$	45.l	45.l	$12$	$16$	$4$	$0.359$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$4$	$0$	$-6$	$-6$	$-6$	$-2$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q-\beta _{5}q^{2}+(-1+\beta _{9}-\beta _{11}-\beta _{12}+\cdots)q^{3}+\cdots$
45.3.c.a	$45$	$3$	45.c	3.b	$2$	$4$	$4$	$1.226$	$\Q(\sqrt{-2}, \sqrt{-5})$	None		$2$	$0$	$0$	$0$	$0$	$16$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}-\beta _{2})q^{2}+(-3-2\beta _{3})q^{4}+\cdots$
45.3.d.a	$45$	$3$	45.d	15.d	$2$	$4$	$4$	$1.226$	$\Q(\sqrt{-2}, \sqrt{7})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$2\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}+3q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\beta _{2}q^{7}+\cdots$
45.3.g.a	$45$	$3$	45.g	5.c	$4$	$4$	$2$	$1.226$	$\Q(i, \sqrt{10})$	None		$4$	$0$	$0$	$0$	$0$	$-20$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(2\beta _{1}+\beta _{3})q^{5}+(-5+\cdots)q^{7}+\cdots$
45.3.g.b	$45$	$3$	45.g	5.c	$4$	$4$	$2$	$1.226$	$\Q(i, \sqrt{6})$	None		$2$	$0$	$4$	$0$	$4$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+\beta _{1}+\beta _{2})q^{2}+(2\beta _{1}+\beta _{2}+2\beta _{3})q^{4}+\cdots$
45.3.h.a	$45$	$3$	45.h	45.h	$6$	$20$	$10$	$1.226$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$4$	$0$	$0$	$0$	$-12$	$0$		$3^{10}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+(\beta _{5}-\beta _{6})q^{3}+(-2-\beta _{2}+\cdots)q^{4}+\cdots$
45.3.i.a	$45$	$3$	45.i	9.d	$6$	$16$	$8$	$1.226$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$2$	$0$	$0$	$4$	$0$	$2$		$3^{3}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{3}q^{2}+(-\beta _{7}+\beta _{11})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots$
45.3.k.a	$45$	$3$	45.k	45.k	$12$	$40$	$10$	$1.226$		None		$4$	$0$	$-2$	$-6$	$-2$	$-2$			$\mathrm{SU}(2)[C_{12}]$
45.4.a.a	$45$	$4$	45.a	1.a	$1$	$1$	$1$	$2.655$	$\Q$	None	✓	$1$	$1$	$-5$	$0$	$5$	$-30$	$-$	$1$	$\mathrm{SU}(2)$	$q-5q^{2}+17q^{4}+5q^{5}-30q^{7}-45q^{8}+\cdots$
45.4.a.b	$45$	$4$	45.a	1.a	$1$	$1$	$1$	$2.655$	$\Q$	None	✓	$1$	$0$	$-3$	$0$	$5$	$20$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{2}+q^{4}+5q^{5}+20q^{7}+21q^{8}+\cdots$
45.4.a.c	$45$	$4$	45.a	1.a	$1$	$1$	$1$	$2.655$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$-5$	$-24$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-7q^{4}-5q^{5}-24q^{7}+15q^{8}+\cdots$
45.4.a.d	$45$	$4$	45.a	1.a	$1$	$1$	$1$	$2.655$	$\Q$	None	✓	$1$	$0$	$4$	$0$	$5$	$6$	$+$	$1$	$\mathrm{SU}(2)$	$q+4q^{2}+8q^{4}+5q^{5}+6q^{7}+20q^{10}+\cdots$
45.4.a.e	$45$	$4$	45.a	1.a	$1$	$1$	$1$	$2.655$	$\Q$	None	✓	$1$	$0$	$5$	$0$	$-5$	$-30$	$+$	$1$	$\mathrm{SU}(2)$	$q+5q^{2}+17q^{4}-5q^{5}-30q^{7}+45q^{8}+\cdots$
45.4.b.a	$45$	$4$	45.b	5.b	$2$	$2$	$2$	$2.655$	$\Q(\sqrt{-5}) $	$\Q(\sqrt{-15}) $		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{2}+3q^{4}+5\beta q^{5}+11\beta q^{8}-5^{2}q^{10}+\cdots$
45.4.b.b	$45$	$4$	45.b	5.b	$2$	$4$	$4$	$2.655$	$\Q(i, \sqrt{41})$	None		$2$	$0$	$0$	$0$	$-6$	$0$		$2\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+(-5+\beta _{3})q^{4}+(-2-\beta _{2}+\cdots)q^{5}+\cdots$
