LMFDB - Newform search results

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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is twist minimal	Is self-dual

$Nk^2$	Coefficient ring index	Coefficient ring gens.	Projective image	Projective image type

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Results (1-50 of 58 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	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	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1640.1.j.a	$1640$	$1$	1640.j	1640.j	$2$	$1$	$1$	$0.818$	$\Q$	$D_{2}$	$\Q(\sqrt{-10}) $, $\Q(\sqrt{-410}) $	$\Q(\sqrt{41}) $	✓	✓	1640.1.j.a	$4$	$0$	$-1$	$0$	$-1$	$0$		$1$		$q-q^{2}+q^{4}-q^{5}-q^{8}-q^{9}+q^{10}+\cdots$
1640.1.j.b	$1640$	$1$	1640.j	1640.j	$2$	$1$	$1$	$0.818$	$\Q$	$D_{2}$	$\Q(\sqrt{-10}) $, $\Q(\sqrt{-410}) $	$\Q(\sqrt{41}) $	✓	✓	1640.1.j.a	$4$	$0$	$1$	$0$	$1$	$0$		$1$		$q+q^{2}+q^{4}+q^{5}+q^{8}-q^{9}+q^{10}+\cdots$
1640.1.j.c	$1640$	$1$	1640.j	1640.j	$2$	$2$	$2$	$0.818$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-410}) $	None	✓	✓	1640.1.j.c	$4$	$0$	$-2$	$0$	$2$	$0$		$1$		$q-q^{2}-\beta q^{3}+q^{4}+q^{5}+\beta q^{6}-q^{8}+\cdots$
1640.1.j.d	$1640$	$1$	1640.j	1640.j	$2$	$2$	$2$	$0.818$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-410}) $	None	✓	✓	1640.1.j.c	$4$	$0$	$2$	$0$	$-2$	$0$		$1$		$q+q^{2}-\beta q^{3}+q^{4}-q^{5}-\beta q^{6}+q^{8}+\cdots$
1640.1.be.a	$1640$	$1$	1640.be	1640.ae	$4$	$2$	$1$	$0.818$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-10}) $	None		✓	1640.1.be.a	$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q+iq^{2}-q^{4}+iq^{5}+(-1-i)q^{7}+\cdots$
1640.1.be.b	$1640$	$1$	1640.be	1640.ae	$4$	$2$	$1$	$0.818$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-10}) $	None		✓	1640.1.be.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q-iq^{2}-q^{4}-iq^{5}+(1+i)q^{7}+iq^{8}+\cdots$
1640.1.cf.a	$1640$	$1$	1640.cf	1640.bf	$10$	$4$	$1$	$0.818$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-10}) $	None		✓	1640.1.cf.a	$4$	$0$	$-1$	$0$	$-1$	$-2$		$1$		$q-\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}-\zeta_{10}q^{5}+(-\zeta_{10}+\cdots)q^{7}+\cdots$
1640.1.cf.b	$1640$	$1$	1640.cf	1640.bf	$10$	$4$	$1$	$0.818$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-10}) $	None		✓	1640.1.cf.a	$4$	$0$	$1$	$0$	$1$	$2$		$1$		$q+\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}+\zeta_{10}q^{5}+(\zeta_{10}+\cdots)q^{7}+\cdots$
1640.1.ct.a	$1640$	$1$	1640.ct	1640.bt	$10$	$4$	$1$	$0.818$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-10}) $	None		✓	1640.1.ct.a	$4$	$0$	$-1$	$0$	$-1$	$0$		$1$		$q+\zeta_{10}^{2}q^{2}+\zeta_{10}^{4}q^{4}+\zeta_{10}^{4}q^{5}+\cdots$
1640.1.ct.b	$1640$	$1$	1640.ct	1640.bt	$10$	$4$	$1$	$0.818$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-10}) $	None		✓	1640.1.ct.a	$4$	$0$	$1$	$0$	$1$	$0$		$1$		$q-\zeta_{10}^{2}q^{2}+\zeta_{10}^{4}q^{4}-\zeta_{10}^{4}q^{5}+\cdots$
