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 136 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
605.1.f.a	$605$	$1$	605.f	5.c	$4$	$2$	$1$	$0.302$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-11}) $	None		✓	✓	✓	605.1.f.a	$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q+(i+1)q^{3}+i q^{4}-i q^{5}+i q^{9}+\cdots$
605.1.h.a	$605$	$1$	605.h	55.h	$10$	$4$	$1$	$0.302$	$\Q(\zeta_{10})$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-55}) $	$\Q(\sqrt{5}) $			✓	✓	55.1.d.a	$16$	$0$	$0$	$0$	$1$	$0$		$1$		$q+\zeta_{10}^{3}q^{4}+\zeta_{10}q^{5}+\zeta_{10}^{4}q^{9}-\zeta_{10}q^{16}+\cdots$
605.1.l.a	$605$	$1$	605.l	55.k	$20$	$8$	$1$	$0.302$	$\Q(\zeta_{20})$	$D_{4}$	$\Q(\sqrt{-11}) $	None		✓	✓	✓	605.1.f.a	$16$	$0$	$0$	$-2$	$0$	$0$		$1$		$q+(-\zeta_{20}-\zeta_{20}^{6})q^{3}-\zeta_{20}^{9}q^{4}-\zeta_{20}^{3}q^{5}+\cdots$
605.2.a.a	$605$	$2$	605.a	1.a	$1$	$1$	$1$	$4.831$	$\Q$	$_{}$	None	None	✓	✓			605.2.a.a	$1$	$1$	$-1$	$-3$	$1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-3q^{3}-q^{4}+q^{5}+3q^{6}-3q^{7}+\cdots$
605.2.a.b	$605$	$2$	605.a	1.a	$1$	$1$	$1$	$4.831$	$\Q$	$_{}$	None	None	✓				55.2.a.a	$1$	$1$	$-1$	$0$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+q^{5}+3q^{8}-3q^{9}-q^{10}+\cdots$
605.2.a.c	$605$	$2$	605.a	1.a	$1$	$1$	$1$	$4.831$	$\Q$	$_{}$	None	None	✓	✓			605.2.a.a	$1$	$1$	$1$	$-3$	$1$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-3q^{3}-q^{4}+q^{5}-3q^{6}+3q^{7}+\cdots$
605.2.a.d	$605$	$2$	605.a	1.a	$1$	$2$	$2$	$4.831$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				55.2.a.b	$1$	$0$	$-2$	$0$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+2\beta q^{3}+(1-2\beta )q^{4}+\cdots$
605.2.a.e	$605$	$2$	605.a	1.a	$1$	$2$	$2$	$4.831$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	✓			605.2.a.e	$2$	$1$	$0$	$-2$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+q^{4}-q^{5}-\beta q^{6}-\beta q^{7}+\cdots$
605.2.a.f	$605$	$2$	605.a	1.a	$1$	$2$	$2$	$4.831$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	✓			605.2.a.f	$2$	$0$	$0$	$4$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+2q^{3}+q^{4}+q^{5}+2\beta q^{6}+\cdots$
605.2.a.g	$605$	$2$	605.a	1.a	$1$	$3$	$3$	$4.831$	3.3.404.1	$_{}$	None	None	✓	✓			605.2.a.g	$1$	$0$	$-1$	$1$	$-3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+\beta _{1}q^{3}+(3+\beta _{1}-\beta _{2})q^{4}+\cdots$
605.2.a.h	$605$	$2$	605.a	1.a	$1$	$3$	$3$	$4.831$	3.3.404.1	$_{}$	None	None	✓	✓			605.2.a.g	$1$	$0$	$1$	$1$	$-3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+\beta _{1}q^{3}+(3+\beta _{1}-\beta _{2})q^{4}+\cdots$
605.2.a.i	$605$	$2$	605.a	1.a	$1$	$4$	$4$	$4.831$	4.4.2525.1	$_{}$	None	None	✓		✓		55.2.g.a	$1$	$1$	$-3$	$-2$	$4$	$-11$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{3})q^{2}-\beta _{1}q^{3}+(1+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
605.2.a.j	$605$	$2$	605.a	1.a	$1$	$4$	$4$	$4.831$	4.4.725.1	$_{}$	None	None	✓		✓		55.2.g.b	$1$	$1$	$-1$	$0$	$-4$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1+\beta _{2}+\beta _{3})q^{3}+(-1+\cdots)q^{4}+\cdots$
