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 138 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
154.2.a.a	$154$	$2$	154.a	1.a	$1$	$1$	$1$	$1.230$	$\Q$	None	✓	✓	✓	✓	154.2.a.a	$1$	$1$	$-1$	$0$	$-4$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-4q^{5}-q^{7}-q^{8}-3q^{9}+\cdots$
154.2.a.b	$154$	$2$	154.a	1.a	$1$	$1$	$1$	$1.230$	$\Q$	None	✓	✓	✓	✓	154.2.a.b	$1$	$0$	$-1$	$2$	$2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}+2q^{5}-2q^{6}-q^{7}+\cdots$
154.2.a.c	$154$	$2$	154.a	1.a	$1$	$1$	$1$	$1.230$	$\Q$	None	✓	✓	✓	✓	154.2.a.c	$1$	$0$	$1$	$0$	$2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{5}-q^{7}+q^{8}-3q^{9}+\cdots$
154.2.a.d	$154$	$2$	154.a	1.a	$1$	$2$	$2$	$1.230$	$\Q(\sqrt{5}) $	None	✓	✓	✓	✓	154.2.a.d	$1$	$0$	$2$	$-2$	$2$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+(-1-\beta )q^{3}+q^{4}+(1+\beta )q^{5}+\cdots$
154.2.c.a	$154$	$2$	154.c	77.b	$2$	$8$	$8$	$1.230$	8.0.$\cdots$.1	None		✓	✓	✓	154.2.c.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{2}q^{3}-q^{4}+\beta _{6}q^{5}-\beta _{3}q^{6}+\cdots$
154.2.e.a	$154$	$2$	154.e	7.c	$3$	$2$	$1$	$1.230$	$\Q(\sqrt{-3}) $	None		✓			154.2.e.a	$2$	$1$	$-1$	$-3$	$-2$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
154.2.e.b	$154$	$2$	154.e	7.c	$3$	$2$	$1$	$1.230$	$\Q(\sqrt{-3}) $	None		✓			154.2.e.b	$2$	$0$	$-1$	$-1$	$0$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
154.2.e.c	$154$	$2$	154.e	7.c	$3$	$2$	$1$	$1.230$	$\Q(\sqrt{-3}) $	None		✓			154.2.e.c	$2$	$0$	$1$	$-1$	$0$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
154.2.e.d	$154$	$2$	154.e	7.c	$3$	$2$	$1$	$1.230$	$\Q(\sqrt{-3}) $	None		✓			154.2.e.d	$2$	$0$	$1$	$3$	$4$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
154.2.e.e	$154$	$2$	154.e	7.c	$3$	$4$	$2$	$1.230$	$\Q(\sqrt{2}, \sqrt{-3})$	None		✓			154.2.e.e	$2$	$0$	$-2$	$2$	$4$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{2}q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots$
154.2.e.f	$154$	$2$	154.e	7.c	$3$	$4$	$2$	$1.230$	$\Q(\sqrt{-3}, \sqrt{7})$	None		✓			154.2.e.f	$2$	$0$	$2$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{2})q^{2}+(\beta _{1}+\beta _{3})q^{3}+\beta _{2}q^{4}+\cdots$
154.2.f.a	$154$	$2$	154.f	11.c	$5$	$4$	$1$	$1.230$	$\Q(\zeta_{10})$	None		✓			154.2.f.a	$2$	$0$	$-1$	$1$	$-1$	$-1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$
154.2.f.b	$154$	$2$	154.f	11.c	$5$	$4$	$1$	$1.230$	$\Q(\zeta_{10})$	None		✓			154.2.f.b	$2$	$0$	$-1$	$5$	$3$	$1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$
