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 70 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
1904.1.n.a	$1904$	$1$	1904.n	119.d	$2$	$2$	$2$	$0.950$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-119}) $	None	✓				119.1.d.a	$2$	$0$	$0$	$-1$	$1$	$2$		$1$		$q-\beta q^{3}+(1-\beta )q^{5}+q^{7}+\beta q^{9}+q^{15}+\cdots$
1904.1.n.b	$1904$	$1$	1904.n	119.d	$2$	$2$	$2$	$0.950$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-119}) $	None	✓				119.1.d.a	$2$	$0$	$0$	$1$	$-1$	$-2$		$1$		$q+\beta q^{3}+(-1+\beta )q^{5}-q^{7}+\beta q^{9}+\cdots$
1904.1.bg.a	$1904$	$1$	1904.bg	1904.ag	$4$	$2$	$1$	$0.950$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-119}) $	None		✓			1904.1.bg.a	$4$	$0$	$0$	$-2$	$-2$	$0$		$1$		$q-i q^{2}+(i-1)q^{3}-q^{4}+(-i-1)q^{5}+\cdots$
1904.1.bg.b	$1904$	$1$	1904.bg	1904.ag	$4$	$2$	$1$	$0.950$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-119}) $	None		✓			1904.1.bg.a	$4$	$0$	$0$	$2$	$2$	$0$		$1$		$q-i q^{2}+(-i+1)q^{3}-q^{4}+(i+1)q^{5}+\cdots$
1904.1.bg.c	$1904$	$1$	1904.bg	1904.ag	$4$	$8$	$4$	$0.950$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-119}) $	None		✓			1904.1.bg.c	$4$	$0$	$0$	$-2$	$-2$	$0$		$1$		$q-\zeta_{20}^{9}q^{2}+(-\zeta_{20}+\zeta_{20}^{4})q^{3}-\zeta_{20}^{8}q^{4}+\cdots$
1904.1.bg.d	$1904$	$1$	1904.bg	1904.ag	$4$	$8$	$4$	$0.950$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-119}) $	None		✓			1904.1.bg.c	$4$	$0$	$0$	$2$	$2$	$0$		$1$		$q-\zeta_{20}q^{2}+(\zeta_{20}^{6}+\zeta_{20}^{9})q^{3}+\zeta_{20}^{2}q^{4}+\cdots$
1904.1.bt.a	$1904$	$1$	1904.bt	476.o	$6$	$8$	$4$	$0.950$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-17}) $	None		✓	✓	✓	1904.1.bt.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{24}^{9}+\zeta_{24}^{11})q^{3}+\zeta_{24}^{9}q^{7}+\cdots$
1904.1.dm.a	$1904$	$1$	1904.dm	476.ab	$12$	$8$	$2$	$0.950$	$\Q(\zeta_{24})$	$S_{4}$	None	None		✓	✓	✓	1904.1.dm.a	$8$	$0$	$0$	$0$	$-4$	$0$		$1$		$q-\zeta_{24}^{11}q^{3}+(-\zeta_{24}^{4}+\zeta_{24}^{10})q^{5}+\cdots$
1904.2.a.a	$1904$	$2$	1904.a	1.a	$1$	$1$	$1$	$15.204$	$\Q$	$_{}$	None	None	✓				238.2.a.e	$1$	$1$	$0$	$-2$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots$
1904.2.a.b	$1904$	$2$	1904.a	1.a	$1$	$1$	$1$	$15.204$	$\Q$	$_{}$	None	None	✓				238.2.a.b	$1$	$0$	$0$	$-2$	$4$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+4q^{5}-q^{7}+q^{9}+4q^{11}+\cdots$
1904.2.a.c	$1904$	$2$	1904.a	1.a	$1$	$1$	$1$	$15.204$	$\Q$	$_{}$	None	None	✓				238.2.a.a	$1$	$1$	$0$	$0$	$-2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+q^{7}-3q^{9}+2q^{11}-q^{17}+\cdots$
1904.2.a.d	$1904$	$2$	1904.a	1.a	$1$	$1$	$1$	$15.204$	$\Q$	$_{}$	None	None	✓				238.2.a.d	$1$	$1$	$0$	$0$	$2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-q^{7}-3q^{9}-2q^{13}+q^{17}+\cdots$
