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 (47 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
4788.2.a.a	$4788$	$2$	4788.a	1.a	$1$	$1$	$1$	$38.232$	$\Q$	None	✓				1596.2.a.e	$1$	$0$	$0$	$0$	$-2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-q^{7}-6q^{11}+2q^{13}+2q^{17}+\cdots$
4788.2.a.b	$4788$	$2$	4788.a	1.a	$1$	$1$	$1$	$38.232$	$\Q$	None	✓				1596.2.a.b	$1$	$1$	$0$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{7}-2q^{11}+2q^{13}-q^{19}-2q^{23}+\cdots$
4788.2.a.c	$4788$	$2$	4788.a	1.a	$1$	$1$	$1$	$38.232$	$\Q$	None	✓				1596.2.a.a	$1$	$0$	$0$	$0$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{7}+2q^{11}+6q^{13}+8q^{17}+q^{19}+\cdots$
4788.2.a.d	$4788$	$2$	4788.a	1.a	$1$	$1$	$1$	$38.232$	$\Q$	None	✓				1596.2.a.c	$1$	$0$	$0$	$0$	$2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-q^{7}+2q^{11}+2q^{13}-2q^{17}+\cdots$
4788.2.a.e	$4788$	$2$	4788.a	1.a	$1$	$1$	$1$	$38.232$	$\Q$	None	✓				532.2.a.a	$1$	$1$	$0$	$0$	$2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+q^{7}-4q^{11}+4q^{13}-6q^{17}+\cdots$
4788.2.a.f	$4788$	$2$	4788.a	1.a	$1$	$1$	$1$	$38.232$	$\Q$	None	✓				1596.2.a.d	$1$	$1$	$0$	$0$	$2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+q^{7}+2q^{11}-6q^{13}-2q^{17}+\cdots$
4788.2.a.g	$4788$	$2$	4788.a	1.a	$1$	$2$	$2$	$38.232$	$\Q(\sqrt{21}) $	None	✓				532.2.a.c	$1$	$1$	$0$	$0$	$-6$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}+q^{7}+(2-\beta )q^{11}-q^{13}+(-2+\cdots)q^{17}+\cdots$
4788.2.a.h	$4788$	$2$	4788.a	1.a	$1$	$2$	$2$	$38.232$	$\Q(\sqrt{2}) $	None	✓				1596.2.a.h	$1$	$1$	$0$	$0$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}+q^{7}-2q^{11}-2\beta q^{13}-3\beta q^{17}+\cdots$
4788.2.a.i	$4788$	$2$	4788.a	1.a	$1$	$2$	$2$	$38.232$	$\Q(\sqrt{3}) $	None	✓	✓			4788.2.a.i	$2$	$0$	$0$	$0$	$0$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{7}-\beta q^{11}-4q^{13}-2\beta q^{17}+q^{19}+\cdots$
4788.2.a.j	$4788$	$2$	4788.a	1.a	$1$	$2$	$2$	$38.232$	$\Q(\sqrt{3}) $	None	✓				1596.2.a.i	$1$	$1$	$0$	$0$	$2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{5}-q^{7}-2\beta q^{11}-4q^{13}+\cdots$
4788.2.a.k	$4788$	$2$	4788.a	1.a	$1$	$2$	$2$	$38.232$	$\Q(\sqrt{7}) $	None	✓				1596.2.a.f	$1$	$0$	$0$	$0$	$2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{5}-q^{7}-2\beta q^{11}+(-3+\beta )q^{17}+\cdots$
4788.2.a.l	$4788$	$2$	4788.a	1.a	$1$	$2$	$2$	$38.232$	$\Q(\sqrt{5}) $	None	✓				532.2.a.b	$1$	$0$	$0$	$0$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+q^{7}+(2-5\beta )q^{11}+(1-2\beta )q^{13}+\cdots$
4788.2.a.m	$4788$	$2$	4788.a	1.a	$1$	$2$	$2$	$38.232$	$\Q(\sqrt{5}) $	None	✓				1596.2.a.g	$1$	$0$	$0$	$0$	$2$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{5}+q^{7}+2q^{11}+2\beta q^{13}+\cdots$
