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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 (41 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
1029.1.l.a	$1029$	$1$	1029.l	147.l	$14$	$6$	$1$	$0.514$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-3}) $	None			✓	✓	147.1.l.a	$4$	$0$	$0$	$1$	$0$	$0$		$1$		$q-\zeta_{14}^{2}q^{3}+\zeta_{14}^{6}q^{4}+\zeta_{14}^{4}q^{9}+\cdots$
1029.1.n.a	$1029$	$1$	1029.n	147.n	$42$	$12$	$1$	$0.514$	$\Q(\zeta_{21})$	$D_{7}$	$\Q(\sqrt{-3}) $	None					147.1.l.a	$8$	$0$	$0$	$-1$	$0$	$0$		$1$		$q+\zeta_{42}^{13}q^{3}+\zeta_{42}^{4}q^{4}-\zeta_{42}^{5}q^{9}+\cdots$
1029.1.n.b	$1029$	$1$	1029.n	147.n	$42$	$12$	$1$	$0.514$	$\Q(\zeta_{21})$	$D_{7}$	$\Q(\sqrt{-3}) $	None					147.1.l.a	$8$	$0$	$0$	$1$	$0$	$0$		$1$		$q-\zeta_{42}^{13}q^{3}+\zeta_{42}^{4}q^{4}-\zeta_{42}^{5}q^{9}+\cdots$
1029.1.t.a	$1029$	$1$	1029.t	1029.t	$98$	$42$	$1$	$0.514$	$\Q(\zeta_{98})$	$D_{49}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	1029.1.t.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{98}^{23}q^{3}+\zeta_{98}^{6}q^{4}+\zeta_{98}^{24}q^{7}+\cdots$
1029.2.a.a	$1029$	$2$	1029.a	1.a	$1$	$3$	$3$	$8.217$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	✓			1029.2.a.a	$1$	$1$	$-1$	$-3$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}-\beta _{1}q^{5}+\beta _{1}q^{6}+\cdots$
1029.2.a.b	$1029$	$2$	1029.a	1.a	$1$	$3$	$3$	$8.217$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	✓			1029.2.a.b	$1$	$0$	$-1$	$-3$	$6$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+2q^{5}+\beta _{1}q^{6}+\cdots$
1029.2.a.c	$1029$	$2$	1029.a	1.a	$1$	$3$	$3$	$8.217$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	✓			1029.2.a.b	$1$	$1$	$-1$	$3$	$-6$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}-2q^{5}-\beta _{1}q^{6}+\cdots$
1029.2.a.d	$1029$	$2$	1029.a	1.a	$1$	$3$	$3$	$8.217$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	✓			1029.2.a.a	$1$	$1$	$-1$	$3$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+\beta _{1}q^{5}-\beta _{1}q^{6}+\cdots$
1029.2.a.e	$1029$	$2$	1029.a	1.a	$1$	$9$	$9$	$8.217$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	✓	✓		1029.2.a.e	$1$	$1$	$-2$	$-9$	$-6$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{1}-\beta _{2}+\beta _{6}+\cdots)q^{4}+\cdots$
1029.2.a.f	$1029$	$2$	1029.a	1.a	$1$	$9$	$9$	$8.217$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	✓			1029.2.a.e	$1$	$0$	$-2$	$9$	$6$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{1}-\beta _{2}+\beta _{6}+\cdots)q^{4}+\cdots$
1029.2.a.g	$1029$	$2$	1029.a	1.a	$1$	$9$	$9$	$8.217$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	✓	✓		1029.2.a.g	$1$	$0$	$5$	$-9$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}-q^{3}+(2+\beta _{5}-\beta _{6})q^{4}+\cdots$
1029.2.a.h	$1029$	$2$	1029.a	1.a	$1$	$9$	$9$	$8.217$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	✓			1029.2.a.g	$1$	$0$	$5$	$9$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+q^{3}+(2+\beta _{5}-\beta _{6})q^{4}+\cdots$
