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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 239 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
300.1.b.a	$300$	$1$	300.b	15.d	$2$	$2$	$2$	$0.150$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{3}-iq^{7}-q^{9}+iq^{13}+q^{19}+\cdots$
300.1.g.a	$300$	$1$	300.g	3.b	$2$	$1$	$1$	$0.150$	$\Q$	$D_{3}$	$\Q(\sqrt{-3}) $	None	✓	$2$	$0$	$0$	$-1$	$0$	$1$		$1$		$q-q^{3}+q^{7}+q^{9}+q^{13}-q^{19}-q^{21}+\cdots$
300.1.g.b	$300$	$1$	300.g	3.b	$2$	$1$	$1$	$0.150$	$\Q$	$D_{3}$	$\Q(\sqrt{-3}) $	None	✓	$2$	$0$	$0$	$1$	$0$	$-1$		$1$		$q+q^{3}-q^{7}+q^{9}-q^{13}-q^{19}-q^{21}+\cdots$
300.1.l.a	$300$	$1$	300.l	60.l	$4$	$4$	$2$	$0.150$	$\Q(\zeta_{8})$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-5}) $	$\Q(\sqrt{3}) $		$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{2}-\zeta_{8}^{3}q^{3}+\zeta_{8}^{2}q^{4}-q^{6}+\cdots$
300.2.a.a	$300$	$2$	300.a	1.a	$1$	$1$	$1$	$2.396$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-4q^{7}+q^{9}-4q^{11}-4q^{17}+\cdots$
300.2.a.b	$300$	$2$	300.a	1.a	$1$	$1$	$1$	$2.396$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}+6q^{11}-5q^{13}+\cdots$
300.2.a.c	$300$	$2$	300.a	1.a	$1$	$1$	$1$	$2.396$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}+6q^{11}+5q^{13}+\cdots$
300.2.a.d	$300$	$2$	300.a	1.a	$1$	$1$	$1$	$2.396$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+4q^{7}+q^{9}-4q^{11}+4q^{17}+\cdots$
300.2.d.a	$300$	$2$	300.d	5.b	$2$	$2$	$2$	$2.396$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+iq^{7}-q^{9}+6q^{11}+5iq^{13}+\cdots$
300.2.e.a	$300$	$2$	300.e	12.b	$2$	$4$	$4$	$2.396$	$\Q(\sqrt{3}, \sqrt{-5})$	$_{}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}+(\beta _{1}-\beta _{3})q^{3}+\beta _{2}q^{4}+(2+\cdots)q^{6}+\cdots$
300.2.e.b	$300$	$2$	300.e	12.b	$2$	$4$	$4$	$2.396$	$\Q(\sqrt{2}, \sqrt{-5})$	$_{}$	$\Q(\sqrt{-5}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{2}+(-\beta _{1}-\beta _{2})q^{3}+2q^{4}+(-1+\cdots)q^{6}+\cdots$
300.2.e.c	$300$	$2$	300.e	12.b	$2$	$8$	$8$	$2.396$	8.0.342102016.5	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{2}+(-\beta _{6}+\beta _{7})q^{3}+(\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots$
300.2.e.d	$300$	$2$	300.e	12.b	$2$	$8$	$8$	$2.396$	8.0.4521217600.1	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{6}q^{2}-\beta _{2}q^{3}+(\beta _{1}-\beta _{2}-\beta _{3})q^{4}+\cdots$
300.2.e.e	$300$	$2$	300.e	12.b	$2$	$8$	$8$	$2.396$	8.0.4521217600.1	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{6}q^{2}+\beta _{3}q^{3}+(\beta _{1}-\beta _{2}-\beta _{3})q^{4}+\cdots$
300.2.h.a	$300$	$2$	300.h	60.h	$2$	$8$	$8$	$2.396$	8.0.342102016.5	$_{}$	None	None		$4$	$0$	$-2$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{4}q^{3}+(-\beta _{1}+\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots$
300.2.h.b	$300$	$2$	300.h	60.h	$2$	$8$	$8$	$2.396$	8.0.342102016.5	$_{}$	None	None		$4$	$0$	$2$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+\beta _{4}q^{3}+(-\beta _{1}+\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots$
300.2.h.c	$300$	$2$	300.h	60.h	$2$	$16$	$16$	$2.396$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{6}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{10}q^{3}-\beta _{4}q^{4}-\beta _{12}q^{6}+\cdots$