4788.2.a.n	$4788$	$2$	4788.a	1.a	$1$	$2$	$2$	$38.232$	$\Q(\sqrt{5}) $	None	✓				532.2.a.d	$1$	$0$	$0$	$0$	$4$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+2\beta )q^{5}-q^{7}+(1+\beta )q^{11}+(-3+\cdots)q^{13}+\cdots$
4788.2.a.o	$4788$	$2$	4788.a	1.a	$1$	$3$	$3$	$38.232$	3.3.733.1	None	✓		✓		532.2.a.e	$1$	$1$	$0$	$0$	$-2$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1}+\beta _{2})q^{5}-q^{7}+(1+\beta _{2})q^{11}+\cdots$
4788.2.a.p	$4788$	$2$	4788.a	1.a	$1$	$3$	$3$	$38.232$	3.3.1016.1	None	✓		✓		1596.2.a.j	$1$	$0$	$0$	$0$	$0$	$3$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{5}+q^{7}-2q^{11}+(1+\beta _{1})q^{13}+\cdots$
4788.2.a.q	$4788$	$2$	4788.a	1.a	$1$	$4$	$4$	$38.232$	$\Q(\sqrt{2}, \sqrt{5})$	None	✓	✓	✓	✓	4788.2.a.q	$2$	$1$	$0$	$0$	$0$	$-4$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{5}-q^{7}+(-\beta _{1}-\beta _{3})q^{11}+(-1+\cdots)q^{13}+\cdots$
4788.2.a.r	$4788$	$2$	4788.a	1.a	$1$	$4$	$4$	$38.232$	$\Q(\sqrt{2}, \sqrt{5})$	None	✓	✓	✓	✓	4788.2.a.r	$2$	$1$	$0$	$0$	$0$	$4$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{5}+q^{7}+(-\beta _{1}+\beta _{2})q^{11}+(-3+\cdots)q^{13}+\cdots$
4788.2.a.s	$4788$	$2$	4788.a	1.a	$1$	$4$	$4$	$38.232$	4.4.32448.1	None	✓	✓	✓		4788.2.a.s	$2$	$0$	$0$	$0$	$0$	$4$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{5}+q^{7}+(\beta _{1}+\beta _{2})q^{11}+(3-\beta _{3})q^{13}+\cdots$
4788.2.a.t	$4788$	$2$	4788.a	1.a	$1$	$6$	$6$	$38.232$	6.6.56310016.1	None	✓	✓	✓	✓	4788.2.a.t	$2$	$0$	$0$	$0$	$0$	$-6$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+\beta _{4}q^{5}-q^{7}+\beta _{5}q^{11}+(1-\beta _{3})q^{13}+\cdots$
4788.2.b.a	$4788$	$2$	4788.b	57.d	$2$	$2$	$2$	$38.232$	$\Q(\sqrt{-2}) $	None		✓			4788.2.b.a	$2$	$0$	$0$	$0$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2\beta q^{5}+q^{7}+2\beta q^{11}+3\beta q^{13}+\cdots$
4788.2.b.b	$4788$	$2$	4788.b	57.d	$2$	$2$	$2$	$38.232$	$\Q(\sqrt{-2}) $	None		✓			4788.2.b.a	$2$	$0$	$0$	$0$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2\beta q^{5}+q^{7}+2\beta q^{11}-3\beta q^{13}+\cdots$
4788.2.b.c	$4788$	$2$	4788.b	57.d	$2$	$16$	$16$	$38.232$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓			4788.2.b.c	$4$	$0$	$0$	$0$	$0$	$16$		$2^{10}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{6}-\beta _{8})q^{5}+q^{7}+\beta _{12}q^{11}-\beta _{11}q^{13}+\cdots$
4788.2.b.d	$4788$	$2$	4788.b	57.d	$2$	$20$	$20$	$38.232$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		✓	✓		4788.2.b.d	$4$	$0$	$0$	$0$	$0$	$-20$		$2^{14}\cdot 3^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{11}q^{5}-q^{7}+\beta _{10}q^{11}-\beta _{5}q^{13}+\cdots$
4788.2.i.a	$4788$	$2$	4788.i	133.c	$2$	$2$	$2$	$38.232$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $		✓			4788.2.i.a	$4$	$0$	$0$	$0$	$0$	$-4$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+(-2-\zeta_{6})q^{7}-2q^{13}+(4+\zeta_{6})q^{19}+\cdots$
