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 53 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
4356.2.a.a	$4356$	$2$	4356.a	1.a	$1$	$1$	$1$	$34.783$	$\Q$	None	✓				1452.2.a.g	$1$	$0$	$0$	$0$	$-3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}-2q^{7}-5q^{13}-3q^{17}+4q^{19}+\cdots$
4356.2.a.b	$4356$	$2$	4356.a	1.a	$1$	$1$	$1$	$34.783$	$\Q$	None	✓				1452.2.a.g	$1$	$0$	$0$	$0$	$-3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}+2q^{7}+5q^{13}+3q^{17}-4q^{19}+\cdots$
4356.2.a.c	$4356$	$2$	4356.a	1.a	$1$	$1$	$1$	$34.783$	$\Q$	None	✓				132.2.a.a	$1$	$0$	$0$	$0$	$-2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-2q^{7}-6q^{13}-4q^{17}+2q^{19}+\cdots$
4356.2.a.d	$4356$	$2$	4356.a	1.a	$1$	$1$	$1$	$34.783$	$\Q$	None	✓				132.2.a.b	$1$	$0$	$0$	$0$	$-2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+2q^{7}+2q^{13}+4q^{17}+6q^{19}+\cdots$
4356.2.a.e	$4356$	$2$	4356.a	1.a	$1$	$1$	$1$	$34.783$	$\Q$	$\Q(\sqrt{-3}) $	✓	✓			4356.2.a.e	$2$	$1$	$0$	$0$	$0$	$-1$	$+$	$1$	$N(\mathrm{U}(1))$	$q-q^{7}+2q^{13}-q^{19}-5q^{25}-7q^{31}+\cdots$
4356.2.a.f	$4356$	$2$	4356.a	1.a	$1$	$1$	$1$	$34.783$	$\Q$	$\Q(\sqrt{-3}) $	✓	✓			4356.2.a.e	$2$	$1$	$0$	$0$	$0$	$1$	$+$	$1$	$N(\mathrm{U}(1))$	$q+q^{7}-2q^{13}+q^{19}-5q^{25}-7q^{31}+\cdots$
4356.2.a.g	$4356$	$2$	4356.a	1.a	$1$	$1$	$1$	$34.783$	$\Q$	$\Q(\sqrt{-3}) $	✓				36.2.a.a	$2$	$1$	$0$	$0$	$0$	$4$	$+$	$1$	$N(\mathrm{U}(1))$	$q+4q^{7}-2q^{13}-8q^{19}-5q^{25}-4q^{31}+\cdots$
4356.2.a.h	$4356$	$2$	4356.a	1.a	$1$	$1$	$1$	$34.783$	$\Q$	None	✓				1452.2.a.a	$1$	$0$	$0$	$0$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{7}+3q^{13}-7q^{17}-4q^{19}+\cdots$
4356.2.a.i	$4356$	$2$	4356.a	1.a	$1$	$1$	$1$	$34.783$	$\Q$	None	✓				1452.2.a.a	$1$	$0$	$0$	$0$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+2q^{7}-3q^{13}+7q^{17}+4q^{19}+\cdots$
4356.2.a.j	$4356$	$2$	4356.a	1.a	$1$	$1$	$1$	$34.783$	$\Q$	None	✓				44.2.a.a	$1$	$0$	$0$	$0$	$3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}-2q^{7}+4q^{13}+6q^{17}-8q^{19}+\cdots$
4356.2.a.k	$4356$	$2$	4356.a	1.a	$1$	$1$	$1$	$34.783$	$\Q$	None	✓				1452.2.a.d	$1$	$0$	$0$	$0$	$4$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}-5q^{7}-2q^{13}-4q^{17}+3q^{19}+\cdots$
4356.2.a.l	$4356$	$2$	4356.a	1.a	$1$	$1$	$1$	$34.783$	$\Q$	None	✓				1452.2.a.d	$1$	$0$	$0$	$0$	$4$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}+5q^{7}+2q^{13}+4q^{17}-3q^{19}+\cdots$
4356.2.a.m	$4356$	$2$	4356.a	1.a	$1$	$2$	$2$	$34.783$	$\Q(\sqrt{3}) $	None	✓				484.2.a.e	$2$	$1$	$0$	$0$	$-6$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}-2\beta q^{7}+3\beta q^{13}-3\beta q^{17}+\cdots$
4356.2.a.n	$4356$	$2$	4356.a	1.a	$1$	$2$	$2$	$34.783$	$\Q(\sqrt{33}) $	$\Q(\sqrt{-11}) $	✓				484.2.a.d	$2$	$1$	$0$	$0$	$-3$	$0$	$+$	$1$	$N(\mathrm{U}(1))$	$q+(-1-\beta )q^{5}+(-5+\beta )q^{23}+(4+3\beta )q^{25}+\cdots$
