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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 (44 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				A-L signs			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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	2	3	5	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
3600.2.a.a	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	None	✓				600.2.a.e	$1$	$0$	$0$	$0$	$0$	$-5$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-5q^{7}-6q^{11}+3q^{13}-2q^{17}-q^{19}+\cdots$
3600.2.a.b	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	$\Q(\sqrt{-3}) $	✓				225.2.a.c	$2$	$1$	$0$	$0$	$0$	$-5$	$-$	$+$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	$q-5q^{7}+5q^{13}+q^{19}+7q^{31}-10q^{37}+\cdots$
3600.2.a.c	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	None	✓				360.2.f.b	$1$	$0$	$0$	$0$	$0$	$-4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{7}-4q^{11}-4q^{13}+6q^{17}+4q^{19}+\cdots$
3600.2.a.d	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	None	✓				60.2.d.a	$1$	$0$	$0$	$0$	$0$	$-4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{7}-4q^{11}-4q^{17}+4q^{23}+6q^{29}+\cdots$
3600.2.a.e	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	$\Q(\sqrt{-3}) $	✓				36.2.a.a	$2$	$0$	$0$	$0$	$0$	$-4$	$-$	$+$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	$q-4q^{7}-2q^{13}-8q^{19}+4q^{31}+10q^{37}+\cdots$
3600.2.a.f	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	None	✓				30.2.a.a	$1$	$1$	$0$	$0$	$0$	$-4$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{7}-2q^{13}+6q^{17}+4q^{19}+6q^{29}+\cdots$
3600.2.a.g	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	None	✓				360.2.f.b	$1$	$0$	$0$	$0$	$0$	$-4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{7}+4q^{11}-4q^{13}-6q^{17}+4q^{19}+\cdots$
3600.2.a.h	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	None	✓				40.2.a.a	$1$	$0$	$0$	$0$	$0$	$-4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{7}+4q^{11}+2q^{13}+2q^{17}-4q^{19}+\cdots$
3600.2.a.i	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	None	✓				600.2.a.b	$1$	$1$	$0$	$0$	$0$	$-3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{7}+2q^{11}-3q^{13}-6q^{17}+7q^{19}+\cdots$
3600.2.a.j	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	None	✓				75.2.a.a	$1$	$1$	$0$	$0$	$0$	$-3$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{7}+2q^{11}-q^{13}+2q^{17}+5q^{19}+\cdots$
3600.2.a.k	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	None	✓				40.2.c.a	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}-4q^{11}+4q^{13}+4q^{19}-2q^{23}+\cdots$
3600.2.a.l	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	None	✓				50.2.a.a	$1$	$0$	$0$	$0$	$0$	$-2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}-3q^{11}-4q^{13}+3q^{17}-5q^{19}+\cdots$
3600.2.a.m	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	None	✓				200.2.a.a	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}+q^{11}+4q^{13}-5q^{17}-q^{19}+\cdots$
3600.2.a.n	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	None	✓				120.2.f.a	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}+2q^{11}-2q^{13}+6q^{17}-8q^{19}+\cdots$
3600.2.a.o	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	None	✓				30.2.c.a	$1$	$0$	$0$	$0$	$0$	$-2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}+2q^{11}+6q^{13}-2q^{17}-4q^{23}+\cdots$
3600.2.a.p	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	None	✓				1800.2.a.k	$1$	$1$	$0$	$0$	$0$	$-1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{7}-4q^{11}-q^{13}+4q^{17}-q^{19}+\cdots$
3600.2.a.q	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	$\Q(\sqrt{-3}) $	✓				900.2.a.d	$2$	$0$	$0$	$0$	$0$	$-1$	$-$	$+$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	$q-q^{7}+7q^{13}+7q^{19}-11q^{31}+10q^{37}+\cdots$
3600.2.a.r	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	None	✓				1800.2.a.k	$1$	$1$	$0$	$0$	$0$	$-1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{7}+4q^{11}-q^{13}-4q^{17}-q^{19}+\cdots$
3600.2.a.s	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	None	✓				300.2.a.b	$1$	$1$	$0$	$0$	$0$	$-1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{7}+6q^{11}-5q^{13}-6q^{17}-5q^{19}+\cdots$
3600.2.a.t	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	None	✓				120.2.a.b	$1$	$0$	$0$	$0$	$0$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{11}-6q^{13}-6q^{17}+4q^{19}+\cdots$
3600.2.a.u	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	None	✓				15.2.a.a	$1$	$1$	$0$	$0$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{11}+2q^{13}+2q^{17}-4q^{19}+\cdots$
3600.2.a.v	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	None	✓				24.2.a.a	$1$	$0$	$0$	$0$	$0$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{11}+2q^{13}+2q^{17}+4q^{19}+\cdots$
