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 214 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
306.2.a.a	$306$	$2$	306.a	1.a	$1$	$1$	$1$	$2.443$	$\Q$	None	✓		✓	✓	34.2.a.a	$1$	$1$	$-1$	$0$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-4q^{7}-q^{8}-6q^{11}+2q^{13}+\cdots$
306.2.a.b	$306$	$2$	306.a	1.a	$1$	$1$	$1$	$2.443$	$\Q$	None	✓		✓	✓	102.2.a.c	$1$	$0$	$-1$	$0$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}+4q^{11}+\cdots$
306.2.a.c	$306$	$2$	306.a	1.a	$1$	$1$	$1$	$2.443$	$\Q$	None	✓				102.2.a.b	$1$	$0$	$1$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{7}+q^{8}+2q^{13}+2q^{14}+\cdots$
306.2.a.d	$306$	$2$	306.a	1.a	$1$	$1$	$1$	$2.443$	$\Q$	None	✓				102.2.a.a	$1$	$0$	$1$	$0$	$4$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+4q^{5}-2q^{7}+q^{8}+4q^{10}+\cdots$
306.2.a.e	$306$	$2$	306.a	1.a	$1$	$2$	$2$	$2.443$	$\Q(\sqrt{6}) $	None	✓	✓	✓	✓	306.2.a.e	$1$	$0$	$-2$	$0$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta q^{5}+(2+\beta )q^{7}-q^{8}+\cdots$
306.2.a.f	$306$	$2$	306.a	1.a	$1$	$2$	$2$	$2.443$	$\Q(\sqrt{6}) $	None	✓	✓	✓	✓	306.2.a.e	$1$	$0$	$2$	$0$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta q^{5}+(2-\beta )q^{7}+q^{8}+\cdots$
306.2.b.a	$306$	$2$	306.b	17.b	$2$	$2$	$2$	$2.443$	$\Q(\sqrt{-1}) $	None					102.2.b.a	$2$	$0$	$-2$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}+\beta q^{5}+\beta q^{7}-q^{8}+\cdots$
306.2.b.b	$306$	$2$	306.b	17.b	$2$	$2$	$2$	$2.443$	$\Q(\sqrt{-2}) $	None		✓			306.2.b.b	$2$	$0$	$-2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}+\beta q^{5}-3\beta q^{7}-q^{8}-\beta q^{10}+\cdots$
306.2.b.c	$306$	$2$	306.b	17.b	$2$	$2$	$2$	$2.443$	$\Q(\sqrt{-2}) $	None		✓			306.2.b.b	$2$	$0$	$2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}+\beta q^{5}+3\beta q^{7}+q^{8}+\beta q^{10}+\cdots$
306.2.b.d	$306$	$2$	306.b	17.b	$2$	$2$	$2$	$2.443$	$\Q(\sqrt{-2}) $	None					34.2.b.a	$2$	$0$	$2$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}+\beta q^{11}+\cdots$
306.2.e.a	$306$	$2$	306.e	9.c	$3$	$2$	$1$	$2.443$	$\Q(\sqrt{-3}) $	None		✓			306.2.e.a	$2$	$0$	$1$	$3$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
306.2.e.b	$306$	$2$	306.e	9.c	$3$	$4$	$2$	$2.443$	$\Q(\sqrt{-2}, \sqrt{-3})$	None		✓			306.2.e.b	$2$	$0$	$-2$	$2$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{2})q^{2}+(-\beta _{1}+\beta _{2}+\beta _{3})q^{3}+\cdots$
306.2.e.c	$306$	$2$	306.e	9.c	$3$	$6$	$3$	$2.443$	$\Q(\zeta_{18})$	None		✓			306.2.e.c	$2$	$0$	$-3$	$0$	$-3$	$6$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta_1 q^{2}+(-\beta_{5}+\beta_{3})q^{3}+(\beta_1-1)q^{4}+\cdots$