4788.2.i.b	$4788$	$2$	4788.i	133.c	$2$	$2$	$2$	$38.232$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $		✓			4788.2.i.a	$4$	$1$	$0$	$0$	$0$	$-4$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+(-2+\zeta_{6})q^{7}+2q^{13}+(-4-\zeta_{6})q^{19}+\cdots$
4788.2.i.c	$4788$	$2$	4788.i	133.c	$2$	$4$	$4$	$38.232$	$\Q(\sqrt{-3}, \sqrt{-19})$	$\Q(\sqrt{-19}) $					532.2.g.a	$4$	$0$	$0$	$0$	$0$	$3$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+(\beta _{1}-\beta _{3})q^{5}+(1+\beta _{2}-\beta _{3})q^{7}+(2+\cdots)q^{11}+\cdots$
4788.2.i.d	$4788$	$2$	4788.i	133.c	$2$	$8$	$8$	$38.232$	8.0.2702336256.1	$\Q(\sqrt{-19}) $		✓			4788.2.i.d	$8$	$0$	$0$	$0$	$0$	$-6$		$2^{4}$	$\mathrm{U}(1)[D_{2}]$	$q+(\beta _{1}-\beta _{6}+\beta _{7})q^{5}+(-1+\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots$
4788.2.i.e	$4788$	$2$	4788.i	133.c	$2$	$8$	$8$	$38.232$	8.0.$\cdots$.5	None					532.2.g.b	$4$	$0$	$0$	$0$	$0$	$-4$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{5}+(-1-\beta _{2}-\beta _{4})q^{7}+\beta _{4}q^{11}+\cdots$
4788.2.i.f	$4788$	$2$	4788.i	133.c	$2$	$14$	$14$	$38.232$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	None					1596.2.i.a	$2$	$0$	$0$	$0$	$0$	$-1$		$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{10}q^{5}+\beta _{12}q^{7}-\beta _{1}q^{11}+(-1+\cdots)q^{13}+\cdots$
4788.2.i.g	$4788$	$2$	4788.i	133.c	$2$	$14$	$14$	$38.232$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	None					1596.2.i.a	$2$	$0$	$0$	$0$	$0$	$-1$		$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{10}q^{5}+\beta _{12}q^{7}-\beta _{1}q^{11}+(1+\beta _{7}+\cdots)q^{13}+\cdots$
4788.2.i.h	$4788$	$2$	4788.i	133.c	$2$	$16$	$16$	$38.232$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		✓	✓		4788.2.i.h	$8$	$0$	$0$	$0$	$0$	$16$		$2^{17}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{12}q^{5}+(1-\beta _{3}-\beta _{10})q^{7}+\beta _{5}q^{11}+\cdots$
4788.2.j.a	$4788$	$2$	4788.j	21.c	$2$	$48$	$48$	$38.232$		None		✓	✓	✓	4788.2.j.a	$4$	$0$	$0$	$0$	$0$	$8$			$\mathrm{SU}(2)[C_{2}]$
4788.2.w.a	$4788$	$2$	4788.w	19.c	$3$	$2$	$1$	$38.232$	$\Q(\sqrt{-3}) $	None					1596.2.s.b	$2$	$0$	$0$	$0$	$-3$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-3+3\zeta_{6})q^{5}+q^{7}-3q^{11}+4\zeta_{6}q^{13}+\cdots$
4788.2.w.b	$4788$	$2$	4788.w	19.c	$3$	$2$	$1$	$38.232$	$\Q(\sqrt{-3}) $	None					532.2.j.a	$2$	$0$	$0$	$0$	$-3$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-3+3\zeta_{6})q^{5}+q^{7}-5\zeta_{6}q^{13}+\cdots$
4788.2.w.c	$4788$	$2$	4788.w	19.c	$3$	$2$	$1$	$38.232$	$\Q(\sqrt{-3}) $	None					1596.2.s.a	$2$	$0$	$0$	$0$	$1$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{5}+q^{7}+q^{11}-4\zeta_{6}q^{13}+\cdots$
