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 110 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	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	Image	CM	RM	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
76.1.c.a	$76$	$1$	76.c	19.b	$2$	$1$	$1$	$0.038$	$\Q$	$D_{3}$	$\Q(\sqrt{-19}) $	None	✓	✓	✓	✓	76.1.c.a	$2$	$0$	$0$	$0$	$-1$	$-1$		$1$		$q-q^{5}-q^{7}+q^{9}-q^{11}-q^{17}+q^{19}+\cdots$
76.2.a.a	$76$	$2$	76.a	1.a	$1$	$1$	$1$	$0.607$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	76.2.a.a	$1$	$0$	$0$	$2$	$-1$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-q^{5}-3q^{7}+q^{9}+5q^{11}+\cdots$
76.2.d.a	$76$	$2$	76.d	76.d	$2$	$8$	$8$	$0.607$	8.0.$\cdots$.1	$_{}$	None	None		✓	✓	✓	76.2.d.a	$4$	$0$	$0$	$0$	$-4$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{4}q^{3}+(-1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
76.2.e.a	$76$	$2$	76.e	19.c	$3$	$2$	$1$	$0.607$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓	✓	✓	76.2.e.a	$2$	$0$	$0$	$1$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots$
76.2.f.a	$76$	$2$	76.f	76.f	$6$	$16$	$8$	$0.607$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓	✓	✓	76.2.f.a	$4$	$0$	$-3$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{1}-\beta _{14})q^{2}+\beta _{15}q^{3}+(-1+\cdots)q^{4}+\cdots$
76.2.i.a	$76$	$2$	76.i	19.e	$9$	$12$	$2$	$0.607$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓	✓	✓	76.2.i.a	$2$	$0$	$0$	$-3$	$0$	$3$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(-1-\beta _{5}+\beta _{7}+\beta _{9}+\beta _{11})q^{3}+\cdots$
76.2.k.a	$76$	$2$	76.k	76.k	$18$	$48$	$8$	$0.607$		$_{}$	None	None		✓	✓	✓	76.2.k.a	$4$	$0$	$-6$	$0$	$-12$	$0$			$\mathrm{SU}(2)[C_{18}]$
76.3.b.a	$76$	$3$	76.b	4.b	$2$	$4$	$4$	$2.071$	$\Q(\sqrt{-3}, \sqrt{-19})$	$_{}$	None	None		✓			76.3.b.a	$2$	$0$	$-4$	$0$	$-4$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\beta _{1})q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(-2+\cdots)q^{4}+\cdots$
76.3.b.b	$76$	$3$	76.b	4.b	$2$	$14$	$14$	$2.071$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None		✓	✓		76.3.b.b	$2$	$0$	$2$	$0$	$0$	$0$		$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}-\beta _{7}q^{3}+\beta _{5}q^{4}+\beta _{12}q^{5}+\cdots$
76.3.c.a	$76$	$3$	76.c	19.b	$2$	$2$	$2$	$2.071$	$\Q(\sqrt{-29}) $	$_{}$	None	None		✓			76.3.c.a	$2$	$0$	$0$	$0$	$-8$	$-2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}-4q^{5}-q^{7}-20q^{9}+14q^{11}+\cdots$
76.3.c.b	$76$	$3$	76.c	19.b	$2$	$2$	$2$	$2.071$	$\Q(\sqrt{57}) $	$_{}$	$\Q(\sqrt{-19}) $	None	✓	✓			76.3.c.b	$2$	$0$	$0$	$0$	$9$	$5$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(5-\beta )q^{5}+(1+3\beta )q^{7}+9q^{9}+(1+\cdots)q^{11}+\cdots$
