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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 (33 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
2255.1.h.a	$2255$	$1$	2255.h	2255.h	$2$	$1$	$1$	$1.125$	$\Q$	$D_{2}$	$\Q(\sqrt{-451}) $, $\Q(\sqrt{-2255}) $	$\Q(\sqrt{5}) $	✓	✓			2255.1.h.a	$4$	$0$	$0$	$0$	$-1$	$0$		$1$		$q-q^{4}-q^{5}-q^{9}-q^{11}+q^{16}+2q^{19}+\cdots$
2255.1.h.b	$2255$	$1$	2255.h	2255.h	$2$	$1$	$1$	$1.125$	$\Q$	$D_{2}$	$\Q(\sqrt{-451}) $, $\Q(\sqrt{-2255}) $	$\Q(\sqrt{5}) $	✓	✓			2255.1.h.a	$4$	$0$	$0$	$0$	$-1$	$0$		$1$		$q-q^{4}-q^{5}-q^{9}+q^{11}+q^{16}-2q^{19}+\cdots$
2255.1.h.c	$2255$	$1$	2255.h	2255.h	$2$	$2$	$2$	$1.125$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-2255}) $	None	✓	✓			2255.1.h.c	$2$	$0$	$-1$	$-1$	$2$	$0$		$1$		$q-\beta q^{2}+(-1+\beta )q^{3}+\beta q^{4}+q^{5}+\cdots$
2255.1.h.d	$2255$	$1$	2255.h	2255.h	$2$	$2$	$2$	$1.125$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-2255}) $	None	✓	✓			2255.1.h.c	$2$	$0$	$-1$	$1$	$2$	$0$		$1$		$q-\beta q^{2}+(1-\beta )q^{3}+\beta q^{4}+q^{5}+q^{6}+\cdots$
2255.1.h.e	$2255$	$1$	2255.h	2255.h	$2$	$2$	$2$	$1.125$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-451}) $	None		✓			2255.1.h.e	$4$	$0$	$0$	$0$	$1$	$0$		$1$		$q-q^{4}+\zeta_{6}q^{5}+(-\zeta_{6}-\zeta_{6}^{2})q^{7}-q^{9}+\cdots$
2255.1.h.f	$2255$	$1$	2255.h	2255.h	$2$	$2$	$2$	$1.125$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-451}) $	None		✓			2255.1.h.e	$4$	$0$	$0$	$0$	$1$	$0$		$1$		$q-q^{4}-\zeta_{6}^{2}q^{5}+(-\zeta_{6}-\zeta_{6}^{2})q^{7}+\cdots$
2255.1.h.g	$2255$	$1$	2255.h	2255.h	$2$	$2$	$2$	$1.125$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-2255}) $	None	✓	✓			2255.1.h.c	$2$	$0$	$1$	$-1$	$2$	$0$		$1$		$q+\beta q^{2}+(-1+\beta )q^{3}+\beta q^{4}+q^{5}+\cdots$
2255.1.h.h	$2255$	$1$	2255.h	2255.h	$2$	$2$	$2$	$1.125$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-2255}) $	None	✓	✓			2255.1.h.c	$2$	$0$	$1$	$1$	$2$	$0$		$1$		$q+\beta q^{2}+(1-\beta )q^{3}+\beta q^{4}+q^{5}-q^{6}+\cdots$
2255.1.h.i	$2255$	$1$	2255.h	2255.h	$2$	$4$	$4$	$1.125$	$\Q(\zeta_{20})^+$	$D_{10}$	$\Q(\sqrt{-2255}) $	None	✓	✓			2255.1.h.i	$4$	$0$	$0$	$0$	$-4$	$0$		$1$		$q+\beta _{3}q^{2}-\beta _{1}q^{3}+(1-\beta _{2})q^{4}-q^{5}+\cdots$
