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 141 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
665.1.n.a	$665$	$1$	665.n	665.n	$4$	$2$	$1$	$0.332$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-19}) $	None		✓			665.1.n.a	$4$	$0$	$0$	$0$	$-2$	$-2$		$1$		$q-i q^{4}-q^{5}-q^{7}-i q^{9}-q^{16}+\cdots$
665.1.n.b	$665$	$1$	665.n	665.n	$4$	$2$	$1$	$0.332$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-19}) $	None		✓			665.1.n.a	$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q-i q^{4}+q^{5}+i q^{7}-i q^{9}-q^{16}+\cdots$
665.1.x.a	$665$	$1$	665.x	665.x	$6$	$2$	$1$	$0.332$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-19}) $	None		✓			665.1.x.a	$4$	$0$	$0$	$0$	$-1$	$1$		$1$		$q-\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+\zeta_{6}q^{9}+\cdots$
665.1.x.b	$665$	$1$	665.x	665.x	$6$	$2$	$1$	$0.332$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-19}) $	None		✓			665.1.x.a	$4$	$0$	$0$	$0$	$2$	$-1$		$1$		$q-\zeta_{6}^{2}q^{4}+q^{5}-\zeta_{6}q^{7}+\zeta_{6}q^{9}+\zeta_{6}^{2}q^{11}+\cdots$
665.1.ca.a	$665$	$1$	665.ca	665.ba	$12$	$4$	$1$	$0.332$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-19}) $	None		✓			665.1.ca.a	$4$	$0$	$0$	$0$	$-4$	$2$		$1$		$q-\zeta_{12}^{5}q^{4}-q^{5}-\zeta_{12}^{4}q^{7}-\zeta_{12}q^{9}+\cdots$
665.1.ca.b	$665$	$1$	665.ca	665.ba	$12$	$4$	$1$	$0.332$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-19}) $	None		✓			665.1.ca.a	$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-\zeta_{12}^{5}q^{4}-\zeta_{12}^{2}q^{5}+\zeta_{12}q^{7}-\zeta_{12}q^{9}+\cdots$
665.2.a.a	$665$	$2$	665.a	1.a	$1$	$1$	$1$	$5.310$	$\Q$	$_{}$	None	None	✓	✓			665.2.a.a	$1$	$1$	$-2$	$-1$	$1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-q^{3}+2q^{4}+q^{5}+2q^{6}+q^{7}+\cdots$
665.2.a.b	$665$	$2$	665.a	1.a	$1$	$1$	$1$	$5.310$	$\Q$	$_{}$	None	None	✓	✓			665.2.a.b	$1$	$0$	$-2$	$3$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+3q^{3}+2q^{4}+q^{5}-6q^{6}+\cdots$
665.2.a.c	$665$	$2$	665.a	1.a	$1$	$1$	$1$	$5.310$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	665.2.a.c	$1$	$1$	$-1$	$-1$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}-q^{5}+q^{6}+q^{7}+\cdots$
665.2.a.d	$665$	$2$	665.a	1.a	$1$	$1$	$1$	$5.310$	$\Q$	$_{}$	None	None	✓	✓			665.2.a.d	$1$	$1$	$1$	$-1$	$1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}+q^{5}-q^{6}+q^{7}+\cdots$
665.2.a.e	$665$	$2$	665.a	1.a	$1$	$1$	$1$	$5.310$	$\Q$	$_{}$	None	None	✓	✓			665.2.a.e	$1$	$1$	$1$	$0$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+q^{5}-q^{7}-3q^{8}-3q^{9}+\cdots$
665.2.a.f	$665$	$2$	665.a	1.a	$1$	$2$	$2$	$5.310$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	✓	✓		665.2.a.f	$1$	$1$	$-2$	$-1$	$2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta q^{3}-q^{4}+q^{5}+\beta q^{6}-q^{7}+\cdots$
665.2.a.g	$665$	$2$	665.a	1.a	$1$	$3$	$3$	$5.310$	3.3.148.1	$_{}$	None	None	✓	✓	✓	✓	665.2.a.g	$1$	$0$	$1$	$1$	$3$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots$
665.2.a.h	$665$	$2$	665.a	1.a	$1$	$4$	$4$	$5.310$	4.4.11348.1	$_{}$	None	None	✓	✓	✓	✓	665.2.a.h	$1$	$0$	$1$	$2$	$-4$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{3})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
665.2.a.i	$665$	$2$	665.a	1.a	$1$	$6$	$6$	$5.310$	6.6.79799552.1	$_{}$	None	None	✓	✓	✓	✓	665.2.a.i	$1$	$1$	$-1$	$-4$	$-6$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1-\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots$
665.2.a.j	$665$	$2$	665.a	1.a	$1$	$7$	$7$	$5.310$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	665.2.a.j	$1$	$0$	$3$	$1$	$-7$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{3}q^{3}+(2+\beta _{2})q^{4}-q^{5}+\cdots$
665.2.a.k	$665$	$2$	665.a	1.a	$1$	$8$	$8$	$5.310$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	✓	✓		665.2.a.k	$1$	$0$	$2$	$-3$	$8$	$8$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{2}q^{3}+(1-\beta _{2}+\beta _{3})q^{4}+\cdots$