4788.2.w.d	$4788$	$2$	4788.w	19.c	$3$	$8$	$4$	$38.232$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None					1596.2.s.d	$2$	$0$	$0$	$0$	$-2$	$-8$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{1}-\beta _{3}-\beta _{7})q^{5}-q^{7}+(1+\cdots)q^{11}+\cdots$
4788.2.w.e	$4788$	$2$	4788.w	19.c	$3$	$8$	$4$	$38.232$	8.0.2127515625.3	None					1596.2.s.e	$2$	$0$	$0$	$0$	$-2$	$8$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{5}+q^{7}+(1+2\beta _{3}-\beta _{4}+2\beta _{7})q^{11}+\cdots$
4788.2.w.f	$4788$	$2$	4788.w	19.c	$3$	$8$	$4$	$38.232$	8.0.$\cdots$.2	None					532.2.j.b	$2$	$0$	$0$	$0$	$2$	$8$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}+\beta _{6})q^{5}+q^{7}+(-\beta _{2}-\beta _{7})q^{11}+\cdots$
4788.2.w.g	$4788$	$2$	4788.w	19.c	$3$	$8$	$4$	$38.232$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None					1596.2.s.c	$2$	$0$	$0$	$0$	$6$	$8$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{1}-\beta _{3})q^{5}+q^{7}+(-1-\beta _{2}+\cdots)q^{11}+\cdots$
4788.2.w.h	$4788$	$2$	4788.w	19.c	$3$	$10$	$5$	$38.232$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None					532.2.j.c	$2$	$0$	$0$	$0$	$1$	$-10$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{9}q^{5}-q^{7}+(-1-\beta _{5})q^{11}+(\beta _{1}+\cdots)q^{13}+\cdots$
4788.2.w.i	$4788$	$2$	4788.w	19.c	$3$	$12$	$6$	$38.232$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None					1596.2.s.f	$2$	$0$	$0$	$0$	$0$	$-12$		$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{3}+\beta _{5})q^{5}-q^{7}+(1+\beta _{1}-\beta _{4}+\cdots)q^{11}+\cdots$
4788.2.w.j	$4788$	$2$	4788.w	19.c	$3$	$20$	$10$	$38.232$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		✓			4788.2.w.j	$4$	$0$	$0$	$0$	$0$	$-20$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{5}-q^{7}+(\beta _{1}-\beta _{3}-\beta _{7}-\beta _{15}+\cdots)q^{11}+\cdots$
4788.2.w.k	$4788$	$2$	4788.w	19.c	$3$	$20$	$10$	$38.232$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		✓			4788.2.w.k	$4$	$0$	$0$	$0$	$0$	$20$		$3^{5}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{5}+q^{7}-\beta _{17}q^{11}+(1+\beta _{4}+\cdots)q^{13}+\cdots$
4788.2.dq.a	$4788$	$2$	4788.dq	21.g	$6$	$96$	$48$	$38.232$		None		✓	✓	✓	4788.2.dq.a	$4$	$0$	$0$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{6}]$
4788.2.fc.a	$4788$	$2$	4788.fc	57.f	$6$	$40$	$20$	$38.232$		None		✓			4788.2.fc.a	$4$	$0$	$0$	$0$	$0$	$-40$			$\mathrm{SU}(2)[C_{6}]$
4788.2.fc.b	$4788$	$2$	4788.fc	57.f	$6$	$40$	$20$	$38.232$		None		✓			4788.2.fc.b	$4$	$0$	$0$	$0$	$0$	$40$			$\mathrm{SU}(2)[C_{6}]$

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Elliptic curves over $\Q$
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Genus 2 curves over $\Q$
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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.