2255.1.h.j	$2255$	$1$	2255.h	2255.h	$2$	$4$	$4$	$1.125$	$\Q(\zeta_{20})^+$	$D_{10}$	$\Q(\sqrt{-2255}) $	None	✓	✓			2255.1.h.i	$4$	$0$	$0$	$0$	$-4$	$0$		$1$		$q-\beta _{3}q^{2}-\beta _{1}q^{3}+(1-\beta _{2})q^{4}-q^{5}+\cdots$
2255.1.bo.a	$2255$	$1$	2255.bo	2255.ao	$10$	$4$	$1$	$1.125$	$\Q(\zeta_{10})$	$D_{10}$	None	$\Q(\sqrt{5}) $		✓	✓	✓	2255.1.bo.a	$4$	$0$	$0$	$0$	$1$	$0$		$1$		$q-\zeta_{10}^{2}q^{4}+\zeta_{10}q^{5}-\zeta_{10}^{2}q^{9}-\zeta_{10}^{2}q^{11}+\cdots$
2255.1.bp.a	$2255$	$1$	2255.bp	2255.ap	$10$	$4$	$1$	$1.125$	$\Q(\zeta_{10})$	$D_{10}$	None	$\Q(\sqrt{5}) $		✓	✓	✓	2255.1.bo.a	$4$	$0$	$0$	$0$	$-4$	$0$		$1$		$q-\zeta_{10}^{4}q^{4}-q^{5}+\zeta_{10}^{3}q^{9}+\zeta_{10}^{2}q^{11}+\cdots$
2255.1.bw.a	$2255$	$1$	2255.bw	2255.aw	$10$	$4$	$1$	$1.125$	$\Q(\zeta_{10})$	$D_{10}$	None	$\Q(\sqrt{5}) $		✓	✓	✓	2255.1.bw.a	$4$	$0$	$0$	$0$	$-4$	$0$		$1$		$q-\zeta_{10}^{2}q^{4}-q^{5}+\zeta_{10}^{4}q^{9}+\zeta_{10}q^{11}+\cdots$
2255.1.bz.a	$2255$	$1$	2255.bz	2255.az	$10$	$4$	$1$	$1.125$	$\Q(\zeta_{10})$	$D_{10}$	None	$\Q(\sqrt{5}) $		✓	✓	✓	2255.1.bw.a	$4$	$0$	$0$	$0$	$1$	$0$		$1$		$q-\zeta_{10}^{4}q^{4}-\zeta_{10}^{2}q^{5}+\zeta_{10}^{4}q^{9}+\cdots$
2255.2.a.a	$2255$	$2$	2255.a	1.a	$1$	$1$	$1$	$18.006$	$\Q$	$_{}$	None	None	✓	✓			2255.2.a.a	$1$	$0$	$-1$	$0$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+q^{5}+4q^{7}+3q^{8}-3q^{9}+\cdots$
2255.2.a.b	$2255$	$2$	2255.a	1.a	$1$	$5$	$5$	$18.006$	5.5.446609.1	$_{}$	None	None	✓	✓			2255.2.a.b	$1$	$1$	$0$	$-2$	$5$	$-7$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots$
2255.2.a.c	$2255$	$2$	2255.a	1.a	$1$	$6$	$6$	$18.006$	6.6.2501557.1	$_{}$	None	None	✓	✓	✓		2255.2.a.c	$1$	$1$	$-3$	$-1$	$6$	$6$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1}+\beta _{5})q^{2}-\beta _{1}q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots$
2255.2.a.d	$2255$	$2$	2255.a	1.a	$1$	$11$	$11$	$18.006$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	2255.2.a.d	$1$	$1$	$-1$	$-1$	$-11$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{3}+\beta _{4})q^{4}+\cdots$
2255.2.a.e	$2255$	$2$	2255.a	1.a	$1$	$13$	$13$	$18.006$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	2255.2.a.e	$1$	$1$	$-5$	$-3$	$13$	$-19$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{4}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots$