300.2.i.a	$300$	$2$	300.i	15.e	$4$	$4$	$2$	$2.396$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$4$	$0$	$0$	$-2$	$0$	$4$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+\beta _{3})q^{3}+(1-\beta _{2})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots$
300.2.i.b	$300$	$2$	300.i	15.e	$4$	$4$	$2$	$2.396$	$\Q(i, \sqrt{6})$	$_{}$	$\Q(\sqrt{-3}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+\beta _{1}q^{3}+2\beta _{3}q^{7}+3\beta _{2}q^{9}+4\beta _{1}q^{13}+\cdots$
300.2.i.c	$300$	$2$	300.i	15.e	$4$	$4$	$2$	$2.396$	$\Q(i, \sqrt{6})$	$_{}$	$\Q(\sqrt{-3}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+\beta _{1}q^{3}-3\beta _{3}q^{7}+3\beta _{2}q^{9}-\beta _{1}q^{13}+\cdots$
300.2.j.a	$300$	$2$	300.j	20.e	$4$	$8$	$4$	$2.396$	$\Q(\zeta_{24})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(\zeta_{24}-\zeta_{24}^{4}+\zeta_{24}^{5})q^{2}+\zeta_{24}q^{3}+\cdots$
300.2.j.b	$300$	$2$	300.j	20.e	$4$	$8$	$4$	$2.396$	8.0.157351936.1	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(\beta _{2}+\beta _{4})q^{2}+\beta _{6}q^{3}+(\beta _{3}+\beta _{5})q^{4}+\cdots$
300.2.j.c	$300$	$2$	300.j	20.e	$4$	$8$	$4$	$2.396$	$\Q(\zeta_{24})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-\zeta_{24}-\zeta_{24}^{7})q^{2}-\zeta_{24}^{5}q^{3}+(\zeta_{24}^{2}+\cdots)q^{4}+\cdots$
300.2.j.d	$300$	$2$	300.j	20.e	$4$	$12$	$6$	$2.396$	12.0.$\cdots$.1	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+\beta _{9}q^{3}+(\beta _{2}+\beta _{8}+\beta _{9})q^{4}+\cdots$
300.2.m.a	$300$	$2$	300.m	25.d	$5$	$8$	$2$	$2.396$	$\Q(\zeta_{15})$	$_{}$	None	None		$2$	$0$	$0$	$-2$	$5$	$-8$		$5$	$\mathrm{SU}(2)[C_{5}]$	$q+\zeta_{15}^{5}q^{3}+(-1-2\zeta_{15}^{2}-\zeta_{15}^{3}+\cdots)q^{5}+\cdots$
300.2.m.b	$300$	$2$	300.m	25.d	$5$	$8$	$2$	$2.396$	8.0.26265625.1	$_{}$	None	None		$2$	$0$	$0$	$2$	$-5$	$8$		$5$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{3}q^{3}+(-1+\beta _{6}-\beta _{7})q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots$
300.2.n.a	$300$	$2$	300.n	300.n	$10$	$224$	$56$	$2.396$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
300.2.o.a	$300$	$2$	300.o	25.e	$10$	$24$	$6$	$2.396$		$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$0$			$\mathrm{SU}(2)[C_{10}]$
300.2.r.a	$300$	$2$	300.r	300.r	$10$	$224$	$56$	$2.396$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
300.2.w.a	$300$	$2$	300.w	100.l	$20$	$240$	$30$	$2.396$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{20}]$
300.2.x.a	$300$	$2$	300.x	75.l	$20$	$80$	$10$	$2.396$		$_{}$	None	None		$4$	$0$	$0$	$-2$	$0$	$4$			$\mathrm{SU}(2)[C_{20}]$
300.3.b.a	$300$	$3$	300.b	15.d	$2$	$2$	$2$	$8.174$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+3iq^{3}+2iq^{7}-9q^{9}+22iq^{13}+\cdots$
300.3.b.b	$300$	$3$	300.b	15.d	$2$	$2$	$2$	$8.174$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+3iq^{3}-13iq^{7}-9q^{9}-23iq^{13}+\cdots$
300.3.b.c	$300$	$3$	300.b	15.d	$2$	$4$	$4$	$8.174$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}+\beta _{3})q^{3}+\beta _{1}q^{7}+(1-2\beta _{2}+\cdots)q^{9}+\cdots$
300.3.b.d	$300$	$3$	300.b	15.d	$2$	$4$	$4$	$8.174$	$\Q(i, \sqrt{35})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-8\beta _{2}q^{7}+(9+\beta _{3})q^{9}+(-3+\cdots)q^{11}+\cdots$