154.2.f.c	$154$	$2$	154.f	11.c	$5$	$4$	$1$	$1.230$	$\Q(\zeta_{10})$	None		✓			154.2.f.c	$2$	$0$	$1$	$-2$	$-2$	$1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-\zeta_{10}+\cdots)q^{3}+\cdots$
154.2.f.d	$154$	$2$	154.f	11.c	$5$	$4$	$1$	$1.230$	$\Q(\zeta_{10})$	None		✓			154.2.f.d	$2$	$0$	$1$	$5$	$-1$	$1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(2\zeta_{10}+\cdots)q^{3}+\cdots$
154.2.f.e	$154$	$2$	154.f	11.c	$5$	$8$	$2$	$1.230$	8.0.58140625.2	None		✓	✓		154.2.f.e	$2$	$0$	$2$	$-1$	$5$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\beta _{2}+\beta _{3}-\beta _{4})q^{2}+(1-2\beta _{1}+\cdots)q^{3}+\cdots$
154.2.i.a	$154$	$2$	154.i	77.i	$6$	$16$	$8$	$1.230$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓	✓	✓	154.2.i.a	$4$	$0$	$0$	$0$	$-12$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+(-\beta _{3}+\beta _{4}+\beta _{13})q^{3}+\beta _{10}q^{4}+\cdots$
154.2.k.a	$154$	$2$	154.k	77.l	$10$	$32$	$8$	$1.230$		None		✓	✓	✓	154.2.k.a	$4$	$0$	$0$	$0$	$0$	$10$			$\mathrm{SU}(2)[C_{10}]$
154.2.m.a	$154$	$2$	154.m	77.m	$15$	$8$	$1$	$1.230$	$\Q(\zeta_{15})$	None		✓			154.2.m.a	$4$	$0$	$-1$	$1$	$-5$	$-4$		$1$	$\mathrm{SU}(2)[C_{15}]$	$q-\zeta_{15}^{7}q^{2}+(2\zeta_{15}-\zeta_{15}^{2}-\zeta_{15}^{5}+\cdots)q^{3}+\cdots$
154.2.m.b	$154$	$2$	154.m	77.m	$15$	$24$	$3$	$1.230$		None		✓			154.2.m.b	$4$	$0$	$-3$	$-3$	$3$	$-5$			$\mathrm{SU}(2)[C_{15}]$
154.2.m.c	$154$	$2$	154.m	77.m	$15$	$32$	$4$	$1.230$		None		✓	✓		154.2.m.c	$4$	$0$	$4$	$2$	$-2$	$7$			$\mathrm{SU}(2)[C_{15}]$
154.2.n.a	$154$	$2$	154.n	77.n	$30$	$64$	$8$	$1.230$		None		✓	✓	✓	154.2.n.a	$4$	$0$	$0$	$0$	$12$	$-10$			$\mathrm{SU}(2)[C_{30}]$
154.3.b.a	$154$	$3$	154.b	7.b	$2$	$16$	$16$	$4.196$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		✓	✓	✓	154.3.b.a	$2$	$0$	$0$	$0$	$0$	$-4$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{2}-\beta _{1}q^{3}+2q^{4}+\beta _{8}q^{5}+\beta _{9}q^{6}+\cdots$
154.3.d.a	$154$	$3$	154.d	11.b	$2$	$12$	$12$	$4.196$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓	✓	✓	154.3.d.a	$2$	$0$	$0$	$-4$	$12$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{6}q^{2}+\beta _{2}q^{3}-2q^{4}+(1-\beta _{5}+\beta _{8}+\cdots)q^{5}+\cdots$
154.3.g.a	$154$	$3$	154.g	77.h	$6$	$32$	$16$	$4.196$		None		✓	✓	✓	154.3.g.a	$4$	$0$	$0$	$0$	$4$	$0$			$\mathrm{SU}(2)[C_{6}]$
154.3.h.a	$154$	$3$	154.h	7.d	$6$	$24$	$12$	$4.196$		None		✓	✓	✓	154.3.h.a	$2$	$0$	$0$	$12$	$0$	$-12$			$\mathrm{SU}(2)[C_{6}]$
154.3.j.a	$154$	$3$	154.j	11.d	$10$	$48$	$12$	$4.196$		None		✓	✓	✓	154.3.j.a	$2$	$0$	$0$	$4$	$-12$	$0$			$\mathrm{SU}(2)[C_{10}]$