605.2.a.k	$605$	$2$	605.a	1.a	$1$	$4$	$4$	$4.831$	4.4.725.1	$_{}$	None	None	✓		✓		55.2.g.b	$1$	$0$	$1$	$0$	$-4$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-1+\beta _{2}+\beta _{3})q^{3}+(-1+\cdots)q^{4}+\cdots$
605.2.a.l	$605$	$2$	605.a	1.a	$1$	$4$	$4$	$4.831$	4.4.2525.1	$_{}$	None	None	✓				55.2.g.a	$1$	$0$	$3$	$-2$	$4$	$11$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2}-\beta _{3})q^{2}+(-1+\beta _{1})q^{3}+\cdots$
605.2.a.m	$605$	$2$	605.a	1.a	$1$	$6$	$6$	$4.831$	6.6.27433728.1	$_{}$	None	None	✓	✓	✓		605.2.a.m	$2$	$0$	$0$	$6$	$6$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1-\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots$
605.2.b.a	$605$	$2$	605.b	5.b	$2$	$2$	$2$	$4.831$	$\Q(\sqrt{-11}) $	$_{}$	$\Q(\sqrt{-11}) $	None		✓			605.2.b.a	$4$	$0$	$0$	$0$	$3$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(-1+2\beta )q^{3}+2q^{4}+(1+\beta )q^{5}+\cdots$
605.2.b.b	$605$	$2$	605.b	5.b	$2$	$4$	$4$	$4.831$	4.0.4400.1	$_{}$	$\Q(\sqrt{-55}) $	None		✓			605.2.b.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{2}q^{2}+(-2-\beta _{3})q^{4}+\beta _{3}q^{5}-\beta _{1}q^{7}+\cdots$
605.2.b.c	$605$	$2$	605.b	5.b	$2$	$4$	$4$	$4.831$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	None	None					55.2.b.a	$2$	$0$	$0$	$0$	$-3$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+\cdots$
605.2.b.d	$605$	$2$	605.b	5.b	$2$	$4$	$4$	$4.831$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	None	None		✓			605.2.b.d	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{3}q^{3}+\beta _{2}q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
605.2.b.e	$605$	$2$	605.b	5.b	$2$	$4$	$4$	$4.831$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	None	None		✓			605.2.b.d	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{3}q^{3}+\beta _{2}q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
605.2.b.f	$605$	$2$	605.b	5.b	$2$	$8$	$8$	$4.831$	8.0.1480160000.1	$_{}$	None	None					55.2.j.a	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(\beta _{1}-\beta _{6}+\beta _{7})q^{3}+\beta _{2}q^{4}+\cdots$
605.2.b.g	$605$	$2$	605.b	5.b	$2$	$8$	$8$	$4.831$	8.0.1480160000.1	$_{}$	None	None					55.2.j.a	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{6}-\beta _{7})q^{3}+\beta _{2}q^{4}+\cdots$
605.2.b.h	$605$	$2$	605.b	5.b	$2$	$12$	$12$	$4.831$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓	✓		605.2.b.h	$4$	$0$	$0$	$0$	$-6$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{9}q^{2}-\beta _{8}q^{3}+(-2-\beta _{6})q^{4}+\beta _{4}q^{5}+\cdots$
605.2.e.a	$605$	$2$	605.e	55.e	$4$	$20$	$10$	$4.831$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		✓			605.2.e.a	$4$	$0$	$0$	$4$	$4$	$0$		$2^{7}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}-\beta _{12}q^{3}+(-\beta _{4}+\beta _{10}-\beta _{13}+\cdots)q^{4}+\cdots$
