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 203 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
35.2.a.a	$35$	$2$	35.a	1.a	$1$	$1$	$1$	$0.279$	$\Q$	None	✓	✓	✓	✓	35.2.a.a	$1$	$0$	$0$	$1$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}-q^{5}+q^{7}-2q^{9}-3q^{11}+\cdots$
35.2.a.b	$35$	$2$	35.a	1.a	$1$	$2$	$2$	$0.279$	$\Q(\sqrt{17}) $	None	✓	✓	✓	✓	35.2.a.b	$1$	$0$	$-1$	$-1$	$2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+\beta )q^{3}+(2+\beta )q^{4}+q^{5}+\cdots$
35.2.b.a	$35$	$2$	35.b	5.b	$2$	$2$	$2$	$0.279$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	35.2.b.a	$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 i q^{2}-i q^{3}-2 q^{4}+(-i-2)q^{5}+\cdots$
35.2.e.a	$35$	$2$	35.e	7.c	$3$	$4$	$2$	$0.279$	$\Q(\sqrt{2}, \sqrt{-3})$	None		✓	✓	✓	35.2.e.a	$2$	$0$	$-2$	$-2$	$-2$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{1}-\beta _{2})q^{2}+(\beta _{1}+\beta _{2}+\beta _{3})q^{3}+\cdots$
35.2.f.a	$35$	$2$	35.f	35.f	$4$	$4$	$2$	$0.279$	$\Q(i, \sqrt{10})$	None		✓	✓	✓	35.2.f.a	$4$	$0$	$-4$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-\beta _{2})q^{2}+\beta _{1}q^{3}-\beta _{1}q^{5}+(-\beta _{1}+\cdots)q^{6}+\cdots$
35.2.j.a	$35$	$2$	35.j	35.j	$6$	$4$	$2$	$0.279$	$\Q(\zeta_{12})$	None		✓	✓	✓	35.2.j.a	$4$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}-\zeta_{12}^{2}q^{4}+\cdots$
35.2.k.a	$35$	$2$	35.k	35.k	$12$	$4$	$1$	$0.279$	$\Q(\zeta_{12})$	None		✓			35.2.k.a	$2$	$0$	$-4$	$-2$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(-1+\zeta_{12})q^{2}+(-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots$
35.2.k.b	$35$	$2$	35.k	35.k	$12$	$4$	$1$	$0.279$	$\Q(\zeta_{12})$	None		✓			35.2.k.a	$2$	$0$	$2$	$-4$	$4$	$-10$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(1-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-1-\zeta_{12}+\cdots)q^{3}+\cdots$
35.3.c.a	$35$	$3$	35.c	35.c	$2$	$1$	$1$	$0.954$	$\Q$	$\Q(\sqrt{-35}) $	✓	✓			35.3.c.a	$2$	$0$	$0$	$-1$	$5$	$-7$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-q^{3}+4q^{4}+5q^{5}-7q^{7}-8q^{9}+\cdots$
35.3.c.b	$35$	$3$	35.c	35.c	$2$	$1$	$1$	$0.954$	$\Q$	$\Q(\sqrt{-35}) $	✓	✓			35.3.c.a	$2$	$0$	$0$	$1$	$-5$	$7$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+q^{3}+4q^{4}-5q^{5}+7q^{7}-8q^{9}+\cdots$
35.3.c.c	$35$	$3$	35.c	35.c	$2$	$4$	$4$	$0.954$	$\Q(i, \sqrt{10})$	None		✓	✓		35.3.c.c	$4$	$0$	$0$	$0$	$0$	$0$		$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+\beta _{3}q^{3}-5q^{4}+(\beta _{2}-\beta _{3})q^{5}+\cdots$
35.3.d.a	$35$	$3$	35.d	7.b	$2$	$2$	$2$	$0.954$	$\Q(\sqrt{-5}) $	None		✓			35.3.d.a	$2$	$0$	$-2$	$0$	$0$	$14$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+2\beta q^{3}-3q^{4}+\beta q^{5}-2\beta q^{6}+\cdots$
