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 158 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
242.2.a.a	$242$	$2$	242.a	1.a	$1$	$1$	$1$	$1.932$	$\Q$	None	✓	✓			242.2.a.a	$1$	$0$	$-1$	$-2$	$-3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}-3q^{5}+2q^{6}+2q^{7}+\cdots$
242.2.a.b	$242$	$2$	242.a	1.a	$1$	$1$	$1$	$1.932$	$\Q$	None	✓	✓	✓	✓	242.2.a.a	$1$	$1$	$1$	$-2$	$-3$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}-3q^{5}-2q^{6}-2q^{7}+\cdots$
242.2.a.c	$242$	$2$	242.a	1.a	$1$	$2$	$2$	$1.932$	$\Q(\sqrt{3}) $	None	✓	✓	✓	✓	242.2.a.c	$1$	$1$	$-2$	$-2$	$0$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1+\beta )q^{3}+q^{4}-\beta q^{5}+(1+\cdots)q^{6}+\cdots$
242.2.a.d	$242$	$2$	242.a	1.a	$1$	$2$	$2$	$1.932$	$\Q(\sqrt{5}) $	None	✓		✓		22.2.c.a	$1$	$0$	$-2$	$3$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1+\beta )q^{3}+q^{4}+(2-2\beta )q^{5}+\cdots$
242.2.a.e	$242$	$2$	242.a	1.a	$1$	$2$	$2$	$1.932$	$\Q(\sqrt{3}) $	None	✓	✓			242.2.a.c	$1$	$0$	$2$	$-2$	$0$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1+\beta )q^{3}+q^{4}-\beta q^{5}+(-1+\cdots)q^{6}+\cdots$
242.2.a.f	$242$	$2$	242.a	1.a	$1$	$2$	$2$	$1.932$	$\Q(\sqrt{5}) $	None	✓				22.2.c.a	$1$	$0$	$2$	$3$	$2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1+\beta )q^{3}+q^{4}+(2-2\beta )q^{5}+\cdots$
242.2.c.a	$242$	$2$	242.c	11.c	$5$	$4$	$1$	$1.932$	$\Q(\zeta_{10})$	None					22.2.c.a	$2$	$0$	$-1$	$1$	$4$	$2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$
242.2.c.b	$242$	$2$	242.c	11.c	$5$	$4$	$1$	$1.932$	$\Q(\zeta_{10})$	None		✓			242.2.a.a	$4$	$0$	$-1$	$2$	$3$	$2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$
242.2.c.c	$242$	$2$	242.c	11.c	$5$	$4$	$1$	$1.932$	$\Q(\zeta_{10})$	None					22.2.c.a	$2$	$0$	$1$	$-4$	$-6$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-\zeta_{10}+\cdots)q^{3}+\cdots$
242.2.c.d	$242$	$2$	242.c	11.c	$5$	$4$	$1$	$1.932$	$\Q(\zeta_{10})$	None					22.2.c.a	$2$	$0$	$1$	$1$	$4$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(\zeta_{10}+\cdots)q^{3}+\cdots$
242.2.c.e	$242$	$2$	242.c	11.c	$5$	$4$	$1$	$1.932$	$\Q(\zeta_{10})$	None		✓			242.2.a.a	$4$	$0$	$1$	$2$	$3$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-2\zeta_{10}^{2}q^{3}+\cdots$
242.2.c.f	$242$	$2$	242.c	11.c	$5$	$8$	$2$	$1.932$	8.0.324000000.3	None		✓			242.2.a.c	$4$	$0$	$-2$	$2$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1-\beta _{2}-\beta _{4}-\beta _{6})q^{2}+(-\beta _{1}+\cdots)q^{3}+\cdots$
242.2.c.g	$242$	$2$	242.c	11.c	$5$	$8$	$2$	$1.932$	8.0.324000000.3	None		✓			242.2.a.c	$4$	$0$	$2$	$2$	$0$	$6$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{4}q^{2}+(-\beta _{2}-\beta _{7})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots$