1029.2.c.a	$1029$	$2$	1029.c	21.c	$2$	$48$	$48$	$8.217$		$_{}$	None	None		✓			1029.2.c.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1029.2.c.b	$1029$	$2$	1029.c	21.c	$2$	$48$	$48$	$8.217$		$_{}$	None	None		✓			1029.2.c.b	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1029.2.e.a	$1029$	$2$	1029.e	7.c	$3$	$6$	$3$	$8.217$	6.0.64827.1	$_{}$	None	None		✓			1029.2.a.a	$2$	$0$	$1$	$-3$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}-\beta _{5}q^{3}+(\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots$
1029.2.e.b	$1029$	$2$	1029.e	7.c	$3$	$6$	$3$	$8.217$	6.0.64827.1	$_{}$	None	None		✓			1029.2.a.b	$2$	$0$	$1$	$-3$	$6$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}-\beta _{5}q^{3}+(\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots$
1029.2.e.c	$1029$	$2$	1029.e	7.c	$3$	$6$	$3$	$8.217$	6.0.64827.1	$_{}$	None	None		✓			1029.2.a.b	$2$	$0$	$1$	$3$	$-6$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+\beta _{5}q^{3}+(\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots$
1029.2.e.d	$1029$	$2$	1029.e	7.c	$3$	$6$	$3$	$8.217$	6.0.64827.1	$_{}$	None	None		✓			1029.2.a.a	$2$	$0$	$1$	$3$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+\beta _{5}q^{3}+(\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots$
1029.2.e.e	$1029$	$2$	1029.e	7.c	$3$	$18$	$9$	$8.217$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None		✓			1029.2.a.g	$2$	$0$	$-5$	$-9$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{2}+\beta _{13})q^{2}+(-1-\beta _{13}+\cdots)q^{3}+\cdots$
1029.2.e.f	$1029$	$2$	1029.e	7.c	$3$	$18$	$9$	$8.217$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None		✓			1029.2.a.g	$2$	$0$	$-5$	$9$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{2}+\beta _{13})q^{2}+(1+\beta _{13}+\cdots)q^{3}+\cdots$
1029.2.e.g	$1029$	$2$	1029.e	7.c	$3$	$18$	$9$	$8.217$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None		✓			1029.2.a.e	$2$	$0$	$2$	$-9$	$-6$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(-1-\beta _{6})q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots$
1029.2.e.h	$1029$	$2$	1029.e	7.c	$3$	$18$	$9$	$8.217$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None		✓			1029.2.a.e	$2$	$0$	$2$	$9$	$6$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(1+\beta _{6})q^{3}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
1029.3.d.a	$1029$	$3$	1029.d	7.b	$2$	$24$	$24$	$28.038$		$_{}$	None	None		✓			1029.3.d.a	$2$	$0$	$-10$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1029.3.d.b	$1029$	$3$	1029.d	7.b	$2$	$24$	$24$	$28.038$		$_{}$	None	None		✓			1029.3.d.b	$2$	$0$	$4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1029.3.d.c	$1029$	$3$	1029.d	7.b	$2$	$48$	$48$	$28.038$		$_{}$	None	None		✓	✓		1029.3.d.c	$2$	$0$	$8$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1029.4.a.a	$1029$	$4$	1029.a	1.a	$1$	$15$	$15$	$60.713$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	None	None	✓	✓			1029.4.a.a	$1$	$1$	$-8$	$-45$	$2$	$0$	$-$	$7^{5}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}-3q^{3}+(4-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