3600.2.a.w	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	None	✓				1800.2.a.k	$1$	$0$	$0$	$0$	$0$	$1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{7}-4q^{11}+q^{13}-4q^{17}-q^{19}+\cdots$
3600.2.a.x	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	$\Q(\sqrt{-3}) $	✓				900.2.a.d	$2$	$1$	$0$	$0$	$0$	$1$	$-$	$+$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	$q+q^{7}-7q^{13}+7q^{19}-11q^{31}-10q^{37}+\cdots$
3600.2.a.y	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	None	✓				1800.2.a.k	$1$	$0$	$0$	$0$	$0$	$1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{7}+4q^{11}+q^{13}+4q^{17}-q^{19}+\cdots$
3600.2.a.z	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	None	✓				300.2.a.b	$1$	$0$	$0$	$0$	$0$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{7}+6q^{11}+5q^{13}+6q^{17}-5q^{19}+\cdots$
3600.2.a.ba	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	None	✓				90.2.a.a	$1$	$0$	$0$	$0$	$0$	$2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}-6q^{11}+4q^{13}+6q^{17}+4q^{19}+\cdots$
3600.2.a.bb	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	None	✓				40.2.c.a	$1$	$1$	$0$	$0$	$0$	$2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}-4q^{11}-4q^{13}+4q^{19}+2q^{23}+\cdots$
3600.2.a.bc	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	None	✓				50.2.a.a	$1$	$1$	$0$	$0$	$0$	$2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}-3q^{11}+4q^{13}-3q^{17}-5q^{19}+\cdots$
3600.2.a.bd	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	None	✓				360.2.a.c	$1$	$1$	$0$	$0$	$0$	$2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}-2q^{11}-4q^{13}+2q^{17}-4q^{19}+\cdots$
3600.2.a.be	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	None	✓				20.2.a.a	$1$	$1$	$0$	$0$	$0$	$2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}-2q^{13}-6q^{17}+4q^{19}-6q^{23}+\cdots$
3600.2.a.bf	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	None	✓				200.2.a.a	$1$	$0$	$0$	$0$	$0$	$2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}+q^{11}-4q^{13}+5q^{17}-q^{19}+\cdots$
3600.2.a.bg	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	None	✓				30.2.c.a	$1$	$0$	$0$	$0$	$0$	$2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}+2q^{11}-6q^{13}+2q^{17}+4q^{23}+\cdots$
3600.2.a.bh	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	None	✓				360.2.a.c	$1$	$1$	$0$	$0$	$0$	$2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}+2q^{11}-4q^{13}-2q^{17}-4q^{19}+\cdots$
3600.2.a.bi	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	None	✓				120.2.f.a	$1$	$1$	$0$	$0$	$0$	$2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}+2q^{11}+2q^{13}-6q^{17}-8q^{19}+\cdots$
3600.2.a.bj	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	None	✓				90.2.a.a	$1$	$0$	$0$	$0$	$0$	$2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}+6q^{11}+4q^{13}-6q^{17}+4q^{19}+\cdots$
3600.2.a.bk	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	None	✓				75.2.a.a	$1$	$0$	$0$	$0$	$0$	$3$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{7}+2q^{11}+q^{13}-2q^{17}+5q^{19}+\cdots$
3600.2.a.bl	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	None	✓				600.2.a.b	$1$	$0$	$0$	$0$	$0$	$3$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{7}+2q^{11}+3q^{13}+6q^{17}+7q^{19}+\cdots$
3600.2.a.bm	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	None	✓				60.2.d.a	$1$	$0$	$0$	$0$	$0$	$4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{7}-4q^{11}+4q^{17}-4q^{23}+6q^{29}+\cdots$
3600.2.a.bn	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	None	✓				360.2.f.b	$1$	$0$	$0$	$0$	$0$	$4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{7}-4q^{11}+4q^{13}-6q^{17}+4q^{19}+\cdots$
3600.2.a.bo	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	None	✓				120.2.a.a	$1$	$0$	$0$	$0$	$0$	$4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{7}+6q^{13}-2q^{17}-4q^{19}+8q^{23}+\cdots$
3600.2.a.bp	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	None	✓				360.2.f.b	$1$	$0$	$0$	$0$	$0$	$4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{7}+4q^{11}+4q^{13}+6q^{17}+4q^{19}+\cdots$
3600.2.a.bq	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	None	✓				600.2.a.e	$1$	$1$	$0$	$0$	$0$	$5$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+5q^{7}-6q^{11}-3q^{13}+2q^{17}-q^{19}+\cdots$
3600.2.a.br	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	$\Q(\sqrt{-3}) $	✓				225.2.a.c	$2$	$0$	$0$	$0$	$0$	$5$	$-$	$+$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	$q+5q^{7}-5q^{13}+q^{19}+7q^{31}+10q^{37}+\cdots$

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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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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.