242.2.e.a	$242$	$2$	242.e	121.e	$11$	$50$	$5$	$1.932$		None		✓			242.2.e.a	$2$	$0$	$5$	$-10$	$1$	$0$			$\mathrm{SU}(2)[C_{11}]$
242.2.e.b	$242$	$2$	242.e	121.e	$11$	$60$	$6$	$1.932$		None		✓	✓		242.2.e.b	$2$	$0$	$-6$	$8$	$-5$	$-8$			$\mathrm{SU}(2)[C_{11}]$
242.2.g.a	$242$	$2$	242.g	121.g	$55$	$200$	$5$	$1.932$		None		✓			242.2.g.a	$2$	$0$	$-5$	$10$	$-1$	$0$			$\mathrm{SU}(2)[C_{55}]$
242.2.g.b	$242$	$2$	242.g	121.g	$55$	$240$	$6$	$1.932$		None		✓	✓		242.2.g.b	$2$	$0$	$6$	$-8$	$5$	$-2$			$\mathrm{SU}(2)[C_{55}]$
242.3.b.a	$242$	$3$	242.b	11.b	$2$	$2$	$2$	$6.594$	$\Q(\sqrt{-2}) $	None		✓			242.3.b.a	$2$	$0$	$0$	$6$	$18$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}+3q^{3}-2q^{4}+9q^{5}+3\beta q^{6}+\cdots$
242.3.b.b	$242$	$3$	242.b	11.b	$2$	$4$	$4$	$6.594$	$\Q(\sqrt{-2}, \sqrt{97})$	None		✓			242.3.b.b	$2$	$0$	$0$	$-2$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+(-1+\beta _{2})q^{3}-2q^{4}+(1+\cdots)q^{5}+\cdots$
242.3.b.c	$242$	$3$	242.b	11.b	$2$	$4$	$4$	$6.594$	$\Q(\sqrt{-2}, \sqrt{3})$	None		✓			242.3.b.c	$2$	$0$	$0$	$8$	$16$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}-\beta _{3})q^{2}+(2-2\beta _{2})q^{3}-2q^{4}+\cdots$
242.3.b.d	$242$	$3$	242.b	11.b	$2$	$8$	$8$	$6.594$	8.0.64000000.1	None			✓		22.3.d.a	$2$	$0$	$0$	$-12$	$-28$	$0$		$2^{4}\cdot 11^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+(-1+\beta _{2})q^{3}-2q^{4}+(-4+\cdots)q^{5}+\cdots$
242.3.d.a	$242$	$3$	242.d	11.d	$10$	$8$	$2$	$6.594$	8.0.64000000.1	None		✓			242.3.b.a	$8$	$0$	$0$	$-6$	$-18$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+\beta _{1}q^{2}+(-3+3\beta _{2}-3\beta _{4}+3\beta _{6}+\cdots)q^{3}+\cdots$
242.3.d.b	$242$	$3$	242.d	11.d	$10$	$8$	$2$	$6.594$	8.0.64000000.1	None					22.3.b.a	$8$	$0$	$0$	$-2$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+\beta _{1}q^{2}+(-1+\beta _{2}-\beta _{4}+\beta _{6})q^{3}+\cdots$
242.3.d.c	$242$	$3$	242.d	11.d	$10$	$8$	$2$	$6.594$	8.0.64000000.1	None					22.3.d.a	$2$	$0$	$0$	$-2$	$2$	$30$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+\beta _{1}q^{2}+(1+\beta _{1}-2\beta _{2}-\beta _{3}+2\beta _{4}+\cdots)q^{3}+\cdots$
242.3.d.d	$242$	$3$	242.d	11.d	$10$	$8$	$2$	$6.594$	8.0.64000000.1	None					22.3.d.a	$2$	$0$	$0$	$8$	$12$	$-20$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+\beta _{1}q^{2}+(2-\beta _{1}-\beta _{2}+\beta _{4}+\beta _{5}+\cdots)q^{3}+\cdots$