665.2.b.a	$665$	$2$	665.b	5.b	$2$	$2$	$2$	$5.310$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			665.2.b.a	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 i q^{2}-3 i q^{3}-2 q^{4}+(i+2)q^{5}+\cdots$
665.2.b.b	$665$	$2$	665.b	5.b	$2$	$26$	$26$	$5.310$		$_{}$	None	None		✓			665.2.b.b	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
665.2.b.c	$665$	$2$	665.b	5.b	$2$	$28$	$28$	$5.310$		$_{}$	None	None		✓	✓		665.2.b.c	$2$	$0$	$0$	$0$	$4$	$0$			$\mathrm{SU}(2)[C_{2}]$
665.2.d.a	$665$	$2$	665.d	133.c	$2$	$16$	$16$	$5.310$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓			665.2.d.a	$4$	$0$	$0$	$0$	$0$	$16$		$2^{13}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}-\beta _{5}q^{3}+(-1+\beta _{4})q^{4}-\beta _{10}q^{5}+\cdots$
665.2.d.b	$665$	$2$	665.d	133.c	$2$	$40$	$40$	$5.310$		$_{}$	None	None		✓	✓		665.2.d.b	$4$	$0$	$0$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{2}]$
665.2.g.a	$665$	$2$	665.g	665.g	$2$	$2$	$2$	$5.310$	$\Q(\sqrt{-19}) $	$_{}$	$\Q(\sqrt{-19}) $	None		✓			665.2.g.a	$4$	$0$	$0$	$0$	$-1$	$-3$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{4}-\beta q^{5}+(-2+\beta )q^{7}+3q^{9}+\cdots$
665.2.g.b	$665$	$2$	665.g	665.g	$2$	$2$	$2$	$5.310$	$\Q(\sqrt{-19}) $	$_{}$	$\Q(\sqrt{-19}) $	None		✓			665.2.g.a	$4$	$0$	$0$	$0$	$1$	$3$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{4}+(1-\beta )q^{5}+(2-\beta )q^{7}+3q^{9}+\cdots$
665.2.g.c	$665$	$2$	665.g	665.g	$2$	$72$	$72$	$5.310$		$_{}$	None	None		✓	✓		665.2.g.c	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
665.2.i.a	$665$	$2$	665.i	19.c	$3$	$2$	$1$	$5.310$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			665.2.i.a	$2$	$1$	$-2$	$-2$	$-1$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{3}+\cdots$
665.2.i.b	$665$	$2$	665.i	19.c	$3$	$2$	$1$	$5.310$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			665.2.i.b	$2$	$0$	$2$	$0$	$-1$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}+\cdots$
665.2.i.c	$665$	$2$	665.i	19.c	$3$	$4$	$2$	$5.310$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None		✓			665.2.i.c	$2$	$1$	$-4$	$-2$	$-2$	$-4$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2-2\beta _{1})q^{2}+(-1-\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots$
665.2.i.d	$665$	$2$	665.i	19.c	$3$	$6$	$3$	$5.310$	6.0.954288.1	$_{}$	None	None		✓			665.2.i.d	$2$	$0$	$0$	$-2$	$3$	$6$		$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{2}-\beta _{3})q^{3}+2\beta _{2}q^{4}+(1+\cdots)q^{5}+\cdots$
665.2.i.e	$665$	$2$	665.i	19.c	$3$	$14$	$7$	$5.310$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None		✓			665.2.i.e	$2$	$0$	$1$	$-3$	$7$	$14$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{4}+\beta _{6}+\beta _{8})q^{2}+\beta _{7}q^{3}+(-3+\cdots)q^{4}+\cdots$
665.2.i.f	$665$	$2$	665.i	19.c	$3$	$16$	$8$	$5.310$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			665.2.i.f	$2$	$0$	$1$	$5$	$-8$	$16$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(1+\beta _{7}+\beta _{8}-\beta _{12})q^{3}+\cdots$
665.2.i.g	$665$	$2$	665.i	19.c	$3$	$16$	$8$	$5.310$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			665.2.i.g	$2$	$0$	$3$	$1$	$-8$	$-16$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+\beta _{15}q^{3}+(\beta _{1}-\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots$
665.2.i.h	$665$	$2$	665.i	19.c	$3$	$20$	$10$	$5.310$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		✓	✓		665.2.i.h	$2$	$0$	$3$	$-1$	$10$	$-20$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}-\beta _{2}q^{3}+(\beta _{6}-\beta _{8}-\beta _{12}+\cdots)q^{4}+\cdots$
665.2.j.a	$665$	$2$	665.j	7.c	$3$	$2$	$1$	$5.310$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			665.2.j.a	$2$	$0$	$-2$	$-2$	$1$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-2\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots$