1904.2.a.e	$1904$	$2$	1904.a	1.a	$1$	$1$	$1$	$15.204$	$\Q$	$_{}$	None	None	✓				238.2.a.c	$1$	$0$	$0$	$2$	$-4$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-4q^{5}-q^{7}+q^{9}+6q^{11}+\cdots$
1904.2.a.f	$1904$	$2$	1904.a	1.a	$1$	$2$	$2$	$15.204$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				238.2.a.f	$1$	$0$	$0$	$-2$	$2$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}+(1-\beta )q^{5}+q^{7}+(3+\cdots)q^{9}+\cdots$
1904.2.a.g	$1904$	$2$	1904.a	1.a	$1$	$2$	$2$	$15.204$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓				952.2.a.b	$1$	$1$	$0$	$-1$	$-3$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(-1-\beta )q^{5}+q^{7}+\beta q^{9}+\cdots$
1904.2.a.h	$1904$	$2$	1904.a	1.a	$1$	$2$	$2$	$15.204$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓		✓		476.2.a.d	$1$	$1$	$0$	$-1$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(-1+\beta )q^{5}-q^{7}+\beta q^{9}+\cdots$
1904.2.a.i	$1904$	$2$	1904.a	1.a	$1$	$2$	$2$	$15.204$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				952.2.a.a	$1$	$0$	$0$	$1$	$-3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(-1-\beta )q^{5}-q^{7}+(-2+\beta )q^{9}+\cdots$
1904.2.a.j	$1904$	$2$	1904.a	1.a	$1$	$2$	$2$	$15.204$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				476.2.a.b	$1$	$0$	$0$	$1$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(-1+\beta )q^{5}+q^{7}+(-2+\beta )q^{9}+\cdots$
1904.2.a.k	$1904$	$2$	1904.a	1.a	$1$	$2$	$2$	$15.204$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓		✓		476.2.a.c	$1$	$1$	$0$	$1$	$1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(1-\beta )q^{5}+q^{7}+\beta q^{9}-4q^{11}+\cdots$
1904.2.a.l	$1904$	$2$	1904.a	1.a	$1$	$2$	$2$	$15.204$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓				476.2.a.a	$1$	$0$	$0$	$3$	$-3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(-2+\beta )q^{5}-q^{7}+(1+\cdots)q^{9}+\cdots$
1904.2.a.m	$1904$	$2$	1904.a	1.a	$1$	$3$	$3$	$15.204$	3.3.229.1	$_{}$	None	None	✓				952.2.a.f	$1$	$1$	$0$	$-1$	$3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+(1-\beta _{1})q^{5}-q^{7}+(\beta _{1}-2\beta _{2})q^{9}+\cdots$
1904.2.a.n	$1904$	$2$	1904.a	1.a	$1$	$3$	$3$	$15.204$	3.3.1229.1	$_{}$	None	None	✓				952.2.a.e	$1$	$0$	$0$	$1$	$3$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(1+\beta _{2})q^{5}+q^{7}+(2+\beta _{2})q^{9}+\cdots$
1904.2.a.o	$1904$	$2$	1904.a	1.a	$1$	$3$	$3$	$15.204$	3.3.229.1	$_{}$	None	None	✓				952.2.a.c	$1$	$1$	$0$	$3$	$-5$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{3}+(-2-\beta _{2})q^{5}-q^{7}+\cdots$
1904.2.a.p	$1904$	$2$	1904.a	1.a	$1$	$3$	$3$	$15.204$	3.3.229.1	$_{}$	None	None	✓				952.2.a.d	$1$	$0$	$0$	$3$	$1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}-\beta _{2}q^{5}+q^{7}+(1-2\beta _{1}+\cdots)q^{9}+\cdots$