306.2.e.d	$306$	$2$	306.e	9.c	$3$	$6$	$3$	$2.443$	6.0.309123.1	None		✓			306.2.e.d	$2$	$0$	$-3$	$2$	$3$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{4})q^{2}+(\beta _{1}+\beta _{2}-\beta _{5})q^{3}+\cdots$
306.2.e.e	$306$	$2$	306.e	9.c	$3$	$6$	$3$	$2.443$	$\Q(\zeta_{18})$	None		✓			306.2.e.e	$2$	$0$	$3$	$0$	$-3$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta_1 q^{2}+(\beta_{5}-\beta_{4}+\cdots+\beta_{2})q^{3}+\cdots$
306.2.e.f	$306$	$2$	306.e	9.c	$3$	$8$	$4$	$2.443$	8.0.5206055409.1	None		✓	✓		306.2.e.f	$2$	$0$	$4$	$-3$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{2}q^{2}-\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
306.2.g.a	$306$	$2$	306.g	17.c	$4$	$2$	$1$	$2.443$	$\Q(\sqrt{-1}) $	None		✓			306.2.g.a	$2$	$1$	$0$	$0$	$-4$	$-6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-i q^{2}-q^{4}+(-2 i-2)q^{5}+(3 i-3)q^{7}+\cdots$
306.2.g.b	$306$	$2$	306.g	17.c	$4$	$2$	$1$	$2.443$	$\Q(\sqrt{-1}) $	None					34.2.c.a	$2$	$1$	$0$	$0$	$-4$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+i q^{2}-q^{4}+(-2 i-2)q^{5}+(2 i-2)q^{7}+\cdots$
306.2.g.c	$306$	$2$	306.g	17.c	$4$	$2$	$1$	$2.443$	$\Q(\sqrt{-1}) $	None		✓			306.2.g.c	$2$	$0$	$0$	$0$	$-4$	$2$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+i q^{2}-q^{4}+(-2 i-2)q^{5}+(-i+1)q^{7}+\cdots$
306.2.g.d	$306$	$2$	306.g	17.c	$4$	$2$	$1$	$2.443$	$\Q(\sqrt{-1}) $	None					34.2.c.b	$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-i q^{2}-q^{4}+(i+1)q^{5}+i q^{8}+\cdots$
306.2.g.e	$306$	$2$	306.g	17.c	$4$	$2$	$1$	$2.443$	$\Q(\sqrt{-1}) $	None		✓			306.2.g.a	$2$	$0$	$0$	$0$	$4$	$-6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+i q^{2}-q^{4}+(2 i+2)q^{5}+(3 i-3)q^{7}+\cdots$
306.2.g.f	$306$	$2$	306.g	17.c	$4$	$2$	$1$	$2.443$	$\Q(\sqrt{-1}) $	None		✓			306.2.g.c	$2$	$0$	$0$	$0$	$4$	$2$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-i q^{2}-q^{4}+(2 i+2)q^{5}+(-i+1)q^{7}+\cdots$
306.2.g.g	$306$	$2$	306.g	17.c	$4$	$4$	$2$	$2.443$	$\Q(\zeta_{8})$	None			✓		102.2.f.a	$2$	$0$	$0$	$0$	$4$	$8$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta_{2} q^{2}-q^{4}+(\beta_{2}+\beta_1+1)q^{5}+\cdots$
306.2.j.a	$306$	$2$	306.j	153.h	$6$	$4$	$2$	$2.443$	$\Q(\zeta_{12})$	None		✓			306.2.j.a	$4$	$0$	$2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1-\zeta_{12}^{2})q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots$
306.2.j.b	$306$	$2$	306.j	153.h	$6$	$16$	$8$	$2.443$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		✓			306.2.j.b	$4$	$0$	$-8$	$0$	$0$	$0$		$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{5}q^{2}-\beta _{1}q^{3}+(-1+\beta _{5})q^{4}+(-\beta _{6}+\cdots)q^{5}+\cdots$