154.3.l.a	$154$	$3$	154.l	77.j	$10$	$64$	$16$	$4.196$		None		✓	✓	✓	154.3.l.a	$4$	$0$	$0$	$0$	$0$	$-26$			$\mathrm{SU}(2)[C_{10}]$
154.3.o.a	$154$	$3$	154.o	77.p	$30$	$128$	$16$	$4.196$		None		✓	✓	✓	154.3.o.a	$4$	$0$	$0$	$0$	$12$	$26$			$\mathrm{SU}(2)[C_{30}]$
154.3.p.a	$154$	$3$	154.p	77.o	$30$	$128$	$16$	$4.196$		None		✓	✓	✓	154.3.p.a	$4$	$0$	$0$	$0$	$-4$	$30$			$\mathrm{SU}(2)[C_{30}]$
154.4.a.a	$154$	$4$	154.a	1.a	$1$	$1$	$1$	$9.086$	$\Q$	None	✓	✓	✓	✓	154.4.a.a	$1$	$0$	$-2$	$-5$	$-1$	$-7$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-5q^{3}+4q^{4}-q^{5}+10q^{6}+\cdots$
154.4.a.b	$154$	$4$	154.a	1.a	$1$	$1$	$1$	$9.086$	$\Q$	None	✓	✓	✓	✓	154.4.a.b	$1$	$1$	$-2$	$0$	$2$	$-7$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{4}+2q^{5}-7q^{7}-8q^{8}+\cdots$
154.4.a.c	$154$	$4$	154.a	1.a	$1$	$1$	$1$	$9.086$	$\Q$	None	✓	✓			154.4.a.c	$1$	$0$	$2$	$-10$	$-14$	$7$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-10q^{3}+4q^{4}-14q^{5}-20q^{6}+\cdots$
154.4.a.d	$154$	$4$	154.a	1.a	$1$	$1$	$1$	$9.086$	$\Q$	None	✓	✓			154.4.a.d	$1$	$0$	$2$	$-2$	$18$	$7$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-2q^{3}+4q^{4}+18q^{5}-4q^{6}+\cdots$
154.4.a.e	$154$	$4$	154.a	1.a	$1$	$1$	$1$	$9.086$	$\Q$	None	✓	✓			154.4.a.e	$1$	$0$	$2$	$7$	$3$	$7$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+7q^{3}+4q^{4}+3q^{5}+14q^{6}+\cdots$
154.4.a.f	$154$	$4$	154.a	1.a	$1$	$2$	$2$	$9.086$	$\Q(\sqrt{137}) $	None	✓	✓	✓	✓	154.4.a.f	$1$	$1$	$-4$	$-5$	$-7$	$14$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+(-2-\beta )q^{3}+4q^{4}+(-4+\cdots)q^{5}+\cdots$
154.4.a.g	$154$	$4$	154.a	1.a	$1$	$2$	$2$	$9.086$	$\Q(\sqrt{37}) $	None	✓	✓	✓	✓	154.4.a.g	$1$	$0$	$-4$	$6$	$26$	$14$	$+$	$2$	$\mathrm{SU}(2)$	$q-2q^{2}+(3+\beta )q^{3}+4q^{4}+(13-\beta )q^{5}+\cdots$
154.4.a.h	$154$	$4$	154.a	1.a	$1$	$2$	$2$	$9.086$	$\Q(\sqrt{57}) $	None	✓	✓	✓	✓	154.4.a.h	$1$	$1$	$4$	$-5$	$-17$	$-14$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(-2-\beta )q^{3}+4q^{4}+(-10+\cdots)q^{5}+\cdots$
154.4.a.i	$154$	$4$	154.a	1.a	$1$	$3$	$3$	$9.086$	3.3.7636.1	None	✓	✓	✓	✓	154.4.a.i	$1$	$0$	$6$	$6$	$26$	$-21$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+2q^{2}+(2-\beta _{1})q^{3}+4q^{4}+(9-\beta _{2})q^{5}+\cdots$
154.4.c.a	$154$	$4$	154.c	77.b	$2$	$24$	$24$	$9.086$		None		✓	✓	✓	154.4.c.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
154.4.e.a	$154$	$4$	154.e	7.c	$3$	$10$	$5$	$9.086$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		✓			154.4.e.a	$2$	$0$	$-10$	$-11$	$-20$	$10$		$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	$q-2\beta _{3}q^{2}+(-2+\beta _{1}+\beta _{2}+2\beta _{3}+\cdots)q^{3}+\cdots$
