LMFDB - Newform search results

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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 (30 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				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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
6174.2.a.a	$6174$	$2$	6174.a	1.a	$1$	$3$	$3$	$49.300$	$\Q(\zeta_{14})^+$	None	✓				2058.2.a.j	$1$	$0$	$-3$	$0$	$-8$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-3-\beta _{2})q^{5}-q^{8}+(3+\cdots)q^{10}+\cdots$
6174.2.a.b	$6174$	$2$	6174.a	1.a	$1$	$3$	$3$	$49.300$	$\Q(\zeta_{14})^+$	None	✓				2058.2.a.i	$1$	$1$	$-3$	$0$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-1-\beta _{1})q^{5}-q^{8}+(1+\cdots)q^{10}+\cdots$
6174.2.a.c	$6174$	$2$	6174.a	1.a	$1$	$3$	$3$	$49.300$	$\Q(\zeta_{14})^+$	None	✓				686.2.a.c	$1$	$0$	$-3$	$0$	$-4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-1-\beta _{1})q^{5}-q^{8}+(1+\cdots)q^{10}+\cdots$
6174.2.a.d	$6174$	$2$	6174.a	1.a	$1$	$3$	$3$	$49.300$	$\Q(\zeta_{14})^+$	None	✓				2058.2.a.i	$1$	$1$	$-3$	$0$	$4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1+\beta _{1})q^{5}-q^{8}+(-1+\cdots)q^{10}+\cdots$
6174.2.a.e	$6174$	$2$	6174.a	1.a	$1$	$3$	$3$	$49.300$	$\Q(\zeta_{14})^+$	None	✓				686.2.a.c	$1$	$1$	$-3$	$0$	$4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1+\beta _{1})q^{5}-q^{8}+(-1+\cdots)q^{10}+\cdots$
6174.2.a.f	$6174$	$2$	6174.a	1.a	$1$	$3$	$3$	$49.300$	$\Q(\zeta_{14})^+$	None	✓				2058.2.a.j	$1$	$0$	$-3$	$0$	$8$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(3-\beta _{1})q^{5}-q^{8}+(-3+\cdots)q^{10}+\cdots$
6174.2.a.g	$6174$	$2$	6174.a	1.a	$1$	$3$	$3$	$49.300$	$\Q(\zeta_{14})^+$	None	✓				2058.2.a.d	$1$	$1$	$3$	$0$	$-5$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-2-\beta _{2})q^{5}+q^{8}+(-2+\cdots)q^{10}+\cdots$
6174.2.a.h	$6174$	$2$	6174.a	1.a	$1$	$3$	$3$	$49.300$	$\Q(\zeta_{14})^+$	None	✓				2058.2.a.c	$1$	$1$	$3$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1-\beta _{2})q^{5}+q^{8}+(-1+\cdots)q^{10}+\cdots$
6174.2.a.i	$6174$	$2$	6174.a	1.a	$1$	$3$	$3$	$49.300$	$\Q(\zeta_{14})^+$	None	✓				2058.2.a.b	$1$	$1$	$3$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2\beta _{1}q^{5}+q^{8}-2\beta _{1}q^{10}+\cdots$
6174.2.a.j	$6174$	$2$	6174.a	1.a	$1$	$3$	$3$	$49.300$	$\Q(\zeta_{14})^+$	None	✓				2058.2.a.a	$1$	$0$	$3$	$0$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1-\beta _{2})q^{5}+q^{8}+(-1+\cdots)q^{10}+\cdots$
6174.2.a.k	$6174$	$2$	6174.a	1.a	$1$	$3$	$3$	$49.300$	$\Q(\zeta_{14})^+$	None	✓				686.2.a.a	$1$	$1$	$3$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-\beta _{1}-\beta _{2})q^{5}+q^{8}+\cdots$
6174.2.a.l	$6174$	$2$	6174.a	1.a	$1$	$3$	$3$	$49.300$	$\Q(\zeta_{14})^+$	None	✓				686.2.a.a	$1$	$0$	$3$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(1-2\beta _{1}+\beta _{2})q^{5}+q^{8}+\cdots$
6174.2.a.m	$6174$	$2$	6174.a	1.a	$1$	$3$	$3$	$49.300$	$\Q(\zeta_{14})^+$	None	✓				2058.2.a.c	$1$	$1$	$3$	$0$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(1-\beta _{1})q^{5}+q^{8}+(1-\beta _{1}+\cdots)q^{10}+\cdots$
6174.2.a.n	$6174$	$2$	6174.a	1.a	$1$	$3$	$3$	$49.300$	$\Q(\zeta_{14})^+$	None	✓				2058.2.a.b	$1$	$0$	$3$	$0$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2\beta _{1}q^{5}+q^{8}+2\beta _{1}q^{10}+\cdots$