1904.2.a.q	$1904$	$2$	1904.a	1.a	$1$	$4$	$4$	$15.204$	4.4.5225.1	$_{}$	None	None	✓		✓		952.2.a.g	$1$	$1$	$0$	$-3$	$-1$	$4$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(-\beta _{1}-\beta _{3})q^{5}+q^{7}+\cdots$
1904.2.a.r	$1904$	$2$	1904.a	1.a	$1$	$4$	$4$	$15.204$	4.4.13448.1	$_{}$	None	None	✓		✓		952.2.a.h	$1$	$0$	$0$	$-3$	$5$	$-4$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta _{3})q^{3}+(1-\beta _{2})q^{5}-q^{7}+\cdots$
1904.2.a.s	$1904$	$2$	1904.a	1.a	$1$	$4$	$4$	$15.204$	4.4.9301.1	$_{}$	None	None	✓		✓		119.2.a.a	$1$	$0$	$0$	$-2$	$2$	$-4$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{3}-\beta _{2}q^{5}-q^{7}+(2-\beta _{3})q^{9}+\cdots$
1904.2.a.t	$1904$	$2$	1904.a	1.a	$1$	$5$	$5$	$15.204$	5.5.453749.1	$_{}$	None	None	✓		✓		119.2.a.b	$1$	$0$	$0$	$2$	$0$	$5$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+\beta _{3}q^{5}+q^{7}+(2-\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots$
1904.2.c.a	$1904$	$2$	1904.c	17.b	$2$	$2$	$2$	$15.204$	$\Q(\sqrt{-1}) $	$_{}$	None	None					952.2.c.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 i q^{3}-2 i q^{5}-i q^{7}-q^{9}+2 i q^{11}+\cdots$
1904.2.c.b	$1904$	$2$	1904.c	17.b	$2$	$2$	$2$	$15.204$	$\Q(\sqrt{-1}) $	$_{}$	None	None					238.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{7}+3 q^{9}+2 q^{13}+(-4 i+1)q^{17}+\cdots$
1904.2.c.c	$1904$	$2$	1904.c	17.b	$2$	$4$	$4$	$15.204$	$\Q(i, \sqrt{29})$	$_{}$	None	None					952.2.c.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}+\beta _{2}q^{7}+(-5+\cdots)q^{9}+\cdots$
1904.2.c.d	$1904$	$2$	1904.c	17.b	$2$	$4$	$4$	$15.204$	$\Q(i, \sqrt{13})$	$_{}$	None	None					952.2.c.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}-\beta _{2})q^{3}-\beta _{1}q^{5}+\beta _{2}q^{7}+(-4+\cdots)q^{9}+\cdots$
1904.2.c.e	$1904$	$2$	1904.c	17.b	$2$	$6$	$6$	$15.204$	6.0.350464.1	$_{}$	None	None					238.2.b.b	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}+\beta _{4})q^{3}+(-\beta _{1}+\beta _{3}+\beta _{4}-\beta _{5})q^{5}+\cdots$
1904.2.c.f	$1904$	$2$	1904.c	17.b	$2$	$8$	$8$	$15.204$	8.0.980441344.2	$_{}$	None	None					476.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{4}+\beta _{7})q^{3}-\beta _{3}q^{5}+\beta _{4}q^{7}+(-1+\cdots)q^{9}+\cdots$
1904.2.c.g	$1904$	$2$	1904.c	17.b	$2$	$8$	$8$	$15.204$	8.0.6179217664.1	$_{}$	None	None					952.2.c.d	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{5}-\beta _{6})q^{3}+(\beta _{5}+\beta _{7})q^{5}-\beta _{5}q^{7}+\cdots$
1904.2.c.h	$1904$	$2$	1904.c	17.b	$2$	$10$	$10$	$15.204$	10.0.$\cdots$.1	$_{}$	None	None					952.2.c.e	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{9}q^{3}+(-\beta _{4}-\beta _{6}-\beta _{7}+\beta _{8}+\beta _{9})q^{5}+\cdots$