1640.1.dd.a	$1640$	$1$	1640.dd	1640.cd	$20$	$8$	$1$	$0.818$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-10}) $	None		✓	1640.1.dd.a	$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-\zeta_{20}^{3}q^{2}+\zeta_{20}^{6}q^{4}+\zeta_{20}q^{5}+(\zeta_{20}^{3}+\cdots)q^{7}+\cdots$
1640.1.dd.b	$1640$	$1$	1640.dd	1640.cd	$20$	$8$	$1$	$0.818$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-10}) $	None		✓	1640.1.dd.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q+\zeta_{20}^{3}q^{2}+\zeta_{20}^{6}q^{4}-\zeta_{20}q^{5}+(-\zeta_{20}^{3}+\cdots)q^{7}+\cdots$
1640.2.a.a	$1640$	$2$	1640.a	1.a	$1$	$1$	$1$	$13.095$	$\Q$	$_{}$	None	None	✓	✓	1640.2.a.a	$1$	$1$	$0$	$-2$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}-2q^{7}+q^{9}-2q^{15}+\cdots$
1640.2.a.b	$1640$	$2$	1640.a	1.a	$1$	$1$	$1$	$13.095$	$\Q$	$_{}$	None	None	✓	✓	1640.2.a.b	$1$	$1$	$0$	$-2$	$1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}+2q^{7}+q^{9}-2q^{15}+\cdots$
1640.2.a.c	$1640$	$2$	1640.a	1.a	$1$	$1$	$1$	$13.095$	$\Q$	$_{}$	None	None	✓	✓	1640.2.a.c	$1$	$0$	$0$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-3q^{9}+4q^{11}+6q^{13}-2q^{17}+\cdots$
1640.2.a.d	$1640$	$2$	1640.a	1.a	$1$	$1$	$1$	$13.095$	$\Q$	$_{}$	None	None	✓	✓	1640.2.a.d	$1$	$1$	$0$	$0$	$1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+2q^{7}-3q^{9}-2q^{11}-2q^{13}+\cdots$
1640.2.a.e	$1640$	$2$	1640.a	1.a	$1$	$1$	$1$	$13.095$	$\Q$	$_{}$	None	None	✓	✓	1640.2.a.e	$1$	$0$	$0$	$0$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+2q^{7}-3q^{9}+4q^{11}+4q^{13}+\cdots$
1640.2.a.f	$1640$	$2$	1640.a	1.a	$1$	$1$	$1$	$13.095$	$\Q$	$_{}$	None	None	✓	✓	1640.2.a.f	$1$	$0$	$0$	$2$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{5}+2q^{7}+q^{9}-4q^{11}+\cdots$
1640.2.a.g	$1640$	$2$	1640.a	1.a	$1$	$1$	$1$	$13.095$	$\Q$	$_{}$	None	None	✓	✓	1640.2.a.g	$1$	$0$	$0$	$2$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{5}+4q^{7}+q^{9}+6q^{11}+\cdots$
1640.2.a.h	$1640$	$2$	1640.a	1.a	$1$	$2$	$2$	$13.095$	$\Q(\sqrt{69}) $	$_{}$	None	None	✓	✓	1640.2.a.h	$1$	$0$	$0$	$-6$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+q^{5}+(1-\beta )q^{7}+6q^{9}+q^{11}+\cdots$
1640.2.a.i	$1640$	$2$	1640.a	1.a	$1$	$2$	$2$	$13.095$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓	1640.2.a.i	$1$	$1$	$0$	$0$	$2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-2\beta )q^{3}+q^{5}+(-2+3\beta )q^{7}+\cdots$
1640.2.a.j	$1640$	$2$	1640.a	1.a	$1$	$2$	$2$	$13.095$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓	1640.2.a.j	$1$	$0$	$0$	$2$	$2$	$-4$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+q^{5}-2q^{7}+(3+2\beta )q^{9}+\cdots$
1640.2.a.k	$1640$	$2$	1640.a	1.a	$1$	$2$	$2$	$13.095$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	✓	1640.2.a.k	$1$	$1$	$0$	$2$	$2$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+(-1-\beta )q^{7}-2q^{9}-3q^{11}+\cdots$
1640.2.a.l	$1640$	$2$	1640.a	1.a	$1$	$4$	$4$	$13.095$	4.4.2225.1	$_{}$	None	None	✓	✓	1640.2.a.l	$1$	$1$	$0$	$-2$	$-4$	$-1$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{3}-q^{5}-\beta _{1}q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots$