300.3.c.a	$300$	$3$	300.c	4.b	$2$	$2$	$2$	$8.174$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$-2$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\zeta_{6})q^{2}+\zeta_{6}q^{3}+(-2+2\zeta_{6})q^{4}+\cdots$
300.3.c.b	$300$	$3$	300.c	4.b	$2$	$2$	$2$	$8.174$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$2$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\zeta_{6})q^{2}-\zeta_{6}q^{3}+(-2+2\zeta_{6})q^{4}+\cdots$
300.3.c.c	$300$	$3$	300.c	4.b	$2$	$2$	$2$	$8.174$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$2$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\zeta_{6})q^{2}-\zeta_{6}q^{3}+(-2+2\zeta_{6})q^{4}+\cdots$
300.3.c.d	$300$	$3$	300.c	4.b	$2$	$8$	$8$	$8.174$	8.0.85100625.1	$_{}$	None	None		$2$	$0$	$-4$	$0$	$0$	$0$		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{2}+\beta _{6}q^{3}+(1-\beta _{3})q^{4}+(-1+\cdots)q^{6}+\cdots$
300.3.c.e	$300$	$3$	300.c	4.b	$2$	$8$	$8$	$8.174$	8.0.4069419264.1	$_{}$	None	None		$2$	$0$	$-2$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{2}-\beta _{5}q^{3}+(-1+\beta _{7})q^{4}+(-1+\cdots)q^{6}+\cdots$
300.3.c.f	$300$	$3$	300.c	4.b	$2$	$8$	$8$	$8.174$	8.0.6080256576.2	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{2}-\beta _{2}q^{3}+(1-\beta _{7})q^{4}+(-1+\cdots)q^{6}+\cdots$
300.3.c.g	$300$	$3$	300.c	4.b	$2$	$8$	$8$	$8.174$	8.0.4069419264.1	$_{}$	None	None		$2$	$0$	$2$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}+\beta _{5}q^{3}+(-1+\beta _{7})q^{4}+(-1+\cdots)q^{6}+\cdots$
300.3.f.a	$300$	$3$	300.f	20.d	$2$	$4$	$4$	$8.174$	$\Q(\zeta_{12})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\zeta_{12}+\zeta_{12}^{3})q^{2}+\zeta_{12}^{3}q^{3}+(2+2\zeta_{12}^{2}+\cdots)q^{4}+\cdots$
300.3.f.b	$300$	$3$	300.f	20.d	$2$	$16$	$16$	$8.174$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{24}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{12}q^{2}-\beta _{9}q^{3}+(-1+\beta _{4})q^{4}+\cdots$
300.3.f.c	$300$	$3$	300.f	20.d	$2$	$16$	$16$	$8.174$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{20}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}-\beta _{4}q^{3}+(1+\beta _{5})q^{4}+(-1+\cdots)q^{6}+\cdots$
300.3.g.a	$300$	$3$	300.g	3.b	$2$	$1$	$1$	$8.174$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓	$2$	$0$	$0$	$-3$	$0$	$-13$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-3q^{3}-13q^{7}+9q^{9}+23q^{13}+11q^{19}+\cdots$
300.3.g.b	$300$	$3$	300.g	3.b	$2$	$1$	$1$	$8.174$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓	$2$	$0$	$0$	$3$	$0$	$-2$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+3q^{3}-2q^{7}+9q^{9}+22q^{13}+26q^{19}+\cdots$
300.3.g.c	$300$	$3$	300.g	3.b	$2$	$1$	$1$	$8.174$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓	$2$	$0$	$0$	$3$	$0$	$13$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+3q^{3}+13q^{7}+9q^{9}-23q^{13}+11q^{19}+\cdots$
300.3.g.d	$300$	$3$	300.g	3.b	$2$	$2$	$2$	$8.174$	$\Q(\sqrt{-5}) $	$_{}$	None	None		$2$	$0$	$0$	$-4$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-2+\beta )q^{3}-2q^{7}+(-1-4\beta )q^{9}+\cdots$
300.3.g.e	$300$	$3$	300.g	3.b	$2$	$2$	$2$	$8.174$	$\Q(\sqrt{-5}) $	$_{}$	None	None		$2$	$0$	$0$	$-4$	$0$	$16$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-2+\beta )q^{3}+8q^{7}+(-1-4\beta )q^{9}+\cdots$

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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.