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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 (36 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	2	7	11	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
4312.2.a.a	$4312$	$2$	4312.a	1.a	$1$	$1$	$1$	$34.431$	$\Q$	None	✓	$1$	$2$	$0$	$-2$	$-4$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-4q^{5}+q^{9}+q^{11}-2q^{13}+\cdots$
4312.2.a.b	$4312$	$2$	4312.a	1.a	$1$	$1$	$1$	$34.431$	$\Q$	None	✓	$1$	$0$	$0$	$-2$	$-2$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-2q^{5}+q^{9}-q^{11}+4q^{15}+\cdots$
4312.2.a.c	$4312$	$2$	4312.a	1.a	$1$	$1$	$1$	$34.431$	$\Q$	None	✓	$1$	$1$	$0$	$-2$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{9}-q^{11}+2q^{13}-2q^{17}+\cdots$
4312.2.a.d	$4312$	$2$	4312.a	1.a	$1$	$1$	$1$	$34.431$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$2$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}-2q^{9}-q^{11}+3q^{13}+\cdots$
4312.2.a.e	$4312$	$2$	4312.a	1.a	$1$	$1$	$1$	$34.431$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$0$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{9}-q^{11}+6q^{13}+2q^{19}+4q^{23}+\cdots$
4312.2.a.f	$4312$	$2$	4312.a	1.a	$1$	$1$	$1$	$34.431$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$2$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-3q^{9}-q^{11}-2q^{13}+2q^{17}+\cdots$
4312.2.a.g	$4312$	$2$	4312.a	1.a	$1$	$1$	$1$	$34.431$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$-2$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}-2q^{9}-q^{11}-3q^{13}+\cdots$
4312.2.a.h	$4312$	$2$	4312.a	1.a	$1$	$1$	$1$	$34.431$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$1$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-2q^{9}+q^{11}+q^{15}+2q^{17}+\cdots$
4312.2.a.i	$4312$	$2$	4312.a	1.a	$1$	$1$	$1$	$34.431$	$\Q$	None	✓	$1$	$0$	$0$	$2$	$-2$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{5}+q^{9}-q^{11}-4q^{13}+\cdots$
4312.2.a.j	$4312$	$2$	4312.a	1.a	$1$	$1$	$1$	$34.431$	$\Q$	None	✓	$1$	$1$	$0$	$2$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{9}-q^{11}-2q^{13}+2q^{17}+\cdots$
4312.2.a.k	$4312$	$2$	4312.a	1.a	$1$	$1$	$1$	$34.431$	$\Q$	None	✓	$1$	$0$	$0$	$2$	$4$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+4q^{5}+q^{9}+q^{11}+2q^{13}+\cdots$
4312.2.a.l	$4312$	$2$	4312.a	1.a	$1$	$1$	$1$	$34.431$	$\Q$	None	✓	$1$	$0$	$0$	$3$	$3$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+3q^{5}+6q^{9}-q^{11}+9q^{15}+\cdots$
4312.2.a.m	$4312$	$2$	4312.a	1.a	$1$	$2$	$2$	$34.431$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$0$	$-2$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}-\beta q^{5}-2\beta q^{9}+q^{11}+\cdots$
4312.2.a.n	$4312$	$2$	4312.a	1.a	$1$	$2$	$2$	$34.431$	$\Q(\sqrt{17}) $	None	✓	$1$	$1$	$0$	$-1$	$-3$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(-2+\beta )q^{5}+(1+\beta )q^{9}-q^{11}+\cdots$
4312.2.a.o	$4312$	$2$	4312.a	1.a	$1$	$2$	$2$	$34.431$	$\Q(\sqrt{2}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{5}-3q^{9}-q^{11}+\beta q^{17}+\beta q^{19}+\cdots$
4312.2.a.p	$4312$	$2$	4312.a	1.a	$1$	$2$	$2$	$34.431$	$\Q(\sqrt{2}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2\beta q^{5}-3q^{9}+q^{11}-\beta q^{13}+2\beta q^{17}+\cdots$
4312.2.a.q	$4312$	$2$	4312.a	1.a	$1$	$2$	$2$	$34.431$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+\beta q^{5}-q^{9}-q^{11}+2q^{15}+\cdots$
4312.2.a.r	$4312$	$2$	4312.a	1.a	$1$	$2$	$2$	$34.431$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-\beta q^{5}-q^{9}+q^{11}+2\beta q^{13}+\cdots$
4312.2.a.s	$4312$	$2$	4312.a	1.a	$1$	$2$	$2$	$34.431$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+\beta q^{5}-q^{9}+q^{11}+2q^{15}+\cdots$