35.3.d.b	$35$	$3$	35.d	7.b	$2$	$2$	$2$	$0.954$	$\Q(\sqrt{-5}) $	None		✓			35.3.d.b	$2$	$0$	$4$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2q^{2}+\beta q^{3}-\beta q^{5}+2\beta q^{6}+(-2+\cdots)q^{7}+\cdots$
35.3.g.a	$35$	$3$	35.g	5.c	$4$	$12$	$6$	$0.954$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓	✓	✓	35.3.g.a	$2$	$0$	$-4$	$-4$	$-8$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{1}q^{2}+\beta _{7}q^{3}+(\beta _{1}+\beta _{3}+\beta _{4}+\beta _{10}+\cdots)q^{4}+\cdots$
35.3.h.a	$35$	$3$	35.h	7.d	$6$	$12$	$6$	$0.954$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓	✓	✓	35.3.h.a	$2$	$0$	$-2$	$-6$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{1}+\beta _{2})q^{2}+(-1+\beta _{7})q^{3}+(-2+\cdots)q^{4}+\cdots$
35.3.i.a	$35$	$3$	35.i	35.i	$6$	$12$	$6$	$0.954$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓	✓	✓	35.3.i.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{11})q^{3}+(1+\beta _{3}+\cdots)q^{4}+\cdots$
35.3.l.a	$35$	$3$	35.l	35.l	$12$	$24$	$6$	$0.954$		None		✓	✓	✓	35.3.l.a	$4$	$0$	$-2$	$-2$	$-4$	$-6$			$\mathrm{SU}(2)[C_{12}]$
35.4.a.a	$35$	$4$	35.a	1.a	$1$	$1$	$1$	$2.065$	$\Q$	None	✓	✓	✓	✓	35.4.a.a	$1$	$1$	$1$	$-8$	$-5$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-8q^{3}-7q^{4}-5q^{5}-8q^{6}+\cdots$
35.4.a.b	$35$	$4$	35.a	1.a	$1$	$2$	$2$	$2.065$	$\Q(\sqrt{2}) $	None	✓	✓	✓	✓	35.4.a.b	$1$	$0$	$8$	$2$	$-10$	$-14$	$+$	$1$	$\mathrm{SU}(2)$	$q+(4+\beta )q^{2}+(1-4\beta )q^{3}+(10+8\beta )q^{4}+\cdots$
35.4.a.c	$35$	$4$	35.a	1.a	$1$	$3$	$3$	$2.065$	3.3.14360.1	None	✓	✓	✓	✓	35.4.a.c	$1$	$0$	$-3$	$2$	$15$	$21$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(1+\beta _{1}-\beta _{2})q^{3}+\cdots$
35.4.b.a	$35$	$4$	35.b	5.b	$2$	$10$	$10$	$2.065$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None		✓	✓	✓	35.4.b.a	$2$	$0$	$0$	$0$	$6$	$0$		$2^{2}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{6}q^{3}+(-4+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$
35.4.e.a	$35$	$4$	35.e	7.c	$3$	$2$	$1$	$2.065$	$\Q(\sqrt{-3}) $	None		✓			35.4.e.a	$2$	$0$	$-3$	$2$	$-5$	$-28$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-3\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
35.4.e.b	$35$	$4$	35.e	7.c	$3$	$4$	$2$	$2.065$	$\Q(\sqrt{2}, \sqrt{-3})$	None		✓			35.4.e.b	$2$	$0$	$6$	$2$	$-10$	$22$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}-3\beta _{2}+\beta _{3})q^{2}+(1+3\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots$
35.4.e.c	$35$	$4$	35.e	7.c	$3$	$10$	$5$	$2.065$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		✓	✓		35.4.e.c	$2$	$0$	$-1$	$8$	$25$	$-62$		$2^{4}$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}-\beta _{2})q^{2}+(-\beta _{3}-\beta _{5}+2\beta _{6}+\cdots)q^{3}+\cdots$
