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	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
361.2.a.a	$361$	$2$	361.a	1.a	$1$	$1$	$1$	$2.883$	$\Q$	$\Q(\sqrt{-19}) $	✓	✓			361.2.a.a	$2$	$1$	$0$	$0$	$-1$	$3$	$+$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}-q^{5}+3q^{7}-3q^{9}-5q^{11}+\cdots$
361.2.a.b	$361$	$2$	361.a	1.a	$1$	$1$	$1$	$2.883$	$\Q$	None	✓				19.2.a.a	$1$	$0$	$0$	$2$	$3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{4}+3q^{5}-q^{7}+q^{9}+3q^{11}+\cdots$
361.2.a.c	$361$	$2$	361.a	1.a	$1$	$2$	$2$	$2.883$	$\Q(\sqrt{5}) $	None	✓	✓			361.2.a.c	$1$	$0$	$-1$	$-3$	$2$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-2+\beta )q^{3}+(-1+\beta )q^{4}+\cdots$
361.2.a.d	$361$	$2$	361.a	1.a	$1$	$2$	$2$	$2.883$	$\Q(\sqrt{5}) $	None	✓	✓			361.2.a.d	$1$	$0$	$0$	$-4$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-2\beta )q^{2}-2q^{3}+3q^{4}+(1-\beta )q^{5}+\cdots$
361.2.a.e	$361$	$2$	361.a	1.a	$1$	$2$	$2$	$2.883$	$\Q(\sqrt{5}) $	None	✓	✓			361.2.a.d	$1$	$0$	$0$	$4$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-2\beta )q^{2}+2q^{3}+3q^{4}+\beta q^{5}+\cdots$
361.2.a.f	$361$	$2$	361.a	1.a	$1$	$2$	$2$	$2.883$	$\Q(\sqrt{5}) $	None	✓	✓			361.2.a.c	$1$	$0$	$1$	$3$	$2$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(2-\beta )q^{3}+(-1+\beta )q^{4}+2\beta q^{5}+\cdots$
361.2.a.g	$361$	$2$	361.a	1.a	$1$	$3$	$3$	$2.883$	$\Q(\zeta_{18})^+$	None	✓				19.2.e.a	$1$	$1$	$-3$	$-3$	$-3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(-1+\beta _{2})q^{3}+(1+\cdots)q^{4}+\cdots$
361.2.a.h	$361$	$2$	361.a	1.a	$1$	$3$	$3$	$2.883$	$\Q(\zeta_{18})^+$	None	✓		✓		19.2.e.a	$1$	$0$	$3$	$3$	$-3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1-\beta _{2})q^{3}+(1-2\beta _{1}+\cdots)q^{4}+\cdots$
361.2.a.i	$361$	$2$	361.a	1.a	$1$	$4$	$4$	$2.883$	$\Q(\zeta_{20})^+$	None	✓	✓	✓		361.2.a.i	$2$	$1$	$0$	$0$	$-4$	$-8$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{1}q^{3}+(1+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots$
361.2.c.a	$361$	$2$	361.c	19.c	$3$	$2$	$1$	$2.883$	$\Q(\sqrt{-3}) $	None					19.2.a.a	$2$	$0$	$0$	$-2$	$-3$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{3}+2\zeta_{6}q^{4}+(-3+3\zeta_{6})q^{5}+\cdots$
361.2.c.b	$361$	$2$	361.c	19.c	$3$	$2$	$1$	$2.883$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-19}) $		✓			361.2.a.a	$4$	$0$	$0$	$0$	$1$	$6$		$1$	$\mathrm{U}(1)[D_{3}]$	$q+2\zeta_{6}q^{4}+(1-\zeta_{6})q^{5}+3q^{7}+3\zeta_{6}q^{9}+\cdots$
361.2.c.c	$361$	$2$	361.c	19.c	$3$	$2$	$1$	$2.883$	$\Q(\sqrt{-3}) $	None					19.2.a.a	$2$	$0$	$0$	$2$	$-3$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{3}+2\zeta_{6}q^{4}+(-3+3\zeta_{6})q^{5}+\cdots$
361.2.c.d	$361$	$2$	361.c	19.c	$3$	$4$	$2$	$2.883$	$\Q(\sqrt{-3}, \sqrt{5})$	None		✓			361.2.a.c	$2$	$0$	$-1$	$-3$	$-2$	$12$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(-2+\beta _{1}-2\beta _{3})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots$