605.2.e.b	$605$	$2$	605.e	55.e	$4$	$32$	$16$	$4.831$		$_{}$	None	None					55.2.l.a	$4$	$0$	$0$	$-4$	$8$	$0$			$\mathrm{SU}(2)[C_{4}]$
605.2.e.c	$605$	$2$	605.e	55.e	$4$	$40$	$20$	$4.831$		$_{}$	None	None		✓	✓		605.2.e.c	$4$	$0$	$0$	$8$	$-4$	$0$			$\mathrm{SU}(2)[C_{4}]$
605.2.g.a	$605$	$2$	605.g	11.c	$5$	$4$	$1$	$4.831$	$\Q(\zeta_{10})$	$_{}$	None	None					55.2.a.a	$4$	$0$	$-1$	$0$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$
605.2.g.b	$605$	$2$	605.g	11.c	$5$	$4$	$1$	$4.831$	$\Q(\zeta_{10})$	$_{}$	None	None		✓			605.2.a.a	$4$	$0$	$-1$	$3$	$-1$	$-3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$
605.2.g.c	$605$	$2$	605.g	11.c	$5$	$4$	$1$	$4.831$	$\Q(\zeta_{10})$	$_{}$	None	None					55.2.a.a	$4$	$0$	$1$	$0$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\zeta_{10}^{3}q^{4}+\cdots$
605.2.g.d	$605$	$2$	605.g	11.c	$5$	$4$	$1$	$4.831$	$\Q(\zeta_{10})$	$_{}$	None	None		✓			605.2.a.a	$4$	$0$	$1$	$3$	$-1$	$3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-3\zeta_{10}^{2}q^{3}+\cdots$
605.2.g.e	$605$	$2$	605.g	11.c	$5$	$8$	$2$	$4.831$	8.0.13140625.1	$_{}$	None	None					55.2.g.b	$2$	$0$	$-3$	$5$	$2$	$-4$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{2}q^{2}+(1-\beta _{2}+\beta _{5}+\beta _{7})q^{3}+(1+\cdots)q^{4}+\cdots$
605.2.g.f	$605$	$2$	605.g	11.c	$5$	$8$	$2$	$4.831$	8.0.64000000.2	$_{}$	None	None					55.2.a.b	$4$	$0$	$-2$	$0$	$2$	$4$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1-\beta _{2}+\beta _{3}-\beta _{4}-\beta _{6})q^{2}+(2\beta _{1}+\cdots)q^{3}+\cdots$
605.2.g.g	$605$	$2$	605.g	11.c	$5$	$8$	$2$	$4.831$	8.0.159390625.1	$_{}$	None	None					55.2.g.a	$2$	$0$	$-1$	$1$	$-2$	$8$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\beta _{2}-\beta _{3}-\beta _{5}-\beta _{6})q^{2}+(-\beta _{1}+\cdots)q^{3}+\cdots$
605.2.g.h	$605$	$2$	605.g	11.c	$5$	$8$	$2$	$4.831$	8.0.324000000.3	$_{}$	None	None		✓			605.2.a.f	$8$	$0$	$0$	$-4$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{7}q^{2}+2\beta _{6}q^{3}+\beta _{4}q^{4}+(-1-\beta _{2}+\cdots)q^{5}+\cdots$
605.2.g.i	$605$	$2$	605.g	11.c	$5$	$8$	$2$	$4.831$	8.0.324000000.3	$_{}$	None	None		✓			605.2.a.e	$8$	$0$	$0$	$2$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{7}q^{2}-\beta _{6}q^{3}+\beta _{4}q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots$
605.2.g.j	$605$	$2$	605.g	11.c	$5$	$8$	$2$	$4.831$	8.0.159390625.1	$_{}$	None	None					55.2.g.a	$2$	$0$	$1$	$1$	$-2$	$-8$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\beta _{2}+\beta _{3}+\beta _{5}+\beta _{6})q^{2}+(-\beta _{1}+\cdots)q^{3}+\cdots$
605.2.g.k	$605$	$2$	605.g	11.c	$5$	$8$	$2$	$4.831$	8.0.13140625.1	$_{}$	None	None					55.2.g.b	$2$	$0$	$2$	$-5$	$2$	$1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{6}q^{2}+(-1+\beta _{1}+\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots$
605.2.g.l	$605$	$2$	605.g	11.c	$5$	$8$	$2$	$4.831$	8.0.64000000.2	$_{}$	None	None					55.2.a.b	$4$	$0$	$2$	$0$	$2$	$-4$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{2}+\beta _{7})q^{2}+2\beta _{1}q^{3}+(2\beta _{1}+2\beta _{3}+\cdots)q^{4}+\cdots$
