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 144 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
1470.2.a.a	$1470$	$2$	1470.a	1.a	$1$	$1$	$1$	$11.738$	$\Q$	None	✓		✓	✓	210.2.i.d	$1$	$1$	$-1$	$-1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots$
1470.2.a.b	$1470$	$2$	1470.a	1.a	$1$	$1$	$1$	$11.738$	$\Q$	None	✓				210.2.a.b	$1$	$0$	$-1$	$-1$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots$
1470.2.a.c	$1470$	$2$	1470.a	1.a	$1$	$1$	$1$	$11.738$	$\Q$	None	✓	✓			1470.2.a.c	$1$	$0$	$-1$	$-1$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots$
1470.2.a.d	$1470$	$2$	1470.a	1.a	$1$	$1$	$1$	$11.738$	$\Q$	None	✓				30.2.a.a	$1$	$1$	$-1$	$-1$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots$
1470.2.a.e	$1470$	$2$	1470.a	1.a	$1$	$1$	$1$	$11.738$	$\Q$	None	✓				210.2.i.c	$1$	$1$	$-1$	$-1$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots$
1470.2.a.f	$1470$	$2$	1470.a	1.a	$1$	$1$	$1$	$11.738$	$\Q$	None	✓				210.2.i.c	$1$	$0$	$-1$	$1$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots$
1470.2.a.g	$1470$	$2$	1470.a	1.a	$1$	$1$	$1$	$11.738$	$\Q$	None	✓				210.2.a.a	$1$	$0$	$-1$	$1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots$
1470.2.a.h	$1470$	$2$	1470.a	1.a	$1$	$1$	$1$	$11.738$	$\Q$	None	✓				210.2.i.d	$1$	$0$	$-1$	$1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots$
1470.2.a.i	$1470$	$2$	1470.a	1.a	$1$	$1$	$1$	$11.738$	$\Q$	None	✓	✓			1470.2.a.c	$1$	$0$	$-1$	$1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots$
1470.2.a.j	$1470$	$2$	1470.a	1.a	$1$	$1$	$1$	$11.738$	$\Q$	None	✓				210.2.a.e	$1$	$1$	$1$	$-1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots$
1470.2.a.k	$1470$	$2$	1470.a	1.a	$1$	$1$	$1$	$11.738$	$\Q$	None	✓				210.2.i.a	$1$	$1$	$1$	$-1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots$
1470.2.a.l	$1470$	$2$	1470.a	1.a	$1$	$1$	$1$	$11.738$	$\Q$	None	✓		✓	✓	210.2.i.b	$1$	$1$	$1$	$-1$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots$
1470.2.a.m	$1470$	$2$	1470.a	1.a	$1$	$1$	$1$	$11.738$	$\Q$	None	✓				210.2.a.d	$1$	$0$	$1$	$-1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots$
1470.2.a.n	$1470$	$2$	1470.a	1.a	$1$	$1$	$1$	$11.738$	$\Q$	None	✓	✓			1470.2.a.n	$1$	$0$	$1$	$-1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots$
1470.2.a.o	$1470$	$2$	1470.a	1.a	$1$	$1$	$1$	$11.738$	$\Q$	None	✓				210.2.i.b	$1$	$0$	$1$	$1$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots$
1470.2.a.p	$1470$	$2$	1470.a	1.a	$1$	$1$	$1$	$11.738$	$\Q$	None	✓	✓			1470.2.a.n	$1$	$0$	$1$	$1$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots$
1470.2.a.q	$1470$	$2$	1470.a	1.a	$1$	$1$	$1$	$11.738$	$\Q$	None	✓				210.2.a.c	$1$	$0$	$1$	$1$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots$
1470.2.a.r	$1470$	$2$	1470.a	1.a	$1$	$1$	$1$	$11.738$	$\Q$	None	✓				210.2.i.a	$1$	$0$	$1$	$1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+q^{8}+\cdots$
1470.2.a.s	$1470$	$2$	1470.a	1.a	$1$	$2$	$2$	$11.738$	$\Q(\sqrt{2}) $	None	✓	✓	✓	✓	1470.2.a.s	$1$	$0$	$-2$	$-2$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots$