4356.2.a.o	$4356$	$2$	4356.a	1.a	$1$	$2$	$2$	$34.783$	$\Q(\sqrt{3}) $	None	✓				1452.2.a.k	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{7}-\beta q^{19}-6q^{23}-5q^{25}-6\beta q^{29}+\cdots$
4356.2.a.p	$4356$	$2$	4356.a	1.a	$1$	$2$	$2$	$34.783$	$\Q(\sqrt{3}) $	$\Q(\sqrt{-3}) $	✓	✓			4356.2.a.p	$4$	$0$	$0$	$0$	$0$	$0$	$-$	$2$	$N(\mathrm{U}(1))$	$q+\beta q^{7}-2\beta q^{13}+\beta q^{19}-5q^{25}+\cdots$
4356.2.a.q	$4356$	$2$	4356.a	1.a	$1$	$2$	$2$	$34.783$	$\Q(\sqrt{3}) $	$\Q(\sqrt{-3}) $	✓	✓			4356.2.a.q	$4$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q-3\beta q^{7}-4\beta q^{13}-5\beta q^{19}-5q^{25}+\cdots$
4356.2.a.r	$4356$	$2$	4356.a	1.a	$1$	$2$	$2$	$34.783$	$\Q(\sqrt{5}) $	None	✓				132.2.i.a	$1$	$1$	$0$	$0$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}+(-3+2\beta )q^{7}+(-1-2\beta )q^{13}+\cdots$
4356.2.a.s	$4356$	$2$	4356.a	1.a	$1$	$2$	$2$	$34.783$	$\Q(\sqrt{5}) $	None	✓				132.2.i.b	$1$	$0$	$0$	$0$	$1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+3\beta )q^{5}+(-3+2\beta )q^{7}+(3+\cdots)q^{13}+\cdots$
4356.2.a.t	$4356$	$2$	4356.a	1.a	$1$	$2$	$2$	$34.783$	$\Q(\sqrt{5}) $	None	✓				44.2.e.a	$1$	$1$	$0$	$0$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}+(1-3\beta )q^{7}+(4-\beta )q^{13}+(-4+\cdots)q^{17}+\cdots$
4356.2.a.u	$4356$	$2$	4356.a	1.a	$1$	$2$	$2$	$34.783$	$\Q(\sqrt{5}) $	None	✓				44.2.e.a	$1$	$0$	$0$	$0$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}+(-1+3\beta )q^{7}+(-4+\beta )q^{13}+\cdots$
4356.2.a.v	$4356$	$2$	4356.a	1.a	$1$	$2$	$2$	$34.783$	$\Q(\sqrt{5}) $	None	✓				132.2.i.b	$1$	$1$	$0$	$0$	$1$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+3\beta )q^{5}+(3-2\beta )q^{7}+(-3+\cdots)q^{13}+\cdots$
4356.2.a.w	$4356$	$2$	4356.a	1.a	$1$	$2$	$2$	$34.783$	$\Q(\sqrt{5}) $	None	✓				132.2.i.a	$1$	$0$	$0$	$0$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}+(3-2\beta )q^{7}+(1+2\beta )q^{13}+\cdots$
4356.2.a.x	$4356$	$2$	4356.a	1.a	$1$	$4$	$4$	$34.783$	4.4.22000.1	None	✓		✓		396.2.j.d	$2$	$1$	$0$	$0$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{5}-q^{7}+(-3-2\beta _{2})q^{13}+(-\beta _{1}+\cdots)q^{17}+\cdots$
4356.2.a.y	$4356$	$2$	4356.a	1.a	$1$	$4$	$4$	$34.783$	$\Q(\sqrt{3}, \sqrt{5})$	None	✓	✓			4356.2.a.y	$4$	$0$	$0$	$0$	$0$	$0$	$-$	$2^{2}\cdot 3$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{5}-2\beta _{1}q^{7}-\beta _{1}q^{13}+\beta _{3}q^{17}+\cdots$
4356.2.a.z	$4356$	$2$	4356.a	1.a	$1$	$4$	$4$	$34.783$	4.4.22000.1	None	✓				396.2.j.d	$2$	$0$	$0$	$0$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{5}+q^{7}+(3+2\beta _{2})q^{13}+(\beta _{1}+\cdots)q^{17}+\cdots$
4356.2.b.a	$4356$	$2$	4356.b	33.d	$2$	$2$	$2$	$34.783$	$\Q(\sqrt{-2}) $	None		✓			4356.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{5}+\beta q^{13}-4q^{17}-2\beta q^{19}+\cdots$
4356.2.b.b	$4356$	$2$	4356.b	33.d	$2$	$2$	$2$	$34.783$	$\Q(\sqrt{-2}) $	None		✓			4356.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{5}-\beta q^{13}+4q^{17}+2\beta q^{19}+\cdots$