361.2.c.e	$361$	$2$	361.c	19.c	$3$	$4$	$2$	$2.883$	$\Q(\sqrt{-3}, \sqrt{5})$	None		✓			361.2.a.d	$2$	$0$	$0$	$-4$	$-1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-2\beta _{1}+\beta _{3})q^{2}+(-2-2\beta _{3})q^{3}+\cdots$
361.2.c.f	$361$	$2$	361.c	19.c	$3$	$4$	$2$	$2.883$	$\Q(\sqrt{-3}, \sqrt{5})$	None		✓			361.2.a.d	$2$	$0$	$0$	$4$	$-1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-2\beta _{1}+\beta _{3})q^{2}+(2+2\beta _{3})q^{3}+\cdots$
361.2.c.g	$361$	$2$	361.c	19.c	$3$	$4$	$2$	$2.883$	$\Q(\sqrt{-3}, \sqrt{5})$	None		✓			361.2.a.c	$2$	$0$	$1$	$3$	$-2$	$12$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(2-\beta _{1}+2\beta _{3})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
361.2.c.h	$361$	$2$	361.c	19.c	$3$	$6$	$3$	$2.883$	$\Q(\zeta_{18})$	None					19.2.e.a	$2$	$0$	$-3$	$-3$	$3$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta_{5}+\beta_1-1)q^{2}+(\beta_{3}-\beta_{2}+\beta_1-1)q^{3}+\cdots$
361.2.c.i	$361$	$2$	361.c	19.c	$3$	$6$	$3$	$2.883$	$\Q(\zeta_{18})$	None					19.2.e.a	$2$	$0$	$3$	$3$	$3$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta_{5}-\beta_{4}-\beta_{3}+\beta_1)q^{2}+(-\beta_{2}+\beta_1)q^{3}+\cdots$
361.2.c.j	$361$	$2$	361.c	19.c	$3$	$8$	$4$	$2.883$	8.0.324000000.2	None		✓	✓		361.2.a.i	$4$	$0$	$0$	$0$	$4$	$-16$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{3}q^{2}-\beta _{3}q^{3}+(\beta _{2}+\beta _{4}+\beta _{6})q^{4}+\cdots$
361.2.e.a	$361$	$2$	361.e	19.e	$9$	$6$	$1$	$2.883$	$\Q(\zeta_{18})$	None					19.2.e.a	$2$	$0$	$-3$	$-6$	$3$	$0$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(\zeta_{18}+\zeta_{18}^{2}-\zeta_{18}^{3}-\zeta_{18}^{4})q^{2}+\cdots$
361.2.e.b	$361$	$2$	361.e	19.e	$9$	$6$	$1$	$2.883$	$\Q(\zeta_{18})$	None					19.2.e.a	$2$	$0$	$-3$	$3$	$3$	$0$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(-1+\zeta_{18}-\zeta_{18}^{2}+\zeta_{18}^{3}-\zeta_{18}^{4}+\cdots)q^{2}+\cdots$
361.2.e.c	$361$	$2$	361.e	19.e	$9$	$6$	$1$	$2.883$	$\Q(\zeta_{18})$	$\Q(\sqrt{-19}) $		✓			361.2.a.a	$12$	$0$	$0$	$0$	$0$	$-9$		$1$	$\mathrm{U}(1)[D_{9}]$	$q+2\zeta_{18}^{5}q^{4}-\zeta_{18}^{4}q^{5}+(-3+3\zeta_{18}^{3}+\cdots)q^{7}+\cdots$
361.2.e.d	$361$	$2$	361.e	19.e	$9$	$6$	$1$	$2.883$	$\Q(\zeta_{18})$	None					19.2.a.a	$6$	$0$	$0$	$0$	$0$	$3$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+2\zeta_{18}q^{3}+2\zeta_{18}^{5}q^{4}+3\zeta_{18}^{4}q^{5}+\cdots$
361.2.e.e	$361$	$2$	361.e	19.e	$9$	$6$	$1$	$2.883$	$\Q(\zeta_{18})$	None					19.2.a.a	$6$	$0$	$0$	$0$	$0$	$3$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q-2\zeta_{18}q^{3}+2\zeta_{18}^{5}q^{4}+3\zeta_{18}^{4}q^{5}+\cdots$
361.2.e.f	$361$	$2$	361.e	19.e	$9$	$6$	$1$	$2.883$	$\Q(\zeta_{18})$	None					19.2.e.a	$2$	$0$	$3$	$-3$	$3$	$0$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(1-\zeta_{18}+\zeta_{18}^{2}-\zeta_{18}^{3}+\zeta_{18}^{4}+\cdots)q^{2}+\cdots$