1470.2.a.t	$1470$	$2$	1470.a	1.a	$1$	$2$	$2$	$11.738$	$\Q(\sqrt{2}) $	None	✓	✓	✓		1470.2.a.s	$1$	$0$	$-2$	$2$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots$
1470.2.a.u	$1470$	$2$	1470.a	1.a	$1$	$2$	$2$	$11.738$	$\Q(\sqrt{2}) $	None	✓	✓	✓	✓	1470.2.a.u	$1$	$0$	$2$	$-2$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots$
1470.2.a.v	$1470$	$2$	1470.a	1.a	$1$	$2$	$2$	$11.738$	$\Q(\sqrt{2}) $	None	✓	✓	✓		1470.2.a.u	$1$	$0$	$2$	$2$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+q^{8}+\cdots$
1470.2.b.a	$1470$	$2$	1470.b	21.c	$2$	$12$	$12$	$11.738$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None					210.2.r.a	$2$	$0$	$0$	$-4$	$12$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{2}-\beta _{1}q^{3}-q^{4}+q^{5}-\beta _{9}q^{6}+\cdots$
1470.2.b.b	$1470$	$2$	1470.b	21.c	$2$	$12$	$12$	$11.738$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None					210.2.r.a	$2$	$0$	$0$	$4$	$-12$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{2}+\beta _{1}q^{3}-q^{4}-q^{5}+\beta _{9}q^{6}+\cdots$
1470.2.b.c	$1470$	$2$	1470.b	21.c	$2$	$16$	$16$	$11.738$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓			1470.2.b.c	$2$	$0$	$0$	$-8$	$-16$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{9}q^{2}-\beta _{11}q^{3}-q^{4}-q^{5}+(-\beta _{5}+\cdots)q^{6}+\cdots$
1470.2.b.d	$1470$	$2$	1470.b	21.c	$2$	$16$	$16$	$11.738$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓			1470.2.b.c	$2$	$0$	$0$	$8$	$16$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{9}q^{2}+\beta _{11}q^{3}-q^{4}+q^{5}+(\beta _{5}+\cdots)q^{6}+\cdots$
1470.2.d.a	$1470$	$2$	1470.d	105.g	$2$	$4$	$4$	$11.738$	$\Q(\sqrt{-3}, \sqrt{-11})$	None					210.2.t.a	$2$	$0$	$-4$	$-1$	$3$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}-\beta _{1}q^{3}+q^{4}+(1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$
1470.2.d.b	$1470$	$2$	1470.d	105.g	$2$	$4$	$4$	$11.738$	$\Q(\sqrt{-3}, \sqrt{-11})$	None					210.2.t.a	$2$	$0$	$-4$	$1$	$-3$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+\beta _{1}q^{3}+q^{4}+(-1-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
1470.2.d.c	$1470$	$2$	1470.d	105.g	$2$	$4$	$4$	$11.738$	$\Q(\sqrt{-3}, \sqrt{-11})$	None					210.2.t.a	$2$	$0$	$4$	$-1$	$-3$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}-\beta _{1}q^{3}+q^{4}+(-2\beta _{2}-\beta _{3})q^{5}+\cdots$
1470.2.d.d	$1470$	$2$	1470.d	105.g	$2$	$4$	$4$	$11.738$	$\Q(\sqrt{-3}, \sqrt{-11})$	None					210.2.t.a	$2$	$0$	$4$	$1$	$3$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+(2\beta _{2}+\beta _{3})q^{5}+\cdots$
1470.2.d.e	$1470$	$2$	1470.d	105.g	$2$	$8$	$8$	$11.738$	8.0.3317760000.3	None					210.2.t.e	$4$	$0$	$-8$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+(\beta _{2}+\beta _{5})q^{3}+q^{4}+(\beta _{2}-\beta _{6}+\cdots)q^{5}+\cdots$
1470.2.d.f	$1470$	$2$	1470.d	105.g	$2$	$8$	$8$	$11.738$	8.0.3317760000.3	None					210.2.t.e	$4$	$0$	$8$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+(\beta _{2}+\beta _{5})q^{3}+q^{4}+(-\beta _{2}-\beta _{6}+\cdots)q^{5}+\cdots$