306.2.j.c	$306$	$2$	306.j	153.h	$6$	$16$	$8$	$2.443$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		✓			306.2.j.c	$4$	$0$	$8$	$0$	$0$	$0$		$3^{4}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{1}q^{2}+\beta _{10}q^{3}+(-1-\beta _{1})q^{4}+\cdots$
306.2.l.a	$306$	$2$	306.l	17.d	$8$	$4$	$1$	$2.443$	$\Q(\zeta_{8})$	None		✓			306.2.l.a	$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(-1+\zeta_{8})q^{5}+\cdots$
306.2.l.b	$306$	$2$	306.l	17.d	$8$	$4$	$1$	$2.443$	$\Q(\zeta_{8})$	None		✓			306.2.l.a	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(1-\zeta_{8})q^{5}+(-2\zeta_{8}+\cdots)q^{7}+\cdots$
306.2.l.c	$306$	$2$	306.l	17.d	$8$	$4$	$1$	$2.443$	$\Q(\zeta_{8})$	None					34.2.d.a	$2$	$0$	$0$	$0$	$8$	$0$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(2-2\zeta_{8})q^{5}+\cdots$
306.2.l.d	$306$	$2$	306.l	17.d	$8$	$8$	$2$	$2.443$	$\Q(\zeta_{16})$	None					102.2.h.a	$2$	$0$	$0$	$0$	$-8$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{8}]$	$q-\beta_{4} q^{2}-\beta_{2} q^{4}+(\beta_{7}-\beta_1-1)q^{5}+\cdots$
306.2.l.e	$306$	$2$	306.l	17.d	$8$	$8$	$2$	$2.443$	$\Q(\zeta_{16})$	None					102.2.h.b	$2$	$0$	$0$	$0$	$-8$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{8}]$	$q-\beta_{4} q^{2}-\beta_{2} q^{4}+(-\beta_{6}+\beta_{5}+\beta_{3}+\cdots-1)q^{5}+\cdots$
306.2.n.a	$306$	$2$	306.n	153.n	$12$	$4$	$1$	$2.443$	$\Q(\zeta_{12})$	None		✓			306.2.n.a	$2$	$0$	$0$	$0$	$-8$	$-2$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+(-\zeta_{12}+2\zeta_{12}^{3})q^{3}+\cdots$
306.2.n.b	$306$	$2$	306.n	153.n	$12$	$4$	$1$	$2.443$	$\Q(\zeta_{12})$	None		✓			306.2.n.b	$2$	$0$	$0$	$0$	$-4$	$4$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots$
306.2.n.c	$306$	$2$	306.n	153.n	$12$	$4$	$1$	$2.443$	$\Q(\zeta_{12})$	None		✓			306.2.n.b	$2$	$0$	$0$	$6$	$-4$	$-8$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+(2-\zeta_{12}^{2})q^{3}+\cdots$
306.2.n.d	$306$	$2$	306.n	153.n	$12$	$4$	$1$	$2.443$	$\Q(\zeta_{12})$	None		✓			306.2.n.a	$2$	$0$	$0$	$6$	$4$	$-2$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+(1+\zeta_{12}^{2})q^{3}+\cdots$
306.2.n.e	$306$	$2$	306.n	153.n	$12$	$24$	$6$	$2.443$		None		✓			306.2.n.e	$4$	$0$	$0$	$-6$	$4$	$4$			$\mathrm{SU}(2)[C_{12}]$
306.2.n.f	$306$	$2$	306.n	153.n	$12$	$32$	$8$	$2.443$		None		✓	✓		306.2.n.f	$4$	$0$	$0$	$-4$	$8$	$4$			$\mathrm{SU}(2)[C_{12}]$
306.2.o.a	$306$	$2$	306.o	51.i	$16$	$8$	$1$	$2.443$	$\Q(\zeta_{16})$	None		✓			306.2.o.a	$2$	$0$	$0$	$0$	$-8$	$-8$		$1$	$\mathrm{SU}(2)[C_{16}]$	$q-\zeta_{16}^{3}q^{2}+\zeta_{16}^{6}q^{4}+(-1-\zeta_{16}^{2}+\cdots)q^{5}+\cdots$
