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 (1-50 of 122 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
1078.2.a.a	$1078$	$2$	1078.a	1.a	$1$	$1$	$1$	$8.608$	$\Q$	None	✓				154.2.e.d	$1$	$1$	$-1$	$-3$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-3q^{3}+q^{4}-4q^{5}+3q^{6}-q^{8}+\cdots$
1078.2.a.b	$1078$	$2$	1078.a	1.a	$1$	$1$	$1$	$8.608$	$\Q$	None	✓				154.2.a.b	$1$	$1$	$-1$	$-2$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}-2q^{5}+2q^{6}-q^{8}+\cdots$
1078.2.a.c	$1078$	$2$	1078.a	1.a	$1$	$1$	$1$	$8.608$	$\Q$	None	✓				154.2.e.c	$1$	$0$	$-1$	$-1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}-2q^{9}+\cdots$
1078.2.a.d	$1078$	$2$	1078.a	1.a	$1$	$1$	$1$	$8.608$	$\Q$	None	✓				154.2.a.a	$1$	$0$	$-1$	$0$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+4q^{5}-q^{8}-3q^{9}-4q^{10}+\cdots$
1078.2.a.e	$1078$	$2$	1078.a	1.a	$1$	$1$	$1$	$8.608$	$\Q$	None	✓				154.2.e.c	$1$	$1$	$-1$	$1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}-2q^{9}+\cdots$
1078.2.a.f	$1078$	$2$	1078.a	1.a	$1$	$1$	$1$	$8.608$	$\Q$	None	✓				154.2.e.d	$1$	$0$	$-1$	$3$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+3q^{3}+q^{4}+4q^{5}-3q^{6}-q^{8}+\cdots$
1078.2.a.g	$1078$	$2$	1078.a	1.a	$1$	$1$	$1$	$8.608$	$\Q$	None	✓				154.2.e.a	$1$	$1$	$1$	$-3$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-3q^{3}+q^{4}-2q^{5}-3q^{6}+q^{8}+\cdots$
1078.2.a.h	$1078$	$2$	1078.a	1.a	$1$	$1$	$1$	$8.608$	$\Q$	None	✓	✓			1078.2.a.h	$1$	$0$	$1$	$-2$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}-2q^{5}-2q^{6}+q^{8}+\cdots$
1078.2.a.i	$1078$	$2$	1078.a	1.a	$1$	$1$	$1$	$8.608$	$\Q$	None	✓				154.2.e.b	$1$	$1$	$1$	$-1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}-2q^{9}+\cdots$
1078.2.a.j	$1078$	$2$	1078.a	1.a	$1$	$1$	$1$	$8.608$	$\Q$	None	✓				154.2.a.c	$1$	$1$	$1$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{5}+q^{8}-3q^{9}-2q^{10}+\cdots$
1078.2.a.k	$1078$	$2$	1078.a	1.a	$1$	$1$	$1$	$8.608$	$\Q$	None	✓				154.2.e.b	$1$	$0$	$1$	$1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}-2q^{9}+\cdots$
1078.2.a.l	$1078$	$2$	1078.a	1.a	$1$	$1$	$1$	$8.608$	$\Q$	None	✓	✓			1078.2.a.h	$1$	$0$	$1$	$2$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}+q^{4}+2q^{5}+2q^{6}+q^{8}+\cdots$
1078.2.a.m	$1078$	$2$	1078.a	1.a	$1$	$1$	$1$	$8.608$	$\Q$	None	✓				154.2.e.a	$1$	$0$	$1$	$3$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+3q^{3}+q^{4}+2q^{5}+3q^{6}+q^{8}+\cdots$
1078.2.a.n	$1078$	$2$	1078.a	1.a	$1$	$2$	$2$	$8.608$	$\Q(\sqrt{7}) $	None	✓				154.2.e.f	$1$	$1$	$-2$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta q^{3}+q^{4}+(-1-\beta )q^{5}-\beta q^{6}+\cdots$
1078.2.a.o	$1078$	$2$	1078.a	1.a	$1$	$2$	$2$	$8.608$	$\Q(\sqrt{2}) $	None	✓	✓			1078.2.a.o	$2$	$1$	$-2$	$0$	$0$	$0$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta q^{5}-q^{8}-3q^{9}-\beta q^{10}+\cdots$
1078.2.a.p	$1078$	$2$	1078.a	1.a	$1$	$2$	$2$	$8.608$	$\Q(\sqrt{2}) $	None	✓	✓			1078.2.a.p	$2$	$0$	$-2$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2\beta q^{5}-q^{8}-3q^{9}+2\beta q^{10}+\cdots$
1078.2.a.q	$1078$	$2$	1078.a	1.a	$1$	$2$	$2$	$8.608$	$\Q(\sqrt{2}) $	None	✓	✓	✓		1078.2.a.q	$2$	$1$	$-2$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta q^{3}+q^{4}-\beta q^{5}-\beta q^{6}-q^{8}+\cdots$