154.4.e.b	$154$	$4$	154.e	7.c	$3$	$10$	$5$	$9.086$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		✓			154.4.e.b	$2$	$0$	$-10$	$7$	$10$	$62$		$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q-2\beta _{1}q^{2}+(1-\beta _{1}+\beta _{4})q^{3}+(-4+\cdots)q^{4}+\cdots$
154.4.e.c	$154$	$4$	154.e	7.c	$3$	$10$	$5$	$9.086$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		✓			154.4.e.c	$2$	$0$	$10$	$-7$	$-20$	$-20$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(2+2\beta _{6})q^{2}+(\beta _{1}-\beta _{2}+\beta _{6})q^{3}+\cdots$
154.4.e.d	$154$	$4$	154.e	7.c	$3$	$10$	$5$	$9.086$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		✓			154.4.e.d	$2$	$0$	$10$	$-1$	$10$	$48$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\beta _{3})q^{2}-\beta _{2}q^{3}-4\beta _{3}q^{4}+(2+\cdots)q^{5}+\cdots$
154.4.f.a	$154$	$4$	154.f	11.c	$5$	$4$	$1$	$9.086$	$\Q(\zeta_{10})$	None		✓			154.4.f.a	$2$	$0$	$2$	$-13$	$-21$	$7$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(2-2\zeta_{10}+2\zeta_{10}^{2}-2\zeta_{10}^{3})q^{2}+\cdots$
154.4.f.b	$154$	$4$	154.f	11.c	$5$	$4$	$1$	$9.086$	$\Q(\zeta_{10})$	None		✓			154.4.f.b	$2$	$0$	$2$	$2$	$24$	$7$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(2-2\zeta_{10}+2\zeta_{10}^{2}-2\zeta_{10}^{3})q^{2}+\cdots$
154.4.f.c	$154$	$4$	154.f	11.c	$5$	$8$	$2$	$9.086$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		✓			154.4.f.c	$2$	$0$	$4$	$20$	$-21$	$14$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-2\beta _{3}q^{2}+(3+\beta _{2}+3\beta _{3})q^{3}+(-4+\cdots)q^{4}+\cdots$
154.4.f.d	$154$	$4$	154.f	11.c	$5$	$16$	$4$	$9.086$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓			154.4.f.d	$2$	$0$	$8$	$-21$	$26$	$-28$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+2\beta _{2}q^{2}+(-2-\beta _{1}+2\beta _{2}+\beta _{3}+\cdots)q^{3}+\cdots$
154.4.f.e	$154$	$4$	154.f	11.c	$5$	$20$	$5$	$9.086$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		✓			154.4.f.e	$2$	$0$	$-10$	$-11$	$-28$	$-35$		$3^{4}$	$\mathrm{SU}(2)[C_{5}]$	$q+2\beta _{7}q^{2}+(\beta _{1}-2\beta _{2}+\beta _{3}-\beta _{4}-\beta _{6}+\cdots)q^{3}+\cdots$
154.4.f.f	$154$	$4$	154.f	11.c	$5$	$20$	$5$	$9.086$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		✓			154.4.f.f	$2$	$0$	$-10$	$19$	$36$	$35$		$11$	$\mathrm{SU}(2)[C_{5}]$	$q+2\beta _{3}q^{2}+(1+\beta _{3}+\beta _{8})q^{3}+4\beta _{5}q^{4}+\cdots$

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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.