361.2.e.g	$361$	$2$	361.e	19.e	$9$	$6$	$1$	$2.883$	$\Q(\zeta_{18})$	None					19.2.e.a	$2$	$0$	$3$	$6$	$3$	$0$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(-\zeta_{18}-\zeta_{18}^{2}+\zeta_{18}^{3}+\zeta_{18}^{4}+\cdots)q^{2}+\cdots$
361.2.e.h	$361$	$2$	361.e	19.e	$9$	$6$	$1$	$2.883$	$\Q(\zeta_{18})$	None					19.2.e.a	$2$	$0$	$6$	$3$	$-6$	$0$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(1+\zeta_{18}-\zeta_{18}^{4}-\zeta_{18}^{5})q^{2}+(1+\cdots)q^{3}+\cdots$
361.2.e.i	$361$	$2$	361.e	19.e	$9$	$12$	$2$	$2.883$	12.0.$\cdots$.1	None		✓			361.2.a.c	$6$	$0$	$0$	$0$	$0$	$-18$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q-\beta _{7}q^{2}+(-\beta _{1}-2\beta _{3})q^{3}+(\beta _{5}+\beta _{10}+\cdots)q^{4}+\cdots$
361.2.e.j	$361$	$2$	361.e	19.e	$9$	$12$	$2$	$2.883$	12.0.$\cdots$.1	None		✓			361.2.a.c	$6$	$0$	$0$	$0$	$0$	$-18$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q-\beta _{1}q^{2}+(-\beta _{1}+\beta _{7}-2\beta _{9})q^{3}+(\beta _{4}+\cdots)q^{4}+\cdots$
361.2.e.k	$361$	$2$	361.e	19.e	$9$	$12$	$2$	$2.883$	12.0.$\cdots$.1	None		✓			361.2.a.d	$6$	$0$	$0$	$0$	$0$	$6$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(-\beta _{5}-2\beta _{10}+\beta _{11})q^{2}+2\beta _{5}q^{3}+\cdots$
361.2.e.l	$361$	$2$	361.e	19.e	$9$	$12$	$2$	$2.883$	12.0.$\cdots$.1	None		✓			361.2.a.d	$6$	$0$	$0$	$0$	$0$	$6$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(-\beta _{5}-2\beta _{10}+\beta _{11})q^{2}-2\beta _{5}q^{3}+\cdots$
361.2.e.m	$361$	$2$	361.e	19.e	$9$	$24$	$4$	$2.883$		None		✓	✓		361.2.a.i	$12$	$0$	$0$	$0$	$0$	$24$			$\mathrm{SU}(2)[C_{9}]$
361.2.g.a	$361$	$2$	361.g	361.g	$19$	$540$	$30$	$2.883$		None		✓	✓	✓	361.2.g.a	$2$	$0$	$-16$	$-32$	$-17$	$-11$			$\mathrm{SU}(2)[C_{19}]$
361.2.i.a	$361$	$2$	361.i	361.i	$57$	$1080$	$30$	$2.883$		None		✓	✓	✓	361.2.i.a	$2$	$0$	$-38$	$-19$	$-37$	$-40$			$\mathrm{SU}(2)[C_{57}]$
361.2.k.a	$361$	$2$	361.k	361.k	$171$	$3348$	$31$	$2.883$		None		✓	✓	✓	361.2.k.a	$2$	$0$	$-108$	$-111$	$-108$	$-111$			$\mathrm{SU}(2)[C_{171}]$
361.3.b.a	$361$	$3$	361.b	19.b	$2$	$6$	$6$	$9.837$	6.0.42172928.2	None		✓			361.3.b.a	$2$	$0$	$0$	$0$	$-14$	$22$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}-\beta _{2})q^{2}+\beta _{4}q^{3}+(-2-\beta _{3}+\cdots)q^{4}+\cdots$
361.3.b.b	$361$	$3$	361.b	19.b	$2$	$6$	$6$	$9.837$	6.0.6967728.1	None					19.3.d.a	$2$	$0$	$0$	$0$	$4$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{2}+(-\beta _{3}-\beta _{5})q^{3}+(-1+2\beta _{1}+\cdots)q^{4}+\cdots$
361.3.b.c	$361$	$3$	361.b	19.b	$2$	$12$	$12$	$9.837$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None					19.3.f.a	$2$	$0$	$0$	$0$	$6$	$-12$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-\beta _{6}-\beta _{8})q^{3}+(\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots$