35.4.f.a	$35$	$4$	35.f	35.f	$4$	$4$	$2$	$2.065$	$\Q(i, \sqrt{5})$	None		✓			35.4.f.a	$4$	$0$	$-8$	$0$	$0$	$-42$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(-2-2\beta _{2})q^{2}+(1+2\beta _{1}+\beta _{2})q^{3}+\cdots$
35.4.f.b	$35$	$4$	35.f	35.f	$4$	$16$	$8$	$2.065$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		✓	✓		35.4.f.b	$4$	$0$	$4$	$0$	$0$	$32$		$2^{2}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{7}q^{2}-\beta _{8}q^{3}+(-4\beta _{3}+\beta _{6}-\beta _{7}+\cdots)q^{4}+\cdots$
35.4.j.a	$35$	$4$	35.j	35.j	$6$	$20$	$10$	$2.065$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		✓	✓	✓	35.4.j.a	$4$	$0$	$0$	$0$	$3$	$0$		$2^{10}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{1}q^{2}-\beta _{14}q^{3}+(-\beta _{2}-3\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots$
35.4.k.a	$35$	$4$	35.k	35.k	$12$	$40$	$10$	$2.065$		None		✓	✓	✓	35.4.k.a	$4$	$0$	$-2$	$-6$	$-30$	$4$			$\mathrm{SU}(2)[C_{12}]$
35.5.c.a	$35$	$5$	35.c	35.c	$2$	$1$	$1$	$3.618$	$\Q$	$\Q(\sqrt{-35}) $	✓	✓			35.5.c.a	$2$	$0$	$0$	$-17$	$25$	$49$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-17q^{3}+2^{4}q^{4}+5^{2}q^{5}+7^{2}q^{7}+\cdots$
35.5.c.b	$35$	$5$	35.c	35.c	$2$	$1$	$1$	$3.618$	$\Q$	$\Q(\sqrt{-35}) $	✓	✓			35.5.c.a	$2$	$0$	$0$	$17$	$-25$	$-49$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+17q^{3}+2^{4}q^{4}-5^{2}q^{5}-7^{2}q^{7}+\cdots$
35.5.c.c	$35$	$5$	35.c	35.c	$2$	$2$	$2$	$3.618$	$\Q(\sqrt{-6}) $	None		✓			35.5.c.c	$2$	$0$	$0$	$-10$	$-10$	$-70$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}-5q^{3}+10q^{4}+(-5+10\beta )q^{5}+\cdots$
35.5.c.d	$35$	$5$	35.c	35.c	$2$	$2$	$2$	$3.618$	$\Q(\sqrt{-6}) $	None		✓			35.5.c.c	$2$	$0$	$0$	$10$	$10$	$70$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}+5q^{3}+10q^{4}+(5-10\beta )q^{5}+\cdots$
35.5.c.e	$35$	$5$	35.c	35.c	$2$	$8$	$8$	$3.618$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		✓	✓		35.5.c.e	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{2}+3\beta _{3}q^{3}+(-22+\beta _{2})q^{4}+\cdots$
35.5.d.a	$35$	$5$	35.d	7.b	$2$	$12$	$12$	$3.618$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓	✓	✓	35.5.d.a	$2$	$0$	$-6$	$0$	$0$	$-50$		$2^{3}\cdot 5^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta _{1})q^{2}-\beta _{3}q^{3}+(11-\beta _{1}+\cdots)q^{4}+\cdots$
35.5.g.a	$35$	$5$	35.g	5.c	$4$	$24$	$12$	$3.618$		None		✓	✓	✓	35.5.g.a	$2$	$0$	$0$	$20$	$-48$	$0$			$\mathrm{SU}(2)[C_{4}]$
35.5.h.a	$35$	$5$	35.h	7.d	$6$	$20$	$10$	$3.618$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		✓	✓	✓	35.5.h.a	$2$	$0$	$6$	$-18$	$0$	$-54$		$5^{4}\cdot 7^{3}$	$\mathrm{SU}(2)[C_{6}]$	$q+(1+\beta _{1}+\beta _{3}+\beta _{4})q^{2}+(-1-\beta _{4}+\cdots)q^{3}+\cdots$
35.5.i.a	$35$	$5$	35.i	35.i	$6$	$28$	$14$	$3.618$		None		✓	✓	✓	35.5.i.a	$4$	$0$	$0$	$0$	$-30$	$0$			$\mathrm{SU}(2)[C_{6}]$