4312.2.a.t	$4312$	$2$	4312.a	1.a	$1$	$2$	$2$	$34.431$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$0$	$1$	$3$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(2-\beta )q^{5}+(1+\beta )q^{9}+q^{11}+\cdots$
4312.2.a.u	$4312$	$2$	4312.a	1.a	$1$	$2$	$2$	$34.431$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$0$	$2$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}-\beta q^{5}+2\beta q^{9}+q^{11}+\cdots$
4312.2.a.v	$4312$	$2$	4312.a	1.a	$1$	$3$	$3$	$34.431$	$\Q(\zeta_{14})^+$	None	✓	$1$	$1$	$0$	$-5$	$-2$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-2-\beta _{2})q^{3}+(1-3\beta _{1}+2\beta _{2})q^{5}+\cdots$
4312.2.a.w	$4312$	$2$	4312.a	1.a	$1$	$3$	$3$	$34.431$	3.3.229.1	None	✓	$1$	$0$	$0$	$-1$	$-1$	$0$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+\beta _{2}q^{5}+(1-\beta _{1})q^{9}+q^{11}+\cdots$
4312.2.a.x	$4312$	$2$	4312.a	1.a	$1$	$3$	$3$	$34.431$	$\Q(\zeta_{14})^+$	None	✓	$1$	$0$	$0$	$5$	$2$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(2-\beta _{1})q^{3}+(2-\beta _{1}+3\beta _{2})q^{5}+(3+\cdots)q^{9}+\cdots$
4312.2.a.y	$4312$	$2$	4312.a	1.a	$1$	$4$	$4$	$34.431$	4.4.89289.1	None	✓	$1$	$1$	$0$	$-2$	$-4$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{3}+(-1+\beta _{1})q^{5}+(3+\cdots)q^{9}+\cdots$
4312.2.a.z	$4312$	$2$	4312.a	1.a	$1$	$4$	$4$	$34.431$	4.4.11348.1	None	✓	$1$	$1$	$0$	$-1$	$-5$	$0$	$+$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+(-1+\beta _{1})q^{5}+(2+\beta _{2}-\beta _{3})q^{9}+\cdots$
4312.2.a.ba	$4312$	$2$	4312.a	1.a	$1$	$4$	$4$	$34.431$	4.4.9248.1	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+\beta _{2}q^{5}-\beta _{3}q^{9}+q^{11}+(-\beta _{1}+\cdots)q^{13}+\cdots$
4312.2.a.bb	$4312$	$2$	4312.a	1.a	$1$	$4$	$4$	$34.431$	$\Q(\sqrt{7}, \sqrt{15})$	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}-\beta _{2}q^{5}+(2-\beta _{3})q^{9}+q^{11}+\cdots$
4312.2.a.bc	$4312$	$2$	4312.a	1.a	$1$	$4$	$4$	$34.431$	$\Q(\zeta_{24})^+$	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+\beta _{1}q^{5}+3q^{9}+q^{11}+(-\beta _{1}+\cdots)q^{13}+\cdots$
4312.2.a.bd	$4312$	$2$	4312.a	1.a	$1$	$4$	$4$	$34.431$	4.4.89289.1	None	✓	$1$	$0$	$0$	$2$	$4$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{3}+(1-\beta _{1})q^{5}+(3+\beta _{1}+\cdots)q^{9}+\cdots$
4312.2.a.be	$4312$	$2$	4312.a	1.a	$1$	$5$	$5$	$34.431$	5.5.352076.1	None	✓	$1$	$1$	$0$	$-3$	$-4$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{3}+(-1+\beta _{1}-\beta _{4})q^{5}+\cdots$
4312.2.a.bf	$4312$	$2$	4312.a	1.a	$1$	$5$	$5$	$34.431$	5.5.559701.1	None	✓	$1$	$0$	$0$	$-1$	$4$	$0$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(1-\beta _{1}+\beta _{2})q^{5}+\beta _{2}q^{9}+\cdots$
4312.2.a.bg	$4312$	$2$	4312.a	1.a	$1$	$5$	$5$	$34.431$	5.5.559701.1	None	✓	$1$	$1$	$0$	$1$	$-4$	$0$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+\beta _{2}q^{9}+\cdots$
4312.2.a.bh	$4312$	$2$	4312.a	1.a	$1$	$5$	$5$	$34.431$	5.5.352076.1	None	✓	$1$	$0$	$0$	$3$	$4$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{3}+(1-\beta _{1}+\beta _{4})q^{5}+(1+\cdots)q^{9}+\cdots$
4312.2.a.bi	$4312$	$2$	4312.a	1.a	$1$	$8$	$8$	$34.431$	8.8.$\cdots$.1	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{3}+(\beta _{3}+\beta _{4}-\beta _{5})q^{5}+(1-\beta _{2}+\cdots)q^{9}+\cdots$
4312.2.a.bj	$4312$	$2$	4312.a	1.a	$1$	$12$	$12$	$34.431$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$+$	$+$	$-$	$2^{7}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-\beta _{9}q^{5}+(3+\beta _{2})q^{9}-q^{11}+\cdots$

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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.