1078.2.a.r	$1078$	$2$	1078.a	1.a	$1$	$2$	$2$	$8.608$	$\Q(\sqrt{2}) $	None	✓	✓	✓		1078.2.a.r	$2$	$0$	$-2$	$0$	$0$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}-q^{8}+5q^{9}+\cdots$
1078.2.a.s	$1078$	$2$	1078.a	1.a	$1$	$2$	$2$	$8.608$	$\Q(\sqrt{7}) $	None	✓				154.2.e.f	$1$	$0$	$-2$	$0$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta q^{3}+q^{4}+(1-\beta )q^{5}-\beta q^{6}+\cdots$
1078.2.a.t	$1078$	$2$	1078.a	1.a	$1$	$2$	$2$	$8.608$	$\Q(\sqrt{2}) $	None	✓		✓	✓	154.2.e.e	$1$	$1$	$2$	$-2$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1+\beta )q^{3}+q^{4}+(-2-\beta )q^{5}+\cdots$
1078.2.a.u	$1078$	$2$	1078.a	1.a	$1$	$2$	$2$	$8.608$	$\Q(\sqrt{2}) $	None	✓	✓			1078.2.a.u	$2$	$0$	$2$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta q^{3}+q^{4}+3\beta q^{5}+\beta q^{6}+\cdots$
1078.2.a.v	$1078$	$2$	1078.a	1.a	$1$	$2$	$2$	$8.608$	$\Q(\sqrt{2}) $	None	✓	✓			1078.2.a.v	$2$	$0$	$2$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2\beta q^{3}+q^{4}+2\beta q^{6}+q^{8}+\cdots$
1078.2.a.w	$1078$	$2$	1078.a	1.a	$1$	$2$	$2$	$8.608$	$\Q(\sqrt{5}) $	None	✓				154.2.a.d	$1$	$0$	$2$	$2$	$-2$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+(1+\beta )q^{3}+q^{4}+(-1-\beta )q^{5}+\cdots$
1078.2.a.x	$1078$	$2$	1078.a	1.a	$1$	$2$	$2$	$8.608$	$\Q(\sqrt{2}) $	None	✓				154.2.e.e	$1$	$0$	$2$	$2$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1+\beta )q^{3}+q^{4}+(2-\beta )q^{5}+\cdots$
1078.2.c.a	$1078$	$2$	1078.c	77.b	$2$	$8$	$8$	$8.608$	$\Q(\zeta_{16})$	None		✓			1078.2.c.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_1 q^{2}+(-\beta_{4}-\beta_{2})q^{3}-q^{4}+\cdots$
1078.2.c.b	$1078$	$2$	1078.c	77.b	$2$	$16$	$16$	$8.608$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None					154.2.i.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{9}q^{2}+\beta _{14}q^{3}-q^{4}+(-\beta _{8}+\beta _{11}+\cdots)q^{5}+\cdots$
1078.2.c.c	$1078$	$2$	1078.c	77.b	$2$	$16$	$16$	$8.608$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓			1078.2.c.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}-\beta _{5}q^{3}-q^{4}+(-\beta _{9}+\beta _{11}+\cdots)q^{5}+\cdots$
1078.2.e.a	$1078$	$2$	1078.e	7.c	$3$	$2$	$1$	$8.608$	$\Q(\sqrt{-3}) $	None		✓			1078.2.a.h	$2$	$0$	$-1$	$-2$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
1078.2.e.b	$1078$	$2$	1078.e	7.c	$3$	$2$	$1$	$8.608$	$\Q(\sqrt{-3}) $	None					154.2.a.c	$2$	$0$	$-1$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-2\zeta_{6}q^{5}+\cdots$
1078.2.e.c	$1078$	$2$	1078.e	7.c	$3$	$2$	$1$	$8.608$	$\Q(\sqrt{-3}) $	None					154.2.a.c	$2$	$0$	$-1$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+2\zeta_{6}q^{5}+\cdots$
1078.2.e.d	$1078$	$2$	1078.e	7.c	$3$	$2$	$1$	$8.608$	$\Q(\sqrt{-3}) $	None					154.2.e.b	$2$	$0$	$-1$	$1$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
1078.2.e.e	$1078$	$2$	1078.e	7.c	$3$	$2$	$1$	$8.608$	$\Q(\sqrt{-3}) $	None		✓			1078.2.a.h	$2$	$0$	$-1$	$2$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
1078.2.e.f	$1078$	$2$	1078.e	7.c	$3$	$2$	$1$	$8.608$	$\Q(\sqrt{-3}) $	None					154.2.e.a	$2$	$0$	$-1$	$3$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
1078.2.e.g	$1078$	$2$	1078.e	7.c	$3$	$2$	$1$	$8.608$	$\Q(\sqrt{-3}) $	None					154.2.e.d	$2$	$0$	$1$	$-3$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
1078.2.e.h	$1078$	$2$	1078.e	7.c	$3$	$2$	$1$	$8.608$	$\Q(\sqrt{-3}) $	None					154.2.a.b	$2$	$0$	$1$	$-2$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