35.5.l.a	$35$	$5$	35.l	35.l	$12$	$56$	$14$	$3.618$		None		✓	✓	✓	35.5.l.a	$4$	$0$	$-2$	$-2$	$16$	$46$			$\mathrm{SU}(2)[C_{12}]$
35.6.a.a	$35$	$6$	35.a	1.a	$1$	$1$	$1$	$5.613$	$\Q$	None	✓	✓	✓	✓	35.6.a.a	$1$	$1$	$-8$	$1$	$25$	$49$	$+$	$1$	$\mathrm{SU}(2)$	$q-8q^{2}+q^{3}+2^{5}q^{4}+5^{2}q^{5}-8q^{6}+\cdots$
35.6.a.b	$35$	$6$	35.a	1.a	$1$	$2$	$2$	$5.613$	$\Q(\sqrt{65}) $	None	✓	✓	✓	✓	35.6.a.b	$1$	$1$	$1$	$3$	$-50$	$-98$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(3-3\beta )q^{3}+(-2^{4}+\beta )q^{4}+\cdots$
35.6.a.c	$35$	$6$	35.a	1.a	$1$	$3$	$3$	$5.613$	3.3.577880.1	None	✓	✓	✓	✓	35.6.a.c	$1$	$0$	$-6$	$26$	$-75$	$147$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-2+\beta _{1})q^{2}+(9+\beta _{2})q^{3}+(38+2\beta _{2})q^{4}+\cdots$
35.6.a.d	$35$	$6$	35.a	1.a	$1$	$4$	$4$	$5.613$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	✓	✓	✓	✓	35.6.a.d	$1$	$0$	$7$	$14$	$100$	$-196$	$-$	$1$	$\mathrm{SU}(2)$	$q+(2-\beta _{1})q^{2}+(4-\beta _{1}+\beta _{3})q^{3}+(15+\cdots)q^{4}+\cdots$
35.6.b.a	$35$	$6$	35.b	5.b	$2$	$14$	$14$	$5.613$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	None		✓	✓	✓	35.6.b.a	$2$	$0$	$0$	$0$	$156$	$0$		$2^{4}\cdot 5^{3}\cdot 7^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}+\beta _{6}q^{3}+(-15+\beta _{1})q^{4}+\cdots$
35.6.e.a	$35$	$6$	35.e	7.c	$3$	$12$	$6$	$5.613$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓			35.6.e.a	$2$	$0$	$5$	$-20$	$150$	$-20$		$2^{4}$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{1}-\beta _{4})q^{2}+(\beta _{1}+\beta _{3}-3\beta _{4}+\cdots)q^{3}+\cdots$
35.6.e.b	$35$	$6$	35.e	7.c	$3$	$16$	$8$	$5.613$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓	✓		35.6.e.b	$2$	$0$	$-3$	$2$	$-200$	$158$		$2^{10}\cdot 7^{5}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(-\beta _{5}+\beta _{6})q^{3}+(\beta _{1}-5^{2}\beta _{2}+\cdots)q^{4}+\cdots$
35.6.f.a	$35$	$6$	35.f	35.f	$4$	$36$	$18$	$5.613$		None		✓	✓	✓	35.6.f.a	$4$	$0$	$-4$	$0$	$0$	$-196$			$\mathrm{SU}(2)[C_{4}]$
35.6.j.a	$35$	$6$	35.j	35.j	$6$	$36$	$18$	$5.613$		None		✓	✓	✓	35.6.j.a	$4$	$0$	$0$	$0$	$-12$	$0$			$\mathrm{SU}(2)[C_{6}]$
35.6.k.a	$35$	$6$	35.k	35.k	$12$	$72$	$18$	$5.613$		None		✓	✓	✓	35.6.k.a	$4$	$0$	$-2$	$-6$	$60$	$190$			$\mathrm{SU}(2)[C_{12}]$
35.7.c.a	$35$	$7$	35.c	35.c	$2$	$1$	$1$	$8.052$	$\Q$	$\Q(\sqrt{-35}) $	✓	✓			35.7.c.a	$2$	$0$	$0$	$-26$	$-125$	$343$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-26q^{3}+2^{6}q^{4}-5^{3}q^{5}+7^{3}q^{7}+\cdots$
35.7.c.b	$35$	$7$	35.c	35.c	$2$	$1$	$1$	$8.052$	$\Q$	$\Q(\sqrt{-35}) $	✓	✓			35.7.c.a	$2$	$0$	$0$	$26$	$125$	$-343$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+26q^{3}+2^{6}q^{4}+5^{3}q^{5}-7^{3}q^{7}+\cdots$

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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.