45.4.e.a	$45$	$4$	45.e	9.c	$3$	$4$	$2$	$2.655$	$\Q(\sqrt{-3}, \sqrt{-11})$	None		$2$	$0$	$1$	$-6$	$-10$	$-9$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{3}q^{2}+(-2-\beta _{1}-\beta _{2}+2\beta _{3})q^{3}+\cdots$
45.4.e.b	$45$	$4$	45.e	9.c	$3$	$6$	$3$	$2.655$	6.0.15759792.1	None		$2$	$0$	$1$	$9$	$-15$	$43$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{5})q^{2}+(1+\beta _{2}-\beta _{5})q^{3}+\cdots$
45.4.e.c	$45$	$4$	45.e	9.c	$3$	$14$	$7$	$2.655$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None		$2$	$0$	$2$	$-5$	$35$	$-22$		$2^{2}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{2})q^{2}+(\beta _{7}-\beta _{10})q^{3}+(-5+\cdots)q^{4}+\cdots$
45.4.f.a	$45$	$4$	45.f	15.e	$4$	$12$	$6$	$2.655$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$24$		$2^{10}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{6}q^{2}+(-6\beta _{1}+\beta _{5})q^{4}+(\beta _{9}+\beta _{10}+\cdots)q^{5}+\cdots$
45.4.j.a	$45$	$4$	45.j	45.j	$6$	$32$	$16$	$2.655$		None		$4$	$0$	$0$	$0$	$3$	$0$			$\mathrm{SU}(2)[C_{6}]$
45.4.l.a	$45$	$4$	45.l	45.l	$12$	$64$	$16$	$2.655$		None		$4$	$0$	$-6$	$0$	$-6$	$-2$			$\mathrm{SU}(2)[C_{12}]$
45.5.c.a	$45$	$5$	45.c	3.b	$2$	$4$	$4$	$4.652$	$\Q(\sqrt{-2}, \sqrt{-5})$	None		$2$	$0$	$0$	$0$	$0$	$-48$		$2\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}+\beta _{2})q^{2}+(-7-2\beta _{3})q^{4}+5\beta _{2}q^{5}+\cdots$
45.5.d.a	$45$	$5$	45.d	15.d	$2$	$8$	$8$	$4.652$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$0$		$2\cdot 3^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}+(5+\beta _{2})q^{4}+(2\beta _{3}+\beta _{5})q^{5}+\cdots$
45.5.g.a	$45$	$5$	45.g	5.c	$4$	$2$	$1$	$4.652$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$-10$	$0$	$50$	$80$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-5-5i)q^{2}+34iq^{4}+5^{2}q^{5}+\cdots$
45.5.g.b	$45$	$5$	45.g	5.c	$4$	$2$	$1$	$4.652$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$2$	$0$	$-40$	$-52$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+i)q^{2}-14iq^{4}+(-20-15i)q^{5}+\cdots$
45.5.g.c	$45$	$5$	45.g	5.c	$4$	$2$	$1$	$4.652$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$10$	$0$	$-50$	$80$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(5+5i)q^{2}+34iq^{4}-5^{2}q^{5}+(40+\cdots)q^{7}+\cdots$
45.5.g.d	$45$	$5$	45.g	5.c	$4$	$4$	$2$	$4.652$	$\Q(i, \sqrt{10})$	None		$4$	$0$	$0$	$0$	$0$	$-20$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}-11\beta _{2}q^{4}+(2\beta _{1}-11\beta _{3})q^{5}+\cdots$
45.5.g.e	$45$	$5$	45.g	5.c	$4$	$8$	$4$	$4.652$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$0$	$0$	$84$	$20$		$2^{3}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{3}q^{2}+(\beta _{1}-12\beta _{2}+\beta _{3}+\beta _{5})q^{4}+\cdots$
45.5.h.a	$45$	$5$	45.h	45.h	$6$	$44$	$22$	$4.652$		None		$4$	$0$	$0$	$0$	$6$	$0$			$\mathrm{SU}(2)[C_{6}]$
45.5.i.a	$45$	$5$	45.i	9.d	$6$	$32$	$16$	$4.652$		None		$2$	$0$	$0$	$-8$	$0$	$-26$			$\mathrm{SU}(2)[C_{6}]$