76.3.g.a	$76$	$3$	76.g	76.g	$6$	$4$	$2$	$2.071$	$\Q(\sqrt{-3}, \sqrt{-10})$	$_{}$	None	None		✓			76.3.g.a	$2$	$0$	$-4$	$6$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-2\beta _{2}q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+(-4+\cdots)q^{4}+\cdots$
76.3.g.b	$76$	$3$	76.g	76.g	$6$	$4$	$2$	$2.071$	$\Q(\sqrt{-3}, \sqrt{-10})$	$_{}$	None	None		✓			76.3.g.a	$2$	$0$	$8$	$-6$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+2q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+4q^{4}+\cdots$
76.3.g.c	$76$	$3$	76.g	76.g	$6$	$28$	$14$	$2.071$		$_{}$	None	None		✓	✓		76.3.g.c	$4$	$0$	$-5$	$0$	$6$	$0$			$\mathrm{SU}(2)[C_{6}]$
76.3.h.a	$76$	$3$	76.h	19.d	$6$	$8$	$4$	$2.071$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None		✓	✓	✓	76.3.h.a	$2$	$0$	$0$	$6$	$-1$	$-12$		$3$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{3}-\beta _{4})q^{3}+(\beta _{5}-\beta _{6})q^{5}+(-2+\cdots)q^{7}+\cdots$
76.3.j.a	$76$	$3$	76.j	19.f	$18$	$18$	$3$	$2.071$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	$_{}$	None	None		✓	✓	✓	76.3.j.a	$2$	$0$	$0$	$-6$	$0$	$9$		$1$	$\mathrm{SU}(2)[C_{18}]$	$q+(-\beta _{4}-\beta _{6}-\beta _{8}-\beta _{10}+\beta _{12})q^{3}+\cdots$
76.3.l.a	$76$	$3$	76.l	76.l	$18$	$108$	$18$	$2.071$		$_{}$	None	None		✓	✓	✓	76.3.l.a	$4$	$0$	$-6$	$0$	$-12$	$0$			$\mathrm{SU}(2)[C_{18}]$
76.4.a.a	$76$	$4$	76.a	1.a	$1$	$2$	$2$	$4.484$	$\Q(\sqrt{33}) $	$_{}$	None	None	✓	✓	✓	✓	76.4.a.a	$1$	$1$	$0$	$-5$	$-5$	$-30$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-2-\beta )q^{3}+(-5+5\beta )q^{5}+(-13+\cdots)q^{7}+\cdots$
76.4.a.b	$76$	$4$	76.a	1.a	$1$	$3$	$3$	$4.484$	3.3.35529.1	$_{}$	None	None	✓	✓	✓	✓	76.4.a.b	$1$	$0$	$0$	$1$	$9$	$44$	$+$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}+\beta _{2})q^{3}+(3+\beta _{2})q^{5}+(15-\beta _{1}+\cdots)q^{7}+\cdots$
76.4.d.a	$76$	$4$	76.d	76.d	$2$	$28$	$28$	$4.484$		$_{}$	None	None		✓	✓	✓	76.4.d.a	$4$	$0$	$0$	$0$	$-4$	$0$			$\mathrm{SU}(2)[C_{2}]$
76.4.e.a	$76$	$4$	76.e	19.c	$3$	$10$	$5$	$4.484$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None		✓	✓	✓	76.4.e.a	$2$	$0$	$0$	$7$	$-4$	$-20$		$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}-\beta _{2}-\beta _{3})q^{3}+(\beta _{3}+\beta _{7}+\beta _{8}+\cdots)q^{5}+\cdots$
76.4.f.a	$76$	$4$	76.f	76.f	$6$	$56$	$28$	$4.484$		$_{}$	None	None		✓	✓	✓	76.4.f.a	$4$	$0$	$-3$	$0$	$-2$	$0$			$\mathrm{SU}(2)[C_{6}]$
76.4.i.a	$76$	$4$	76.i	19.e	$9$	$30$	$5$	$4.484$		$_{}$	None	None		✓	✓	✓	76.4.i.a	$2$	$0$	$0$	$-3$	$0$	$6$			$\mathrm{SU}(2)[C_{9}]$