1470.2.d.g	$1470$	$2$	1470.d	105.g	$2$	$24$	$24$	$11.738$		None		✓			1470.2.d.g	$4$	$0$	$-24$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1470.2.d.h	$1470$	$2$	1470.d	105.g	$2$	$24$	$24$	$11.738$		None		✓			1470.2.d.g	$4$	$0$	$24$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1470.2.g.a	$1470$	$2$	1470.g	5.b	$2$	$2$	$2$	$11.738$	$\Q(\sqrt{-1}) $	None					210.2.n.a	$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}+i q^{3}-q^{4}+(-i-2)q^{5}+\cdots$
1470.2.g.b	$1470$	$2$	1470.g	5.b	$2$	$2$	$2$	$11.738$	$\Q(\sqrt{-1}) $	None					210.2.g.b	$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}-i q^{3}-q^{4}+(-2 i-1)q^{5}+\cdots$
1470.2.g.c	$1470$	$2$	1470.g	5.b	$2$	$2$	$2$	$11.738$	$\Q(\sqrt{-1}) $	None		✓			1470.2.g.c	$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}+i q^{3}-q^{4}+(-2 i-1)q^{5}+\cdots$
1470.2.g.d	$1470$	$2$	1470.g	5.b	$2$	$2$	$2$	$11.738$	$\Q(\sqrt{-1}) $	None		✓			1470.2.g.c	$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}+i q^{3}-q^{4}+(-2 i+1)q^{5}+\cdots$
1470.2.g.e	$1470$	$2$	1470.g	5.b	$2$	$2$	$2$	$11.738$	$\Q(\sqrt{-1}) $	None					210.2.g.a	$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-i q^{3}-q^{4}+(-2 i+1)q^{5}+\cdots$
1470.2.g.f	$1470$	$2$	1470.g	5.b	$2$	$2$	$2$	$11.738$	$\Q(\sqrt{-1}) $	None					210.2.n.a	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}-i q^{3}-q^{4}+(i+2)q^{5}+\cdots$
1470.2.g.g	$1470$	$2$	1470.g	5.b	$2$	$2$	$2$	$11.738$	$\Q(\sqrt{-1}) $	None					30.2.c.a	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}+i q^{3}-q^{4}+(-i+2)q^{5}+\cdots$
1470.2.g.h	$1470$	$2$	1470.g	5.b	$2$	$6$	$6$	$11.738$	6.0.29160000.2	None					210.2.n.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}-\beta _{3}q^{3}-q^{4}-\beta _{2}q^{5}-q^{6}+\cdots$
1470.2.g.i	$1470$	$2$	1470.g	5.b	$2$	$6$	$6$	$11.738$	6.0.29160000.2	None					210.2.n.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}+\beta _{3}q^{3}-q^{4}+\beta _{2}q^{5}+q^{6}+\cdots$
1470.2.g.j	$1470$	$2$	1470.g	5.b	$2$	$8$	$8$	$11.738$	8.0.1698758656.6	None		✓			1470.2.g.j	$2$	$0$	$0$	$0$	$-4$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{2}-\beta _{5}q^{3}-q^{4}+(-1+\beta _{7})q^{5}+\cdots$
1470.2.g.k	$1470$	$2$	1470.g	5.b	$2$	$8$	$8$	$11.738$	8.0.1698758656.6	None		✓			1470.2.g.j	$2$	$0$	$0$	$0$	$4$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{2}+\beta _{5}q^{3}-q^{4}+(1-\beta _{7})q^{5}+\cdots$
1470.2.i.a	$1470$	$2$	1470.i	7.c	$3$	$2$	$1$	$11.738$	$\Q(\sqrt{-3}) $	None					210.2.a.e	$2$	$0$	$-1$	$-1$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
1470.2.i.b	$1470$	$2$	1470.i	7.c	$3$	$2$	$1$	$11.738$	$\Q(\sqrt{-3}) $	None					210.2.a.c	$2$	$0$	$-1$	$-1$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
1470.2.i.c	$1470$	$2$	1470.i	7.c	$3$	$2$	$1$	$11.738$	$\Q(\sqrt{-3}) $	None		✓			1470.2.a.n	$2$	$1$	$-1$	$-1$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
1470.2.i.d	$1470$	$2$	1470.i	7.c	$3$	$2$	$1$	$11.738$	$\Q(\sqrt{-3}) $	None					210.2.a.d	$2$	$0$	$-1$	$-1$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
1470.2.i.e	$1470$	$2$	1470.i	7.c	$3$	$2$	$1$	$11.738$	$\Q(\sqrt{-3}) $	None					210.2.i.b	$2$	$0$	$-1$	$-1$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$

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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.