1640.2.a.m	$1640$	$2$	1640.a	1.a	$1$	$5$	$5$	$13.095$	5.5.135076.1	$_{}$	None	None	✓	✓	1640.2.a.m	$1$	$1$	$0$	$0$	$-5$	$-7$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-q^{5}+(-1-\beta _{3})q^{7}+(1-\beta _{2}+\cdots)q^{9}+\cdots$
1640.2.a.n	$1640$	$2$	1640.a	1.a	$1$	$5$	$5$	$13.095$	5.5.746052.1	$_{}$	None	None	✓	✓	1640.2.a.n	$1$	$0$	$0$	$0$	$-5$	$3$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{4}q^{3}-q^{5}+(1+\beta _{2}+\beta _{3})q^{7}+(1+\cdots)q^{9}+\cdots$
1640.2.a.o	$1640$	$2$	1640.a	1.a	$1$	$5$	$5$	$13.095$	5.5.949576.1	$_{}$	None	None	✓	✓	1640.2.a.o	$1$	$0$	$0$	$4$	$5$	$7$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+q^{5}+(1-\beta _{3})q^{7}+(2+\cdots)q^{9}+\cdots$
1640.2.a.p	$1640$	$2$	1640.a	1.a	$1$	$6$	$6$	$13.095$	6.6.38532512.1	$_{}$	None	None	✓	✓	1640.2.a.p	$1$	$0$	$0$	$4$	$-6$	$3$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}-q^{5}+(1-\beta _{5})q^{7}+(2+\cdots)q^{9}+\cdots$
1640.2.b.a	$1640$	$2$	1640.b	41.b	$2$	$2$	$2$	$13.095$	$\Q(\sqrt{-2}) $	$_{}$	None	None		✓	1640.2.b.a	$2$	$0$	$0$	$0$	$-2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{5}+\beta q^{7}+3q^{9}+\beta q^{11}+\beta q^{17}+\cdots$
1640.2.b.b	$1640$	$2$	1640.b	41.b	$2$	$2$	$2$	$13.095$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓	1640.2.b.b	$2$	$0$	$0$	$0$	$2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+q^{5}+iq^{7}-q^{9}-iq^{11}+\cdots$
1640.2.b.c	$1640$	$2$	1640.b	41.b	$2$	$8$	$8$	$13.095$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None		✓	1640.2.b.c	$2$	$0$	$0$	$0$	$8$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+q^{5}+(-\beta _{1}-\beta _{6})q^{7}+(-1+\cdots)q^{9}+\cdots$
1640.2.b.d	$1640$	$2$	1640.b	41.b	$2$	$10$	$10$	$13.095$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None		✓	1640.2.b.d	$2$	$0$	$0$	$0$	$-10$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{3}-q^{5}+\beta _{9}q^{7}+(-3+\beta _{3}+\cdots)q^{9}+\cdots$
1640.2.b.e	$1640$	$2$	1640.b	41.b	$2$	$10$	$10$	$13.095$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None		✓	1640.2.b.e	$2$	$0$	$0$	$0$	$-10$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-q^{5}+\beta _{4}q^{7}+(-1+\beta _{9})q^{9}+\cdots$
1640.2.b.f	$1640$	$2$	1640.b	41.b	$2$	$10$	$10$	$13.095$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None		✓	1640.2.b.f	$2$	$0$	$0$	$0$	$10$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+q^{5}+\beta _{6}q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots$
1640.2.d.a	$1640$	$2$	1640.d	5.b	$2$	$2$	$2$	$13.095$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓	1640.2.d.a	$2$	$0$	$0$	$0$	$-2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-i)q^{5}-2iq^{7}+3q^{9}-4q^{11}+\cdots$
1640.2.d.b	$1640$	$2$	1640.d	5.b	$2$	$26$	$26$	$13.095$		$_{}$	None	None		✓	1640.2.d.b	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1640.2.d.c	$1640$	$2$	1640.d	5.b	$2$	$32$	$32$	$13.095$		$_{}$	None	None		✓	1640.2.d.c	$2$	$0$	$0$	$0$	$2$	$0$			$\mathrm{SU}(2)[C_{2}]$
1640.2.o.a	$1640$	$2$	1640.o	205.c	$2$	$4$	$4$	$13.095$	$\Q(\zeta_{8})$	$_{}$	None	None		✓	1640.2.o.a	$4$	$0$	$0$	$0$	$4$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\zeta_{8})q^{5}-3q^{9}+\zeta_{8}^{3}q^{11}+\zeta_{8}^{2}q^{13}+\cdots$