76.4.k.a	$76$	$4$	76.k	76.k	$18$	$168$	$28$	$4.484$		$_{}$	None	None		✓	✓	✓	76.4.k.a	$4$	$0$	$-6$	$0$	$-12$	$0$			$\mathrm{SU}(2)[C_{18}]$
76.5.b.a	$76$	$5$	76.b	4.b	$2$	$36$	$36$	$7.856$		$_{}$	None	None		✓	✓	✓	76.5.b.a	$2$	$0$	$6$	$0$	$24$	$0$			$\mathrm{SU}(2)[C_{2}]$
76.5.c.a	$76$	$5$	76.c	19.b	$2$	$2$	$2$	$7.856$	$\Q(\sqrt{57}) $	$_{}$	$\Q(\sqrt{-19}) $	None	✓	✓			76.5.c.a	$2$	$0$	$0$	$0$	$-31$	$73$		$3$	$\mathrm{U}(1)[D_{2}]$	$q+(-17-3\beta )q^{5}+(39+5\beta )q^{7}+3^{4}q^{9}+\cdots$
76.5.c.b	$76$	$5$	76.c	19.b	$2$	$4$	$4$	$7.856$	$\mathbb{Q}[x]/(x^{4} + \cdots)$	$_{}$	None	None		✓	✓		76.5.c.b	$2$	$0$	$0$	$0$	$22$	$24$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(6-\beta _{2})q^{5}+(7-2\beta _{2})q^{7}+\cdots$
76.5.g.a	$76$	$5$	76.g	76.g	$6$	$76$	$38$	$7.856$		$_{}$	None	None		✓	✓	✓	76.5.g.a	$4$	$0$	$-1$	$0$	$-2$	$0$			$\mathrm{SU}(2)[C_{6}]$
76.5.h.a	$76$	$5$	76.h	19.d	$6$	$12$	$6$	$7.856$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓	✓	✓	76.5.h.a	$2$	$0$	$0$	$-12$	$9$	$-52$		$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{1}+\beta _{3})q^{3}+(1-\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots$
76.5.j.a	$76$	$5$	76.j	19.f	$18$	$42$	$7$	$7.856$		$_{}$	None	None		✓	✓	✓	76.5.j.a	$2$	$0$	$0$	$12$	$0$	$-45$			$\mathrm{SU}(2)[C_{18}]$
76.5.l.a	$76$	$5$	76.l	76.l	$18$	$228$	$38$	$7.856$		$_{}$	None	None		✓	✓	✓	76.5.l.a	$4$	$0$	$-6$	$0$	$-12$	$0$			$\mathrm{SU}(2)[C_{18}]$
76.6.a.a	$76$	$6$	76.a	1.a	$1$	$3$	$3$	$12.189$	3.3.272193.1	$_{}$	None	None	✓	✓	✓	✓	76.6.a.a	$1$	$1$	$0$	$-8$	$-9$	$-13$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-3-\beta _{1}-\beta _{2})q^{3}+(-2+3\beta _{1}+\cdots)q^{5}+\cdots$
76.6.a.b	$76$	$6$	76.a	1.a	$1$	$4$	$4$	$12.189$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	76.6.a.b	$1$	$0$	$0$	$10$	$-110$	$30$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+(3+\beta _{3})q^{3}+(-26+\beta _{1}+2\beta _{2}+3\beta _{3})q^{5}+\cdots$
76.6.d.a	$76$	$6$	76.d	76.d	$2$	$48$	$48$	$12.189$		$_{}$	None	None		✓	✓	✓	76.6.d.a	$4$	$0$	$0$	$0$	$-4$	$0$			$\mathrm{SU}(2)[C_{2}]$
76.6.e.a	$76$	$6$	76.e	19.c	$3$	$18$	$9$	$12.189$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None		✓	✓	✓	76.6.e.a	$2$	$0$	$0$	$-11$	$11$	$336$		$2^{16}\cdot 3^{3}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}-\beta _{2}+\beta _{3})q^{3}+(\beta _{2}+\beta _{6}+\beta _{8}+\cdots)q^{5}+\cdots$
76.6.f.a	$76$	$6$	76.f	76.f	$6$	$96$	$48$	$12.189$		$_{}$	None	None		✓	✓	✓	76.6.f.a	$4$	$0$	$-3$	$0$	$-2$	$0$			$\mathrm{SU}(2)[C_{6}]$
76.6.i.a	$76$	$6$	76.i	19.e	$9$	$48$	$8$	$12.189$		$_{}$	None	None		✓	✓	✓	76.6.i.a	$2$	$0$	$0$	$33$	$0$	$-177$			$\mathrm{SU}(2)[C_{9}]$