45.5.k.a	$45$	$5$	45.k	45.k	$12$	$88$	$22$	$4.652$		None		$4$	$0$	$-2$	$6$	$-2$	$-2$			$\mathrm{SU}(2)[C_{12}]$
45.6.a.a	$45$	$6$	45.a	1.a	$1$	$1$	$1$	$7.217$	$\Q$	None	✓	$1$	$1$	$-7$	$0$	$25$	$12$	$+$	$1$	$\mathrm{SU}(2)$	$q-7q^{2}+17q^{4}+5^{2}q^{5}+12q^{7}+105q^{8}+\cdots$
45.6.a.b	$45$	$6$	45.a	1.a	$1$	$1$	$1$	$7.217$	$\Q$	None	✓	$1$	$0$	$-2$	$0$	$-25$	$192$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-28q^{4}-5^{2}q^{5}+192q^{7}+\cdots$
45.6.a.c	$45$	$6$	45.a	1.a	$1$	$1$	$1$	$7.217$	$\Q$	None	✓	$1$	$1$	$2$	$0$	$25$	$-132$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-28q^{4}+5^{2}q^{5}-132q^{7}+\cdots$
45.6.a.d	$45$	$6$	45.a	1.a	$1$	$2$	$2$	$7.217$	$\Q(\sqrt{145}) $	None	✓	$1$	$1$	$-5$	$0$	$-50$	$80$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-2-\beta )q^{2}+(8+5\beta )q^{4}-5^{2}q^{5}+\cdots$
45.6.a.e	$45$	$6$	45.a	1.a	$1$	$2$	$2$	$7.217$	$\Q(\sqrt{409}) $	None	✓	$1$	$0$	$1$	$0$	$-50$	$-112$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(70+\beta )q^{4}-5^{2}q^{5}+(-2^{6}+\cdots)q^{7}+\cdots$
45.6.a.f	$45$	$6$	45.a	1.a	$1$	$2$	$2$	$7.217$	$\Q(\sqrt{145}) $	None	✓	$1$	$0$	$5$	$0$	$50$	$80$	$-$	$1$	$\mathrm{SU}(2)$	$q+(3-\beta )q^{2}+(13-5\beta )q^{4}+5^{2}q^{5}+\cdots$
45.6.b.a	$45$	$6$	45.b	5.b	$2$	$2$	$2$	$7.217$	$\Q(\sqrt{-5}) $	$\Q(\sqrt{-15}) $		$4$	$0$	$0$	$0$	$0$	$0$		$5$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{2}-93q^{4}+5\beta q^{5}-61\beta q^{8}+\cdots$
45.6.b.b	$45$	$6$	45.b	5.b	$2$	$2$	$2$	$7.217$	$\Q(\sqrt{-11}) $	None		$2$	$0$	$0$	$0$	$90$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{2}-12q^{4}+(45-5\beta )q^{5}-9\beta q^{7}+\cdots$
45.6.b.c	$45$	$6$	45.b	5.b	$2$	$4$	$4$	$7.217$	$\Q(i, \sqrt{89})$	None		$2$	$0$	$0$	$0$	$-120$	$0$		$3^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-11+\beta _{3})q^{4}+(-30-5\beta _{1}+\cdots)q^{5}+\cdots$
45.6.b.d	$45$	$6$	45.b	5.b	$2$	$4$	$4$	$7.217$	$\Q(\sqrt{-5}, \sqrt{-14})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{5}\cdot 3^{2}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+12q^{4}+(5\beta _{1}-\beta _{2})q^{5}+\beta _{3}q^{7}+\cdots$
45.6.e.a	$45$	$6$	45.e	9.c	$3$	$18$	$9$	$7.217$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None		$2$	$0$	$-4$	$33$	$225$	$167$		$2^{12}\cdot 3^{17}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(1+\beta _{2}+\beta _{3}-\beta _{9})q^{3}+(-11+\cdots)q^{4}+\cdots$
45.6.e.b	$45$	$6$	45.e	9.c	$3$	$22$	$11$	$7.217$		None		$2$	$0$	$-4$	$-11$	$-275$	$-225$			$\mathrm{SU}(2)[C_{3}]$
45.6.f.a	$45$	$6$	45.f	15.e	$4$	$20$	$10$	$7.217$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$152$		$2^{27}\cdot 3^{24}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{13}q^{2}+(-14\beta _{2}+\beta _{4})q^{4}+(2\beta _{3}+\cdots)q^{5}+\cdots$

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Elliptic curves over $\Q$
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Genus 2 curves over $\Q$
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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.