1029.4.a.b	$1029$	$4$	1029.a	1.a	$1$	$15$	$15$	$60.713$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	None	None	✓	✓			1029.4.a.a	$1$	$1$	$-8$	$45$	$-2$	$0$	$-$	$7^{5}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+3q^{3}+(4-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
1029.4.a.c	$1029$	$4$	1029.a	1.a	$1$	$15$	$15$	$60.713$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	None	None	✓	✓			1029.4.a.c	$1$	$0$	$-1$	$-45$	$30$	$0$	$+$	$2^{3}\cdot 7^{5}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-3q^{3}+(2+\beta _{5}-\beta _{6})q^{4}+\cdots$
1029.4.a.d	$1029$	$4$	1029.a	1.a	$1$	$15$	$15$	$60.713$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	None	None	✓	✓			1029.4.a.c	$1$	$1$	$-1$	$45$	$-30$	$0$	$-$	$2^{3}\cdot 7^{5}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+3q^{3}+(2+\beta _{5}-\beta _{6})q^{4}+\cdots$
1029.4.a.e	$1029$	$4$	1029.a	1.a	$1$	$21$	$21$	$60.713$		$_{}$	None	None	✓	✓	✓		1029.4.a.e	$1$	$1$	$4$	$-63$	$-30$	$0$	$-$		$\mathrm{SU}(2)$
1029.4.a.f	$1029$	$4$	1029.a	1.a	$1$	$21$	$21$	$60.713$		$_{}$	None	None	✓	✓	✓		1029.4.a.f	$1$	$0$	$4$	$-63$	$-2$	$0$	$+$		$\mathrm{SU}(2)$
1029.4.a.g	$1029$	$4$	1029.a	1.a	$1$	$21$	$21$	$60.713$		$_{}$	None	None	✓	✓			1029.4.a.e	$1$	$0$	$4$	$63$	$30$	$0$	$+$		$\mathrm{SU}(2)$
1029.4.a.h	$1029$	$4$	1029.a	1.a	$1$	$21$	$21$	$60.713$		$_{}$	None	None	✓	✓			1029.4.a.f	$1$	$0$	$4$	$63$	$2$	$0$	$+$		$\mathrm{SU}(2)$
1029.6.a.a	$1029$	$6$	1029.a	1.a	$1$	$27$	$27$	$165.035$		$_{}$	None	None	✓	✓			1029.6.a.a	$1$	$1$	$-14$	$-243$	$31$	$0$	$+$		$\mathrm{SU}(2)$
1029.6.a.b	$1029$	$6$	1029.a	1.a	$1$	$27$	$27$	$165.035$		$_{}$	None	None	✓	✓			1029.6.a.a	$1$	$1$	$-14$	$243$	$-31$	$0$	$+$		$\mathrm{SU}(2)$
1029.6.a.c	$1029$	$6$	1029.a	1.a	$1$	$27$	$27$	$165.035$		$_{}$	None	None	✓	✓			1029.6.a.c	$1$	$0$	$7$	$-243$	$150$	$0$	$-$		$\mathrm{SU}(2)$
1029.6.a.d	$1029$	$6$	1029.a	1.a	$1$	$27$	$27$	$165.035$		$_{}$	None	None	✓	✓			1029.6.a.c	$1$	$1$	$7$	$243$	$-150$	$0$	$+$		$\mathrm{SU}(2)$
1029.6.a.e	$1029$	$6$	1029.a	1.a	$1$	$33$	$33$	$165.035$		$_{}$	None	None	✓	✓	✓		1029.6.a.e	$1$	$1$	$-4$	$-297$	$-150$	$0$	$+$		$\mathrm{SU}(2)$
1029.6.a.f	$1029$	$6$	1029.a	1.a	$1$	$33$	$33$	$165.035$		$_{}$	None	None	✓	✓			1029.6.a.e	$1$	$0$	$-4$	$297$	$150$	$0$	$-$		$\mathrm{SU}(2)$
1029.6.a.g	$1029$	$6$	1029.a	1.a	$1$	$33$	$33$	$165.035$		$_{}$	None	None	✓	✓	✓		1029.6.a.g	$1$	$0$	$10$	$-297$	$-31$	$0$	$-$		$\mathrm{SU}(2)$
1029.6.a.h	$1029$	$6$	1029.a	1.a	$1$	$33$	$33$	$165.035$		$_{}$	None	None	✓	✓			1029.6.a.g	$1$	$0$	$10$	$297$	$31$	$0$	$-$		$\mathrm{SU}(2)$

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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.