665.2.j.b	$665$	$2$	665.j	7.c	$3$	$2$	$1$	$5.310$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			665.2.j.b	$2$	$0$	$0$	$0$	$1$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{4}+\zeta_{6}q^{5}+(3-\zeta_{6})q^{7}+\cdots$
665.2.j.c	$665$	$2$	665.j	7.c	$3$	$2$	$1$	$5.310$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			665.2.j.c	$2$	$0$	$0$	$2$	$1$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+\zeta_{6}q^{5}+\cdots$
665.2.j.d	$665$	$2$	665.j	7.c	$3$	$2$	$1$	$5.310$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			665.2.j.d	$2$	$0$	$1$	$1$	$-1$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots$
665.2.j.e	$665$	$2$	665.j	7.c	$3$	$2$	$1$	$5.310$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			665.2.j.e	$2$	$0$	$2$	$0$	$-1$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+2\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{4}-\zeta_{6}q^{5}+\cdots$
665.2.j.f	$665$	$2$	665.j	7.c	$3$	$2$	$1$	$5.310$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			665.2.j.f	$2$	$0$	$2$	$0$	$-1$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+2\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{4}-\zeta_{6}q^{5}+\cdots$
665.2.j.g	$665$	$2$	665.j	7.c	$3$	$6$	$3$	$5.310$	6.0.1415907.1	$_{}$	None	None		✓			665.2.j.g	$2$	$0$	$-1$	$-1$	$-3$	$3$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{4})q^{2}-\beta _{4}q^{3}+(-2-\beta _{2}+\cdots)q^{4}+\cdots$
665.2.j.h	$665$	$2$	665.j	7.c	$3$	$16$	$8$	$5.310$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			665.2.j.h	$2$	$0$	$-1$	$-2$	$-8$	$-2$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{4}+\beta _{10})q^{2}+(-\beta _{6}+\beta _{8}+\beta _{9}+\cdots)q^{3}+\cdots$
665.2.j.i	$665$	$2$	665.j	7.c	$3$	$16$	$8$	$5.310$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			665.2.j.i	$2$	$0$	$-1$	$4$	$-8$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}+\beta _{3})q^{2}+(\beta _{1}-\beta _{2}-\beta _{5}-\beta _{11}+\cdots)q^{3}+\cdots$
665.2.j.j	$665$	$2$	665.j	7.c	$3$	$22$	$11$	$5.310$		$_{}$	None	None		✓			665.2.j.j	$2$	$0$	$0$	$5$	$11$	$-11$			$\mathrm{SU}(2)[C_{3}]$
665.2.j.k	$665$	$2$	665.j	7.c	$3$	$24$	$12$	$5.310$		$_{}$	None	None		✓	✓		665.2.j.k	$2$	$0$	$4$	$-7$	$12$	$0$			$\mathrm{SU}(2)[C_{3}]$
665.2.k.a	$665$	$2$	665.k	133.g	$3$	$2$	$1$	$5.310$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			665.2.k.a	$2$	$1$	$-1$	$-6$	$-1$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}-3q^{3}+(1-\zeta_{6})q^{4}-\zeta_{6}q^{5}+\cdots$
665.2.k.b	$665$	$2$	665.k	133.g	$3$	$2$	$1$	$5.310$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			665.2.k.b	$2$	$1$	$-1$	$-2$	$-1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}-q^{3}+(1-\zeta_{6})q^{4}-\zeta_{6}q^{5}+\cdots$
665.2.k.c	$665$	$2$	665.k	133.g	$3$	$2$	$1$	$5.310$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			665.2.k.c	$2$	$0$	$1$	$-2$	$1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}-q^{3}+(1-\zeta_{6})q^{4}+\zeta_{6}q^{5}+\cdots$
665.2.k.d	$665$	$2$	665.k	133.g	$3$	$2$	$1$	$5.310$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			665.2.k.d	$2$	$0$	$1$	$-2$	$1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}-q^{3}+(1-\zeta_{6})q^{4}+\zeta_{6}q^{5}+\cdots$
665.2.k.e	$665$	$2$	665.k	133.g	$3$	$4$	$2$	$5.310$	$\Q(\sqrt{-3}, \sqrt{7})$	$_{}$	None	None		✓			665.2.k.e	$2$	$1$	$0$	$-4$	$-2$	$-8$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}-q^{3}+5\beta _{2}q^{4}+(-1-\beta _{2}+\cdots)q^{5}+\cdots$
665.2.k.f	$665$	$2$	665.k	133.g	$3$	$44$	$22$	$5.310$		$_{}$	None	None		✓			665.2.k.f	$2$	$0$	$0$	$16$	$-22$	$5$			$\mathrm{SU}(2)[C_{3}]$

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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.