4356.2.b.c	$4356$	$2$	4356.b	33.d	$2$	$8$	$8$	$34.783$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		✓			4356.2.b.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}+(-\beta _{1}-\beta _{2})q^{7}+(-\beta _{1}-\beta _{2}+\cdots)q^{13}+\cdots$
4356.2.b.d	$4356$	$2$	4356.b	33.d	$2$	$8$	$8$	$34.783$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		✓			4356.2.b.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}+(\beta _{1}+\beta _{2})q^{7}+(\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{13}+\cdots$
4356.2.b.e	$4356$	$2$	4356.b	33.d	$2$	$16$	$16$	$34.783$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None			✓		396.2.x.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}+(\beta _{8}-\beta _{9})q^{7}+(-\beta _{6}-2\beta _{8}+\cdots)q^{13}+\cdots$
4356.3.e.a	$4356$	$3$	4356.e	3.b	$2$	$2$	$2$	$118.692$	$\Q(\sqrt{-2}) $	None		✓			4356.3.e.a	$2$	$0$	$0$	$0$	$0$	$-14$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+4\beta q^{5}-7q^{7}-8\beta q^{17}+q^{19}-7\beta q^{23}+\cdots$
4356.3.e.b	$4356$	$3$	4356.e	3.b	$2$	$2$	$2$	$118.692$	$\Q(\sqrt{-2}) $	None		✓			4356.3.e.a	$2$	$0$	$0$	$0$	$0$	$14$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+4\beta q^{5}+7q^{7}+8\beta q^{17}-q^{19}-7\beta q^{23}+\cdots$
4356.3.e.c	$4356$	$3$	4356.e	3.b	$2$	$4$	$4$	$118.692$	$\Q(\sqrt{-2}, \sqrt{31})$	None		✓			4356.3.e.c	$2$	$0$	$0$	$0$	$0$	$-12$		$3$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}+\beta _{2})q^{5}+(-3-\beta _{3})q^{7}+(-3+\cdots)q^{13}+\cdots$
4356.3.e.d	$4356$	$3$	4356.e	3.b	$2$	$4$	$4$	$118.692$	$\Q(\sqrt{-2}, \sqrt{31})$	None		✓			4356.3.e.c	$2$	$0$	$0$	$0$	$0$	$12$		$3$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}+\beta _{2})q^{5}+(3+\beta _{3})q^{7}+(3-2\beta _{3})q^{13}+\cdots$
4356.3.e.e	$4356$	$3$	4356.e	3.b	$2$	$8$	$8$	$118.692$	8.0.$\cdots$.48	None		✓			4356.3.e.e	$4$	$0$	$0$	$0$	$0$	$0$		$2^{5}\cdot 3^{7}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}-\beta _{2}q^{7}+(\beta _{2}-\beta _{3})q^{13}-\beta _{5}q^{17}+\cdots$
4356.3.e.f	$4356$	$3$	4356.e	3.b	$2$	$8$	$8$	$118.692$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None					396.3.e.a	$2$	$0$	$0$	$0$	$0$	$16$		$2^{7}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{6}q^{5}+(2+\beta _{4})q^{7}+(1+\beta _{1}-\beta _{3}+\cdots)q^{13}+\cdots$
4356.3.e.g	$4356$	$3$	4356.e	3.b	$2$	$12$	$12$	$118.692$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		✓			4356.3.e.g	$4$	$0$	$0$	$0$	$0$	$0$		$2^{5}\cdot 3^{15}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{5}+(-\beta _{3}+\beta _{5})q^{7}-\beta _{7}q^{13}+\cdots$
4356.3.e.h	$4356$	$3$	4356.e	3.b	$2$	$16$	$16$	$118.692$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None					396.3.u.a	$2$	$0$	$0$	$0$	$0$	$-8$		$2^{2}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}+(-\beta _{2}+\beta _{6})q^{7}+(-\beta _{3}+\beta _{6}+\cdots)q^{13}+\cdots$