1078.2.e.i	$1078$	$2$	1078.e	7.c	$3$	$2$	$1$	$8.608$	$\Q(\sqrt{-3}) $	None					154.2.a.a	$2$	$0$	$1$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-4\zeta_{6}q^{5}+\cdots$
1078.2.e.j	$1078$	$2$	1078.e	7.c	$3$	$2$	$1$	$8.608$	$\Q(\sqrt{-3}) $	None					154.2.a.a	$2$	$0$	$1$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+4\zeta_{6}q^{5}+\cdots$
1078.2.e.k	$1078$	$2$	1078.e	7.c	$3$	$2$	$1$	$8.608$	$\Q(\sqrt{-3}) $	None					154.2.e.c	$2$	$0$	$1$	$1$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
1078.2.e.l	$1078$	$2$	1078.e	7.c	$3$	$2$	$1$	$8.608$	$\Q(\sqrt{-3}) $	None					154.2.a.b	$2$	$0$	$1$	$2$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
1078.2.e.m	$1078$	$2$	1078.e	7.c	$3$	$4$	$2$	$8.608$	$\Q(\sqrt{2}, \sqrt{-3})$	None					154.2.e.e	$2$	$0$	$-2$	$-2$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{2}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+(-1+\cdots)q^{4}+\cdots$
1078.2.e.n	$1078$	$2$	1078.e	7.c	$3$	$4$	$2$	$8.608$	$\Q(\sqrt{-3}, \sqrt{5})$	None					154.2.a.d	$2$	$0$	$-2$	$-2$	$2$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(-1-\beta _{1}-\beta _{2})q^{3}+(-1+\cdots)q^{4}+\cdots$
1078.2.e.o	$1078$	$2$	1078.e	7.c	$3$	$4$	$2$	$8.608$	$\Q(\sqrt{2}, \sqrt{-3})$	None		✓			1078.2.a.v	$4$	$0$	$-2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{2}q^{2}+2\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+\cdots$
1078.2.e.p	$1078$	$2$	1078.e	7.c	$3$	$4$	$2$	$8.608$	$\Q(\sqrt{2}, \sqrt{-3})$	None		✓			1078.2.a.u	$4$	$0$	$-2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{2}q^{2}+\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+(-3\beta _{1}+\cdots)q^{5}+\cdots$
1078.2.e.q	$1078$	$2$	1078.e	7.c	$3$	$4$	$2$	$8.608$	$\Q(\sqrt{-3}, \sqrt{5})$	None					154.2.a.d	$2$	$0$	$-2$	$2$	$-2$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots$
1078.2.e.r	$1078$	$2$	1078.e	7.c	$3$	$4$	$2$	$8.608$	$\Q(\sqrt{2}, \sqrt{-3})$	None		✓			1078.2.a.r	$4$	$0$	$2$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{2}q^{2}+\beta _{1}q^{3}+(-1-\beta _{2})q^{4}-\beta _{3}q^{6}+\cdots$
1078.2.e.s	$1078$	$2$	1078.e	7.c	$3$	$4$	$2$	$8.608$	$\Q(\sqrt{2}, \sqrt{-3})$	None		✓			1078.2.a.q	$4$	$0$	$2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{2}q^{2}+\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$
1078.2.e.t	$1078$	$2$	1078.e	7.c	$3$	$4$	$2$	$8.608$	$\Q(\sqrt{2}, \sqrt{-3})$	None		✓			1078.2.a.p	$4$	$0$	$2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{2})q^{2}+\beta _{2}q^{4}-2\beta _{1}q^{5}-q^{8}+\cdots$
1078.2.e.u	$1078$	$2$	1078.e	7.c	$3$	$4$	$2$	$8.608$	$\Q(\sqrt{2}, \sqrt{-3})$	None		✓			1078.2.a.o	$4$	$0$	$2$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{2})q^{2}+\beta _{2}q^{4}-\beta _{1}q^{5}-q^{8}+\cdots$
1078.2.e.v	$1078$	$2$	1078.e	7.c	$3$	$4$	$2$	$8.608$	$\Q(\sqrt{-3}, \sqrt{7})$	None					154.2.e.f	$2$	$0$	$2$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{2}q^{2}+\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$
1078.2.i.a	$1078$	$2$	1078.i	77.i	$6$	$16$	$8$	$8.608$	$\Q(\zeta_{48})$	None		✓			1078.2.c.a	$8$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta_1 q^{2}+(-\beta_{10}+\beta_{7}-\beta_{2})q^{3}+\cdots$

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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.