6174.2.a.o	$6174$	$2$	6174.a	1.a	$1$	$3$	$3$	$49.300$	$\Q(\zeta_{14})^+$	None	✓				2058.2.a.a	$1$	$0$	$3$	$0$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(1-\beta _{1})q^{5}+q^{8}+(1-\beta _{1}+\cdots)q^{10}+\cdots$
6174.2.a.p	$6174$	$2$	6174.a	1.a	$1$	$3$	$3$	$49.300$	$\Q(\zeta_{14})^+$	None	✓				2058.2.a.d	$1$	$0$	$3$	$0$	$5$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(2-\beta _{1})q^{5}+q^{8}+(2-\beta _{1}+\cdots)q^{10}+\cdots$
6174.2.a.q	$6174$	$2$	6174.a	1.a	$1$	$6$	$6$	$49.300$	6.6.6456289.1	None	✓	✓			6174.2.a.q	$1$	$1$	$-6$	$0$	$-7$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-1-\beta _{1})q^{5}-q^{8}+(1+\cdots)q^{10}+\cdots$
6174.2.a.r	$6174$	$2$	6174.a	1.a	$1$	$6$	$6$	$49.300$	6.6.72070817.1	None	✓		✓		2058.2.a.m	$1$	$1$	$-6$	$0$	$-3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-\beta _{1}+\beta _{2})q^{5}-q^{8}+\cdots$
6174.2.a.s	$6174$	$2$	6174.a	1.a	$1$	$6$	$6$	$49.300$	6.6.10910144.1	None	✓				686.2.a.f	$2$	$0$	$-6$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-\beta _{5}q^{5}-q^{8}+\beta _{5}q^{10}+\cdots$
6174.2.a.t	$6174$	$2$	6174.a	1.a	$1$	$6$	$6$	$49.300$	6.6.43179584.1	None	✓	✓			6174.2.a.t	$2$	$1$	$-6$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta _{1}q^{5}-q^{8}-\beta _{1}q^{10}+\cdots$
6174.2.a.u	$6174$	$2$	6174.a	1.a	$1$	$6$	$6$	$49.300$	6.6.4456256.1	None	✓	✓			6174.2.a.u	$2$	$0$	$-6$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-\beta _{1}+\beta _{5})q^{5}-q^{8}+\cdots$
6174.2.a.v	$6174$	$2$	6174.a	1.a	$1$	$6$	$6$	$49.300$	6.6.72070817.1	None	✓				2058.2.a.m	$1$	$0$	$-6$	$0$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(\beta _{1}-\beta _{2})q^{5}-q^{8}+(-\beta _{1}+\cdots)q^{10}+\cdots$
6174.2.a.w	$6174$	$2$	6174.a	1.a	$1$	$6$	$6$	$49.300$	6.6.6456289.1	None	✓	✓			6174.2.a.q	$1$	$0$	$-6$	$0$	$7$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1+\beta _{1})q^{5}-q^{8}+(-1+\cdots)q^{10}+\cdots$
6174.2.a.x	$6174$	$2$	6174.a	1.a	$1$	$6$	$6$	$49.300$	6.6.6456289.1	None	✓	✓			6174.2.a.q	$1$	$1$	$6$	$0$	$-7$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1-\beta _{1})q^{5}+q^{8}+(-1+\cdots)q^{10}+\cdots$
6174.2.a.y	$6174$	$2$	6174.a	1.a	$1$	$6$	$6$	$49.300$	6.6.4456256.1	None	✓	✓			6174.2.a.u	$2$	$1$	$6$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-\beta _{1}+\beta _{5})q^{5}+q^{8}+\cdots$
6174.2.a.z	$6174$	$2$	6174.a	1.a	$1$	$6$	$6$	$49.300$	6.6.4456256.1	None	✓		✓		686.2.a.e	$2$	$0$	$6$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-\beta _{1}-\beta _{3}+\beta _{5})q^{5}+\cdots$
6174.2.a.ba	$6174$	$2$	6174.a	1.a	$1$	$6$	$6$	$49.300$	6.6.43179584.1	None	✓	✓			6174.2.a.t	$2$	$0$	$6$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta _{1}q^{5}+q^{8}+\beta _{1}q^{10}+\cdots$
6174.2.a.bb	$6174$	$2$	6174.a	1.a	$1$	$6$	$6$	$49.300$	6.6.6456289.1	None	✓	✓			6174.2.a.q	$1$	$0$	$6$	$0$	$7$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(1+\beta _{1})q^{5}+q^{8}+(1+\beta _{1}+\cdots)q^{10}+\cdots$
6174.2.d.a	$6174$	$2$	6174.d	21.c	$2$	$48$	$48$	$49.300$		None		✓			6174.2.d.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
6174.2.d.b	$6174$	$2$	6174.d	21.c	$2$	$48$	$48$	$49.300$		None		✓			6174.2.d.b	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$

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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.