605.2.g.m	$605$	$2$	605.g	11.c	$5$	$8$	$2$	$4.831$	8.0.13140625.1	$_{}$	None	None					55.2.g.b	$2$	$0$	$3$	$5$	$2$	$4$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{2}q^{2}+(1-\beta _{2}+\beta _{5}+\beta _{7})q^{3}+(1+\cdots)q^{4}+\cdots$
605.2.g.n	$605$	$2$	605.g	11.c	$5$	$8$	$2$	$4.831$	8.0.159390625.1	$_{}$	None	None					55.2.g.a	$2$	$0$	$4$	$1$	$-2$	$3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{1}+\beta _{2}-\beta _{4})q^{2}+\beta _{1}q^{3}+(-2+\cdots)q^{4}+\cdots$
605.2.g.o	$605$	$2$	605.g	11.c	$5$	$12$	$3$	$4.831$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓			605.2.a.g	$4$	$0$	$-1$	$-1$	$3$	$1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{11}q^{2}+\beta _{8}q^{3}+(-\beta _{1}-3\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots$
605.2.g.p	$605$	$2$	605.g	11.c	$5$	$12$	$3$	$4.831$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓			605.2.a.g	$4$	$0$	$1$	$-1$	$3$	$-1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{9}q^{2}-\beta _{1}q^{3}+(-3+\beta _{3}+3\beta _{4}+\cdots)q^{4}+\cdots$
605.2.g.q	$605$	$2$	605.g	11.c	$5$	$24$	$6$	$4.831$		$_{}$	None	None		✓	✓		605.2.a.m	$8$	$0$	$0$	$-6$	$-6$	$0$			$\mathrm{SU}(2)[C_{5}]$
605.2.j.a	$605$	$2$	605.j	55.j	$10$	$8$	$2$	$4.831$	8.0.484000000.6	$_{}$	$\Q(\sqrt{-55}) $	None		✓			605.2.b.b	$8$	$0$	$0$	$0$	$-10$	$0$		$1$	$\mathrm{U}(1)[D_{10}]$	$q+(\beta _{1}-\beta _{4})q^{2}+(1+\beta _{2}-3\beta _{3}+3\beta _{5}+\cdots)q^{4}+\cdots$
605.2.j.b	$605$	$2$	605.j	55.j	$10$	$8$	$2$	$4.831$	8.0.228765625.1	$_{}$	$\Q(\sqrt{-11}) $	None		✓			605.2.b.a	$16$	$0$	$0$	$0$	$-3$	$0$		$1$	$\mathrm{U}(1)[D_{10}]$	$q+(-\beta _{4}-2\beta _{5})q^{3}+(-2+2\beta _{3}+2\beta _{4}+\cdots)q^{4}+\cdots$
605.2.j.c	$605$	$2$	605.j	55.j	$10$	$8$	$2$	$4.831$	8.0.484000000.6	$_{}$	$\Q(\sqrt{-55}) $	None		✓			605.2.b.b	$8$	$0$	$0$	$0$	$10$	$0$		$1$	$\mathrm{U}(1)[D_{10}]$	$q+(\beta _{1}-\beta _{6})q^{2}+(-2\beta _{2}+2\beta _{3}-3\beta _{5}+\cdots)q^{4}+\cdots$
605.2.j.d	$605$	$2$	605.j	55.j	$10$	$16$	$4$	$4.831$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None					55.2.j.a	$4$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(\beta _{1}-\beta _{12}-\beta _{13})q^{2}+(-\beta _{5}-\beta _{13}+\cdots)q^{3}+\cdots$
605.2.j.e	$605$	$2$	605.j	55.j	$10$	$16$	$4$	$4.831$	16.0.$\cdots$.7	$_{}$	None	None		✓			605.2.b.d	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+\beta _{12}q^{2}+\beta _{3}q^{3}-\beta _{10}q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots$
605.2.j.f	$605$	$2$	605.j	55.j	$10$	$16$	$4$	$4.831$	16.0.$\cdots$.7	$_{}$	None	None		✓			605.2.b.d	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+\beta _{12}q^{2}-\beta _{3}q^{3}-\beta _{10}q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots$

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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.