361.3.b.d	$361$	$3$	361.b	19.b	$2$	$24$	$24$	$9.837$		None		✓	✓		361.3.b.d	$2$	$0$	$0$	$0$	$4$	$8$			$\mathrm{SU}(2)[C_{2}]$
361.3.d.a	$361$	$3$	361.d	19.d	$6$	$2$	$1$	$9.837$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-19}) $					19.3.b.a	$4$	$0$	$0$	$0$	$9$	$-10$		$1$	$\mathrm{U}(1)[D_{6}]$	$q-4\zeta_{6}q^{4}+(9-9\zeta_{6})q^{5}-5q^{7}-9\zeta_{6}q^{9}+\cdots$
361.3.d.b	$361$	$3$	361.d	19.d	$6$	$4$	$2$	$9.837$	$\Q(\sqrt{-3}, \sqrt{-13})$	None					19.3.b.b	$4$	$0$	$0$	$0$	$-8$	$-20$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}-\beta _{1}q^{3}+9\beta _{2}q^{4}+(-4+4\beta _{2}+\cdots)q^{5}+\cdots$
361.3.d.c	$361$	$3$	361.d	19.d	$6$	$6$	$3$	$9.837$	6.0.6967728.1	None					19.3.d.a	$2$	$0$	$3$	$9$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1+\beta _{5})q^{2}+(-\beta _{1}-2\beta _{2}-\beta _{3}-\beta _{5})q^{3}+\cdots$
361.3.d.d	$361$	$3$	361.d	19.d	$6$	$12$	$6$	$9.837$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None					19.3.f.a	$2$	$0$	$0$	$-9$	$-3$	$-12$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{1}+\beta _{4}+\beta _{5}+\beta _{7})q^{2}+(-1+\cdots)q^{3}+\cdots$
361.3.d.e	$361$	$3$	361.d	19.d	$6$	$12$	$6$	$9.837$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓			361.3.b.a	$4$	$0$	$0$	$0$	$14$	$44$		$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{4}+\beta _{6})q^{2}+(\beta _{9}+\beta _{11})q^{3}+(2+\cdots)q^{4}+\cdots$
361.3.d.f	$361$	$3$	361.d	19.d	$6$	$12$	$6$	$9.837$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None					19.3.f.a	$2$	$0$	$0$	$9$	$-3$	$-12$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{1}-\beta _{4}+\beta _{6}+\beta _{8})q^{2}+(\beta _{1}-\beta _{3}+\cdots)q^{3}+\cdots$
361.3.d.g	$361$	$3$	361.d	19.d	$6$	$48$	$24$	$9.837$		None		✓	✓		361.3.b.d	$4$	$0$	$0$	$0$	$-4$	$16$			$\mathrm{SU}(2)[C_{6}]$
361.3.f.a	$361$	$3$	361.f	19.f	$18$	$6$	$1$	$9.837$	$\Q(\zeta_{18})$	$\Q(\sqrt{-19}) $					19.3.b.a	$12$	$0$	$0$	$0$	$0$	$15$		$1$	$\mathrm{U}(1)[D_{18}]$	$q-4\zeta_{18}q^{4}+(9\zeta_{18}^{2}-9\zeta_{18}^{5})q^{5}+\cdots$
361.3.f.b	$361$	$3$	361.f	19.f	$18$	$12$	$2$	$9.837$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None					19.3.f.a	$2$	$0$	$-3$	$-9$	$3$	$6$		$1$	$\mathrm{SU}(2)[C_{18}]$	$q+(-\beta _{1}-\beta _{2})q^{2}+(\beta _{1}+\beta _{3}+\beta _{6}-\beta _{7}+\cdots)q^{3}+\cdots$
361.3.f.c	$361$	$3$	361.f	19.f	$18$	$12$	$2$	$9.837$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None					19.3.f.a	$2$	$0$	$-3$	$9$	$3$	$6$		$1$	$\mathrm{SU}(2)[C_{18}]$	$q+(1+\beta _{3}-\beta _{9}+\beta _{11})q^{2}+(1+\beta _{1}+\cdots)q^{3}+\cdots$
361.3.f.d	$361$	$3$	361.f	19.f	$18$	$12$	$2$	$9.837$	12.0.$\cdots$.1	None					19.3.b.b	$12$	$0$	$0$	$0$	$0$	$30$		$1$	$\mathrm{SU}(2)[C_{18}]$	$q+\beta _{1}q^{2}+(\beta _{1}-\beta _{7})q^{3}+9\beta _{2}q^{4}+(-4\beta _{4}+\cdots)q^{5}+\cdots$

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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.