242.3.d.e	$242$	$3$	242.d	11.d	$10$	$8$	$2$	$6.594$	8.0.64000000.1	None					22.3.d.a	$2$	$0$	$0$	$8$	$12$	$20$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+\beta _{1}q^{2}+(2+\beta _{1}-\beta _{2}+\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots$
242.3.d.f	$242$	$3$	242.d	11.d	$10$	$16$	$4$	$6.594$	16.0.$\cdots$.7	None		✓			242.3.b.c	$8$	$0$	$0$	$-8$	$-16$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(-\beta _{5}-\beta _{7})q^{2}+(-2\beta _{8}+2\beta _{10}+\cdots)q^{3}+\cdots$
242.3.d.g	$242$	$3$	242.d	11.d	$10$	$16$	$4$	$6.594$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓			242.3.b.b	$8$	$0$	$0$	$2$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q-\beta _{6}q^{2}+(1+\beta _{1}-\beta _{2}+\beta _{3}+\beta _{15})q^{3}+\cdots$
242.3.f.a	$242$	$3$	242.f	121.f	$22$	$220$	$22$	$6.594$		None		✓	✓	✓	242.3.f.a	$2$	$0$	$0$	$-4$	$-4$	$0$			$\mathrm{SU}(2)[C_{22}]$
242.3.h.a	$242$	$3$	242.h	121.h	$110$	$880$	$22$	$6.594$		None		✓	✓	✓	242.3.h.a	$2$	$0$	$0$	$4$	$4$	$30$			$\mathrm{SU}(2)[C_{110}]$
242.4.a.a	$242$	$4$	242.a	1.a	$1$	$1$	$1$	$14.278$	$\Q$	None	✓				22.4.a.c	$1$	$1$	$-2$	$1$	$-3$	$10$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+q^{3}+4q^{4}-3q^{5}-2q^{6}+\cdots$
242.4.a.b	$242$	$4$	242.a	1.a	$1$	$1$	$1$	$14.278$	$\Q$	None	✓	✓			242.4.a.b	$1$	$1$	$-2$	$4$	$3$	$-8$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{3}+4q^{4}+3q^{5}-8q^{6}+\cdots$
242.4.a.c	$242$	$4$	242.a	1.a	$1$	$1$	$1$	$14.278$	$\Q$	None	✓	✓			242.4.a.c	$1$	$0$	$-2$	$5$	$-15$	$36$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+5q^{3}+4q^{4}-15q^{5}-10q^{6}+\cdots$
242.4.a.d	$242$	$4$	242.a	1.a	$1$	$1$	$1$	$14.278$	$\Q$	None	✓				22.4.a.a	$1$	$0$	$2$	$-7$	$-19$	$-14$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-7q^{3}+4q^{4}-19q^{5}-14q^{6}+\cdots$
242.4.a.e	$242$	$4$	242.a	1.a	$1$	$1$	$1$	$14.278$	$\Q$	None	✓	✓			242.4.a.b	$1$	$0$	$2$	$4$	$3$	$8$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+4q^{3}+4q^{4}+3q^{5}+8q^{6}+\cdots$
242.4.a.f	$242$	$4$	242.a	1.a	$1$	$1$	$1$	$14.278$	$\Q$	None	✓				22.4.a.b	$1$	$0$	$2$	$4$	$14$	$8$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+4q^{3}+4q^{4}+14q^{5}+8q^{6}+\cdots$
242.4.a.g	$242$	$4$	242.a	1.a	$1$	$1$	$1$	$14.278$	$\Q$	None	✓	✓			242.4.a.c	$1$	$1$	$2$	$5$	$-15$	$-36$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+5q^{3}+4q^{4}-15q^{5}+10q^{6}+\cdots$
242.4.a.h	$242$	$4$	242.a	1.a	$1$	$2$	$2$	$14.278$	$\Q(\sqrt{5}) $	None	✓				22.4.c.a	$1$	$1$	$-4$	$-13$	$-1$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+(-5-3\beta )q^{3}+4q^{4}-\beta q^{5}+\cdots$