1640.2.o.b	$1640$	$2$	1640.o	205.c	$2$	$60$	$60$	$13.095$		$_{}$	None	None		✓	1640.2.o.b	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1640.2.bb.a	$1640$	$2$	1640.bb	41.c	$4$	$2$	$1$	$13.095$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓	1640.2.bb.a	$2$	$1$	$0$	$0$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-iq^{5}+(-3+3i)q^{7}+3iq^{9}+(-2+\cdots)q^{11}+\cdots$
1640.2.bb.b	$1640$	$2$	1640.bb	41.c	$4$	$2$	$1$	$13.095$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓	1640.2.bb.b	$2$	$0$	$0$	$0$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+iq^{5}+(-1+i)q^{7}+3iq^{9}+(1-i)q^{11}+\cdots$
1640.2.bb.c	$1640$	$2$	1640.bb	41.c	$4$	$2$	$1$	$13.095$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓	1640.2.bb.c	$2$	$0$	$0$	$2$	$0$	$6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1-i)q^{3}+iq^{5}+(3-3i)q^{7}+iq^{9}+\cdots$
1640.2.bb.d	$1640$	$2$	1640.bb	41.c	$4$	$4$	$2$	$13.095$	$\Q(\zeta_{8})$	$_{}$	None	None		✓	1640.2.bb.d	$2$	$0$	$0$	$0$	$0$	$-4$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}q^{3}-\zeta_{8}^{2}q^{5}+(-1-\zeta_{8}^{2})q^{7}+\cdots$
1640.2.bb.e	$1640$	$2$	1640.bb	41.c	$4$	$4$	$2$	$13.095$	$\Q(i, \sqrt{10})$	$_{}$	None	None		✓	1640.2.bb.e	$2$	$0$	$0$	$0$	$0$	$8$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{2}q^{5}+(2+2\beta _{2})q^{7}-3\beta _{2}q^{9}+(-2+\cdots)q^{11}+\cdots$
1640.2.bb.f	$1640$	$2$	1640.bb	41.c	$4$	$4$	$2$	$13.095$	$\Q(\zeta_{8})$	$_{}$	None	None		✓	1640.2.bb.f	$2$	$0$	$0$	$0$	$0$	$8$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}q^{3}-\zeta_{8}^{2}q^{5}+(2+\zeta_{8}+2\zeta_{8}^{2}+\cdots)q^{7}+\cdots$
1640.2.bb.g	$1640$	$2$	1640.bb	41.c	$4$	$12$	$6$	$13.095$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓	1640.2.bb.g	$2$	$0$	$0$	$0$	$0$	$-4$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{6}q^{3}+\beta _{3}q^{5}+\beta _{10}q^{7}+(\beta _{1}+3\beta _{3}+\cdots)q^{9}+\cdots$
1640.2.bb.h	$1640$	$2$	1640.bb	41.c	$4$	$12$	$6$	$13.095$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓	1640.2.bb.h	$2$	$0$	$0$	$2$	$0$	$4$		$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{4}q^{3}+\beta _{5}q^{5}+\beta _{11}q^{7}+(-2\beta _{5}+\cdots)q^{9}+\cdots$
1640.2.bb.i	$1640$	$2$	1640.bb	41.c	$4$	$20$	$10$	$13.095$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		✓	1640.2.bb.i	$2$	$0$	$0$	$-2$	$0$	$-10$		$2^{8}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{1}q^{3}+\beta _{4}q^{5}-\beta _{12}q^{7}+(-\beta _{4}+\cdots)q^{9}+\cdots$
1640.2.bb.j	$1640$	$2$	1640.bb	41.c	$4$	$22$	$11$	$13.095$		$_{}$	None	None		✓	1640.2.bb.j	$2$	$0$	$0$	$2$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
1640.4.a.a	$1640$	$4$	1640.a	1.a	$1$	$1$	$1$	$96.763$	$\Q$	$_{}$	None	None	✓	✓	1640.4.a.a	$1$	$1$	$0$	$-2$	$5$	$14$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+5q^{5}+14q^{7}-23q^{9}-44q^{13}+\cdots$

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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.