2255.2.a.f	$2255$	$2$	2255.a	1.a	$1$	$13$	$13$	$18.006$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	2255.2.a.f	$1$	$1$	$3$	$-1$	$-13$	$-9$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{11}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots$
2255.2.a.g	$2255$	$2$	2255.a	1.a	$1$	$21$	$21$	$18.006$		$_{}$	None	None	✓	✓	✓	✓	2255.2.a.g	$1$	$0$	$-3$	$1$	$-21$	$5$	$-$		$\mathrm{SU}(2)$
2255.2.a.h	$2255$	$2$	2255.a	1.a	$1$	$21$	$21$	$18.006$		$_{}$	None	None	✓	✓	✓	✓	2255.2.a.h	$1$	$0$	$1$	$7$	$21$	$7$	$-$		$\mathrm{SU}(2)$
2255.2.a.i	$2255$	$2$	2255.a	1.a	$1$	$21$	$21$	$18.006$		$_{}$	None	None	✓	✓	✓		2255.2.a.i	$1$	$0$	$9$	$3$	$21$	$13$	$-$		$\mathrm{SU}(2)$
2255.2.a.j	$2255$	$2$	2255.a	1.a	$1$	$23$	$23$	$18.006$		$_{}$	None	None	✓	✓	✓	✓	2255.2.a.j	$1$	$0$	$-3$	$1$	$-23$	$15$	$-$		$\mathrm{SU}(2)$
2255.4.a.a	$2255$	$4$	2255.a	1.a	$1$	$1$	$1$	$133.049$	$\Q$	$_{}$	None	None	✓	✓			2255.4.a.a	$1$	$2$	$-1$	$-4$	$5$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-4q^{3}-7q^{4}+5q^{5}+4q^{6}+\cdots$
2255.4.a.b	$2255$	$4$	2255.a	1.a	$1$	$44$	$44$	$133.049$		$_{}$	None	None	✓	✓	✓	✓	2255.4.a.b	$1$	$1$	$-17$	$-18$	$220$	$-144$	$-$		$\mathrm{SU}(2)$
2255.4.a.c	$2255$	$4$	2255.a	1.a	$1$	$44$	$44$	$133.049$		$_{}$	None	None	✓	✓	✓	✓	2255.4.a.c	$1$	$1$	$1$	$0$	$-220$	$-74$	$-$		$\mathrm{SU}(2)$
2255.4.a.d	$2255$	$4$	2255.a	1.a	$1$	$46$	$46$	$133.049$		$_{}$	None	None	✓	✓	✓	✓	2255.4.a.d	$1$	$1$	$1$	$0$	$-230$	$-4$	$-$		$\mathrm{SU}(2)$
2255.4.a.e	$2255$	$4$	2255.a	1.a	$1$	$46$	$46$	$133.049$		$_{}$	None	None	✓	✓	✓	✓	2255.4.a.e	$1$	$1$	$3$	$-18$	$230$	$-18$	$-$		$\mathrm{SU}(2)$
2255.4.a.f	$2255$	$4$	2255.a	1.a	$1$	$53$	$53$	$133.049$		$_{}$	None	None	✓	✓	✓		2255.4.a.f	$1$	$0$	$16$	$16$	$265$	$162$	$+$		$\mathrm{SU}(2)$
2255.4.a.g	$2255$	$4$	2255.a	1.a	$1$	$54$	$54$	$133.049$		$_{}$	None	None	✓	✓	✓	✓	2255.4.a.g	$1$	$0$	$-11$	$6$	$-270$	$94$	$+$		$\mathrm{SU}(2)$
2255.4.a.h	$2255$	$4$	2255.a	1.a	$1$	$56$	$56$	$133.049$		$_{}$	None	None	✓	✓	✓	✓	2255.4.a.h	$1$	$0$	$-3$	$6$	$-280$	$24$	$+$		$\mathrm{SU}(2)$
2255.4.a.i	$2255$	$4$	2255.a	1.a	$1$	$56$	$56$	$133.049$		$_{}$	None	None	✓	✓	✓	✓	2255.4.a.i	$1$	$0$	$11$	$12$	$280$	$38$	$+$		$\mathrm{SU}(2)$

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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.