1904.2.c.i	$1904$	$2$	1904.c	17.b	$2$	$10$	$10$	$15.204$	10.0.$\cdots$.1	$_{}$	None	None					119.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{8}q^{3}+(\beta _{5}-\beta _{7})q^{5}-\beta _{7}q^{7}+(-1+\cdots)q^{9}+\cdots$
1904.2.h.a	$1904$	$2$	1904.h	476.e	$2$	$8$	$8$	$15.204$	8.0.$\cdots$.11	$_{}$	$\Q(\sqrt{-17}) $	None		✓			1904.2.h.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(-\beta _{1}+\beta _{4})q^{3}+(-\beta _{1}+\beta _{5})q^{7}+\cdots$
1904.2.h.b	$1904$	$2$	1904.h	476.e	$2$	$16$	$16$	$15.204$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			1904.2.h.b	$8$	$0$	$0$	$0$	$0$	$0$		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}+\beta _{1}q^{5}+(\beta _{4}-\beta _{10})q^{7}+\beta _{2}q^{9}+\cdots$
1904.2.h.c	$1904$	$2$	1904.h	476.e	$2$	$48$	$48$	$15.204$		$_{}$	None	None		✓	✓		1904.2.h.c	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1904.2.j.a	$1904$	$2$	1904.j	28.d	$2$	$8$	$8$	$15.204$	8.0.49787136.1	$_{}$	None	None		✓			1904.2.j.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{3}+(-\beta _{1}+2\beta _{3})q^{5}+(-\beta _{5}+\cdots)q^{7}+\cdots$
1904.2.j.b	$1904$	$2$	1904.j	28.d	$2$	$24$	$24$	$15.204$		$_{}$	None	None		✓			1904.2.j.b	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1904.2.j.c	$1904$	$2$	1904.j	28.d	$2$	$32$	$32$	$15.204$		$_{}$	None	None		✓	✓		1904.2.j.c	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1904.3.g.a	$1904$	$3$	1904.g	4.b	$2$	$32$	$32$	$51.880$		$_{}$	None	None		✓			1904.3.g.a	$2$	$0$	$0$	$0$	$-24$	$0$			$\mathrm{SU}(2)[C_{2}]$
1904.3.g.b	$1904$	$3$	1904.g	4.b	$2$	$64$	$64$	$51.880$		$_{}$	None	None		✓	✓		1904.3.g.b	$2$	$0$	$0$	$0$	$24$	$0$			$\mathrm{SU}(2)[C_{2}]$
1904.4.a.a	$1904$	$4$	1904.a	1.a	$1$	$1$	$1$	$112.340$	$\Q$	$_{}$	None	None	✓				119.4.a.a	$1$	$0$	$0$	$6$	$-20$	$7$	$+$	$1$	$\mathrm{SU}(2)$	$q+6q^{3}-20q^{5}+7q^{7}+9q^{9}-60q^{11}+\cdots$
1904.4.a.b	$1904$	$4$	1904.a	1.a	$1$	$2$	$2$	$112.340$	$\Q(\sqrt{93}) $	$_{}$	None	None	✓				238.4.a.a	$1$	$1$	$0$	$5$	$9$	$14$	$-$	$1$	$\mathrm{SU}(2)$	$q+(3-\beta )q^{3}+(4+\beta )q^{5}+7q^{7}+(5-5\beta )q^{9}+\cdots$
1904.4.a.c	$1904$	$4$	1904.a	1.a	$1$	$2$	$2$	$112.340$	$\Q(\sqrt{69}) $	$_{}$	None	None	✓				238.4.a.b	$1$	$0$	$0$	$11$	$-7$	$-14$	$+$	$1$	$\mathrm{SU}(2)$	$q+(6-\beta )q^{3}+(-3-\beta )q^{5}-7q^{7}+(26+\cdots)q^{9}+\cdots$
1904.4.a.d	$1904$	$4$	1904.a	1.a	$1$	$3$	$3$	$112.340$	3.3.55029.1	$_{}$	None	None	✓				238.4.a.f	$1$	$1$	$0$	$-7$	$19$	$-21$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-2-\beta _{1})q^{3}+(7-\beta _{1}-\beta _{2})q^{5}+\cdots$
1904.4.a.e	$1904$	$4$	1904.a	1.a	$1$	$3$	$3$	$112.340$	3.3.2429.1	$_{}$	None	None	✓				119.4.a.b	$1$	$1$	$0$	$-5$	$-19$	$21$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1}+\beta _{2})q^{3}+(-6+\beta _{2})q^{5}+\cdots$

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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.