76.6.k.a	$76$	$6$	76.k	76.k	$18$	$288$	$48$	$12.189$		$_{}$	None	None		✓	✓	✓	76.6.k.a	$4$	$0$	$-6$	$0$	$-12$	$0$			$\mathrm{SU}(2)[C_{18}]$
76.7.b.a	$76$	$7$	76.b	4.b	$2$	$54$	$54$	$17.484$		$_{}$	None	None		✓	✓	✓	76.7.b.a	$2$	$0$	$-10$	$0$	$-44$	$0$			$\mathrm{SU}(2)[C_{2}]$
76.7.c.a	$76$	$7$	76.c	19.b	$2$	$2$	$2$	$17.484$	$\Q(\sqrt{57}) $	$_{}$	$\Q(\sqrt{-19}) $	None	✓	✓			76.7.c.a	$2$	$0$	$0$	$0$	$54$	$-610$		$2^{3}$	$\mathrm{U}(1)[D_{2}]$	$q+(3^{3}+7\beta )q^{5}+(-305+9\beta )q^{7}+3^{6}q^{9}+\cdots$
76.7.c.b	$76$	$7$	76.c	19.b	$2$	$8$	$8$	$17.484$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None		✓	✓		76.7.c.b	$2$	$0$	$0$	$0$	$2$	$362$		$2^{8}\cdot 3\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+\beta _{7}q^{5}+(46+\beta _{2}+2\beta _{3}+\cdots)q^{7}+\cdots$
76.7.g.a	$76$	$7$	76.g	76.g	$6$	$116$	$58$	$17.484$		$_{}$	None	None		✓	✓	✓	76.7.g.a	$4$	$0$	$-1$	$0$	$-2$	$0$			$\mathrm{SU}(2)[C_{6}]$
76.7.h.a	$76$	$7$	76.h	19.d	$6$	$20$	$10$	$17.484$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		✓	✓	✓	76.7.h.a	$2$	$0$	$0$	$-30$	$-56$	$464$		$2^{22}\cdot 3^{8}\cdot 19^{4}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+\beta _{1}+\beta _{2}-\beta _{3})q^{3}+(-6+6\beta _{3}+\cdots)q^{5}+\cdots$
76.7.j.a	$76$	$7$	76.j	19.f	$18$	$60$	$10$	$17.484$		$_{}$	None	None		✓	✓	✓	76.7.j.a	$2$	$0$	$0$	$30$	$0$	$-216$			$\mathrm{SU}(2)[C_{18}]$
76.7.l.a	$76$	$7$	76.l	76.l	$18$	$348$	$58$	$17.484$		$_{}$	None	None		✓	✓	✓	76.7.l.a	$4$	$0$	$-6$	$0$	$-12$	$0$			$\mathrm{SU}(2)[C_{18}]$
76.8.a.a	$76$	$8$	76.a	1.a	$1$	$5$	$5$	$23.741$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	76.8.a.a	$1$	$1$	$0$	$-14$	$-280$	$414$	$-$	$2^{3}\cdot 3^{2}\cdot 7$	$\mathrm{SU}(2)$	$q+(-3-\beta _{1})q^{3}+(-56+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$
76.8.a.b	$76$	$8$	76.a	1.a	$1$	$6$	$6$	$23.741$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	76.8.a.b	$1$	$0$	$0$	$40$	$279$	$-1565$	$+$	$2^{6}$	$\mathrm{SU}(2)$	$q+(7-\beta _{1})q^{3}+(47-\beta _{1}-\beta _{2})q^{5}+(-262+\cdots)q^{7}+\cdots$
76.8.d.a	$76$	$8$	76.d	76.d	$2$	$68$	$68$	$23.741$		$_{}$	None	None		✓	✓	✓	76.8.d.a	$4$	$0$	$0$	$0$	$-4$	$0$			$\mathrm{SU}(2)[C_{2}]$
76.8.e.a	$76$	$8$	76.e	19.c	$3$	$22$	$11$	$23.741$		$_{}$	None	None		✓	✓	✓	76.8.e.a	$2$	$0$	$0$	$13$	$1$	$560$			$\mathrm{SU}(2)[C_{3}]$
76.8.f.a	$76$	$8$	76.f	76.f	$6$	$136$	$68$	$23.741$		$_{}$	None	None		✓	✓	✓	76.8.f.a	$4$	$0$	$-3$	$0$	$-2$	$0$			$\mathrm{SU}(2)[C_{6}]$

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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.