242.4.a.i	$242$	$4$	242.a	1.a	$1$	$2$	$2$	$14.278$	$\Q(\sqrt{3}) $	None	✓	✓			242.4.a.i	$1$	$0$	$-4$	$-2$	$-12$	$6$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+(-1+\beta )q^{3}+4q^{4}+(-6+\cdots)q^{5}+\cdots$
242.4.a.j	$242$	$4$	242.a	1.a	$1$	$2$	$2$	$14.278$	$\Q(\sqrt{37}) $	None	✓	✓			242.4.a.j	$1$	$1$	$-4$	$6$	$4$	$-42$	$-$	$2$	$\mathrm{SU}(2)$	$q-2q^{2}+(3+\beta )q^{3}+4q^{4}+(2-3\beta )q^{5}+\cdots$
242.4.a.k	$242$	$4$	242.a	1.a	$1$	$2$	$2$	$14.278$	$\Q(\sqrt{5}) $	None	✓				22.4.c.a	$1$	$1$	$4$	$-13$	$-1$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(-5-3\beta )q^{3}+4q^{4}-\beta q^{5}+\cdots$
242.4.a.l	$242$	$4$	242.a	1.a	$1$	$2$	$2$	$14.278$	$\Q(\sqrt{3}) $	None	✓	✓			242.4.a.i	$1$	$1$	$4$	$-2$	$-12$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(-1+\beta )q^{3}+4q^{4}+(-6+\cdots)q^{5}+\cdots$
242.4.a.m	$242$	$4$	242.a	1.a	$1$	$2$	$2$	$14.278$	$\Q(\sqrt{37}) $	None	✓	✓			242.4.a.j	$1$	$0$	$4$	$6$	$4$	$42$	$+$	$2$	$\mathrm{SU}(2)$	$q+2q^{2}+(3+\beta )q^{3}+4q^{4}+(2-3\beta )q^{5}+\cdots$
242.4.a.n	$242$	$4$	242.a	1.a	$1$	$4$	$4$	$14.278$	4.4.978025.2	None	✓		✓		22.4.c.b	$1$	$0$	$-8$	$4$	$25$	$-3$	$+$	$11$	$\mathrm{SU}(2)$	$q-2q^{2}+(1-\beta _{1})q^{3}+4q^{4}+(6-\beta _{2}+\cdots)q^{5}+\cdots$
242.4.a.o	$242$	$4$	242.a	1.a	$1$	$4$	$4$	$14.278$	4.4.978025.2	None	✓		✓		22.4.c.b	$1$	$0$	$8$	$4$	$25$	$3$	$+$	$11$	$\mathrm{SU}(2)$	$q+2q^{2}+(1-\beta _{1})q^{3}+4q^{4}+(6-\beta _{2}+\cdots)q^{5}+\cdots$
242.4.c.a	$242$	$4$	242.c	11.c	$5$	$4$	$1$	$14.278$	$\Q(\zeta_{10})$	None		✓			242.4.a.c	$4$	$0$	$-2$	$-5$	$15$	$36$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-2+2\zeta_{10}-2\zeta_{10}^{2}+2\zeta_{10}^{3})q^{2}+\cdots$
242.4.c.b	$242$	$4$	242.c	11.c	$5$	$4$	$1$	$14.278$	$\Q(\zeta_{10})$	None					22.4.a.b	$4$	$0$	$-2$	$-4$	$-14$	$-8$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-2+2\zeta_{10}-2\zeta_{10}^{2}+2\zeta_{10}^{3})q^{2}+\cdots$
242.4.c.c	$242$	$4$	242.c	11.c	$5$	$4$	$1$	$14.278$	$\Q(\zeta_{10})$	None		✓			242.4.a.b	$4$	$0$	$-2$	$-4$	$-3$	$-8$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-2+2\zeta_{10}-2\zeta_{10}^{2}+2\zeta_{10}^{3})q^{2}+\cdots$
242.4.c.d	$242$	$4$	242.c	11.c	$5$	$4$	$1$	$14.278$	$\Q(\zeta_{10})$	None					22.4.a.c	$4$	$0$	$-2$	$-1$	$3$	$10$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-2+2\zeta_{10}-2\zeta_{10}^{2}+2\zeta_{10}^{3})q^{2}+\cdots$
242.4.c.e	$242$	$4$	242.c	11.c	$5$	$4$	$1$	$14.278$	$\Q(\zeta_{10})$	None					22.4.a.a	$4$	$0$	$-2$	$7$	$19$	$14$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-2+2\zeta_{10}-2\zeta_{10}^{2}+2\zeta_{10}^{3})q^{2}+\cdots$

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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.