306.2.o.b	$306$	$2$	306.o	51.i	$16$	$8$	$1$	$2.443$	$\Q(\zeta_{16})$	None		✓			306.2.o.b	$2$	$0$	$0$	$0$	$-8$	$0$		$1$	$\mathrm{SU}(2)[C_{16}]$	$q+\zeta_{16}^{3}q^{2}+\zeta_{16}^{6}q^{4}+(-1+\zeta_{16}^{5}+\cdots)q^{5}+\cdots$
306.2.o.c	$306$	$2$	306.o	51.i	$16$	$8$	$1$	$2.443$	$\Q(\zeta_{16})$	None		✓			306.2.o.c	$2$	$0$	$0$	$0$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{16}]$	$q+\zeta_{16}^{3}q^{2}+\zeta_{16}^{6}q^{4}+(-\zeta_{16}-\zeta_{16}^{2}+\cdots)q^{5}+\cdots$
306.2.o.d	$306$	$2$	306.o	51.i	$16$	$8$	$1$	$2.443$	$\Q(\zeta_{16})$	None		✓			306.2.o.c	$2$	$0$	$0$	$0$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{16}]$	$q-\zeta_{16}^{3}q^{2}+\zeta_{16}^{6}q^{4}+(\zeta_{16}+\zeta_{16}^{2}+\cdots)q^{5}+\cdots$
306.2.o.e	$306$	$2$	306.o	51.i	$16$	$8$	$1$	$2.443$	$\Q(\zeta_{16})$	None		✓			306.2.o.a	$2$	$0$	$0$	$0$	$8$	$-8$		$1$	$\mathrm{SU}(2)[C_{16}]$	$q+\zeta_{16}^{3}q^{2}+\zeta_{16}^{6}q^{4}+(1+\zeta_{16}^{2}+\cdots)q^{5}+\cdots$
306.2.o.f	$306$	$2$	306.o	51.i	$16$	$8$	$1$	$2.443$	$\Q(\zeta_{16})$	None		✓			306.2.o.b	$2$	$0$	$0$	$0$	$8$	$0$		$1$	$\mathrm{SU}(2)[C_{16}]$	$q-\zeta_{16}^{3}q^{2}+\zeta_{16}^{6}q^{4}+(1-\zeta_{16}^{5}+\cdots)q^{5}+\cdots$
306.2.r.a	$306$	$2$	306.r	153.r	$24$	$64$	$8$	$2.443$		None		✓			306.2.r.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{24}]$
306.2.r.b	$306$	$2$	306.r	153.r	$24$	$80$	$10$	$2.443$		None		✓	✓		306.2.r.b	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{24}]$
306.2.s.a	$306$	$2$	306.s	153.s	$48$	$144$	$9$	$2.443$		None		✓			306.2.s.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{48}]$
306.2.s.b	$306$	$2$	306.s	153.s	$48$	$144$	$9$	$2.443$		None		✓			306.2.s.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{48}]$
306.3.c.a	$306$	$3$	306.c	3.b	$2$	$4$	$4$	$8.338$	$\Q(\sqrt{-2}, \sqrt{-17})$	None		✓			306.3.c.a	$2$	$0$	$0$	$0$	$0$	$-8$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}-2q^{4}+(-2\beta _{1}+\beta _{3})q^{5}+\cdots$
306.3.c.b	$306$	$3$	306.c	3.b	$2$	$4$	$4$	$8.338$	$\Q(\sqrt{-2}, \sqrt{-17})$	None		✓			306.3.c.b	$2$	$0$	$0$	$0$	$0$	$24$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}-2q^{4}+(-2\beta _{1}+\beta _{3})q^{5}+\cdots$
306.3.d.a	$306$	$3$	306.d	51.c	$2$	$2$	$2$	$8.338$	$\Q(\sqrt{-2}) $	None		✓			306.3.d.a	$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}-2q^{4}-q^{5}+3\beta q^{7}-2\beta q^{8}+\cdots$

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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.