4356.3.e.i	$4356$	$3$	4356.e	3.b	$2$	$16$	$16$	$118.692$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None					396.3.u.a	$2$	$0$	$0$	$0$	$0$	$8$		$2^{2}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}+(\beta _{2}-\beta _{6})q^{7}+(\beta _{3}-\beta _{6})q^{13}+\cdots$
4356.3.f.a	$4356$	$3$	4356.f	11.b	$2$	$2$	$2$	$118.692$	$\Q(\sqrt{-2}) $	None		✓			4356.3.f.a	$2$	$0$	$0$	$0$	$-16$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-8q^{5}-3\beta q^{7}-17\beta q^{13}-2^{4}\beta q^{17}+\cdots$
4356.3.f.b	$4356$	$3$	4356.f	11.b	$2$	$2$	$2$	$118.692$	$\Q(\sqrt{-2}) $	None					484.3.d.a	$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{5}-3\beta q^{7}-4\beta q^{13}-13\beta q^{17}+\cdots$
4356.3.f.c	$4356$	$3$	4356.f	11.b	$2$	$2$	$2$	$118.692$	$\Q(\sqrt{-2}) $	None		✓			4356.3.f.a	$2$	$0$	$0$	$0$	$16$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+8q^{5}-3\beta q^{7}-17\beta q^{13}+2^{4}\beta q^{17}+\cdots$
4356.3.f.d	$4356$	$3$	4356.f	11.b	$2$	$4$	$4$	$118.692$	$\Q(\sqrt{-2}, \sqrt{3})$	None					1452.3.f.a	$2$	$0$	$0$	$0$	$-8$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-2+\beta _{2})q^{5}+(\beta _{1}+\beta _{3})q^{7}+(7\beta _{1}+\cdots)q^{13}+\cdots$
4356.3.f.e	$4356$	$3$	4356.f	11.b	$2$	$4$	$4$	$118.692$	$\Q(\sqrt{-2}, \sqrt{3})$	$\Q(\sqrt{-3}) $		✓			4356.3.f.e	$4$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{U}(1)[D_{2}]$	$q+(\beta _{1}-\beta _{2})q^{7}+(11\beta _{1}+\beta _{2})q^{13}+(13\beta _{1}+\cdots)q^{19}+\cdots$
4356.3.f.f	$4356$	$3$	4356.f	11.b	$2$	$4$	$4$	$118.692$	$\Q(\sqrt{-2}, \sqrt{3})$	$\Q(\sqrt{-3}) $		✓			4356.3.f.f	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(-8\beta _{1}+5\beta _{3})q^{7}+(7\beta _{1}-15\beta _{3})q^{13}+\cdots$
4356.3.f.g	$4356$	$3$	4356.f	11.b	$2$	$8$	$8$	$118.692$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None					44.3.f.a	$2$	$0$	$0$	$0$	$-14$	$0$		$2^{4}\cdot 11^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-2-\beta _{4})q^{5}+\beta _{1}q^{7}+(-\beta _{1}+\beta _{7})q^{13}+\cdots$
4356.3.f.h	$4356$	$3$	4356.f	11.b	$2$	$8$	$8$	$118.692$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None					1452.3.f.c	$2$	$0$	$0$	$0$	$-8$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\beta _{3})q^{5}+(\beta _{2}-3\beta _{4}-\beta _{6})q^{7}+\cdots$
4356.3.f.i	$4356$	$3$	4356.f	11.b	$2$	$8$	$8$	$118.692$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		✓			4356.3.f.i	$4$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{5}+(-3\beta _{1}+3\beta _{3})q^{7}+(\beta _{1}-6\beta _{3}+\cdots)q^{13}+\cdots$
4356.3.f.j	$4356$	$3$	4356.f	11.b	$2$	$8$	$8$	$118.692$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None					1452.3.f.b	$2$	$0$	$0$	$0$	$16$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+(2-\beta _{1})q^{5}+(-\beta _{3}+\beta _{5})q^{7}+(-3\beta _{2}+\cdots)q^{13}+\cdots$

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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.