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 92 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
1360.1.d.a	$1360$	$1$	1360.d	340.d	$2$	$1$	$1$	$0.679$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-85}) $	$\Q(\sqrt{85}) $	✓	✓			1360.1.d.a	$4$	$0$	$0$	$0$	$-1$	$0$		$1$		$q-q^{5}+q^{9}+q^{17}+q^{25}+2q^{37}+\cdots$
1360.1.d.b	$1360$	$1$	1360.d	340.d	$2$	$1$	$1$	$0.679$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-85}) $	$\Q(\sqrt{85}) $	✓	✓			1360.1.d.a	$4$	$0$	$0$	$0$	$1$	$0$		$1$		$q+q^{5}+q^{9}-q^{17}+q^{25}-2q^{37}+\cdots$
1360.1.br.a	$1360$	$1$	1360.br	340.n	$4$	$2$	$1$	$0.679$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		✓			1360.1.br.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+i q^{5}-i q^{9}+2 i q^{13}+q^{17}-q^{25}+\cdots$
1360.1.br.b	$1360$	$1$	1360.br	340.n	$4$	$2$	$1$	$0.679$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		✓			1360.1.br.a	$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q+q^{5}-i q^{9}-2 i q^{13}-q^{17}+q^{25}+\cdots$
1360.1.ec.a	$1360$	$1$	1360.ec	340.ac	$16$	$8$	$1$	$0.679$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	1360.1.ec.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{16}^{3}q^{5}-\zeta_{16}q^{9}+(-\zeta_{16}-\zeta_{16}^{7}+\cdots)q^{13}+\cdots$
1360.1.fc.a	$1360$	$1$	1360.fc	340.aj	$16$	$8$	$1$	$0.679$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	1360.1.ec.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{16}^{2}q^{5}-\zeta_{16}^{7}q^{9}+(-\zeta_{16}^{3}+\zeta_{16}^{5}+\cdots)q^{13}+\cdots$
1360.2.a.a	$1360$	$2$	1360.a	1.a	$1$	$1$	$1$	$10.860$	$\Q$	$_{}$	None	None	✓				170.2.a.d	$1$	$1$	$0$	$-3$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-q^{5}-2q^{7}+6q^{9}+4q^{11}+\cdots$
1360.2.a.b	$1360$	$2$	1360.a	1.a	$1$	$1$	$1$	$10.860$	$\Q$	$_{}$	None	None	✓				85.2.a.a	$1$	$1$	$0$	$-2$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{5}+2q^{7}+q^{9}-2q^{11}+\cdots$
1360.2.a.c	$1360$	$2$	1360.a	1.a	$1$	$1$	$1$	$10.860$	$\Q$	$_{}$	None	None	✓				680.2.a.c	$1$	$1$	$0$	$-2$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}-2q^{7}+q^{9}+2q^{11}+\cdots$
1360.2.a.d	$1360$	$2$	1360.a	1.a	$1$	$1$	$1$	$10.860$	$\Q$	$_{}$	None	None	✓				170.2.a.e	$1$	$0$	$0$	$-1$	$-1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-2q^{7}-2q^{9}-q^{13}+q^{15}+\cdots$
1360.2.a.e	$1360$	$2$	1360.a	1.a	$1$	$1$	$1$	$10.860$	$\Q$	$_{}$	None	None	✓				170.2.a.c	$1$	$1$	$0$	$-1$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-2q^{7}-2q^{9}+5q^{13}+\cdots$
1360.2.a.f	$1360$	$2$	1360.a	1.a	$1$	$1$	$1$	$10.860$	$\Q$	$_{}$	None	None	✓				680.2.a.b	$1$	$0$	$0$	$0$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-3q^{9}-2q^{13}+q^{17}+4q^{19}+\cdots$
1360.2.a.g	$1360$	$2$	1360.a	1.a	$1$	$1$	$1$	$10.860$	$\Q$	$_{}$	None	None	✓				340.2.a.a	$1$	$1$	$0$	$0$	$-1$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+4q^{7}-3q^{9}-2q^{11}-6q^{13}+\cdots$
1360.2.a.h	$1360$	$2$	1360.a	1.a	$1$	$1$	$1$	$10.860$	$\Q$	$_{}$	None	None	✓				680.2.a.a	$1$	$1$	$0$	$1$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-2q^{7}-2q^{9}-4q^{11}+\cdots$
1360.2.a.i	$1360$	$2$	1360.a	1.a	$1$	$1$	$1$	$10.860$	$\Q$	$_{}$	None	None	✓				170.2.a.a	$1$	$1$	$0$	$2$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-q^{5}-2q^{7}+q^{9}-6q^{11}+\cdots$
1360.2.a.j	$1360$	$2$	1360.a	1.a	$1$	$1$	$1$	$10.860$	$\Q$	$_{}$	None	None	✓				170.2.a.b	$1$	$0$	$0$	$2$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{5}+2q^{7}+q^{9}+2q^{11}+\cdots$
1360.2.a.k	$1360$	$2$	1360.a	1.a	$1$	$2$	$2$	$10.860$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓		✓		85.2.a.c	$1$	$1$	$0$	$-2$	$2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+q^{5}+(1-\beta )q^{7}+(1+\cdots)q^{9}+\cdots$
1360.2.a.l	$1360$	$2$	1360.a	1.a	$1$	$2$	$2$	$10.860$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				680.2.a.e	$1$	$1$	$0$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-q^{5}-\beta q^{7}-q^{9}+(2-3\beta )q^{11}+\cdots$
1360.2.a.m	$1360$	$2$	1360.a	1.a	$1$	$2$	$2$	$10.860$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓				170.2.a.f	$1$	$0$	$0$	$1$	$2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+q^{5}-2\beta q^{7}+(1+\beta )q^{9}+4q^{11}+\cdots$
1360.2.a.n	$1360$	$2$	1360.a	1.a	$1$	$2$	$2$	$10.860$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				680.2.a.d	$1$	$0$	$0$	$2$	$2$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+q^{5}+(3-\beta )q^{7}+(1+2\beta )q^{9}+\cdots$
1360.2.a.o	$1360$	$2$	1360.a	1.a	$1$	$2$	$2$	$10.860$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓		✓		85.2.a.b	$1$	$0$	$0$	$4$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(2+\beta )q^{3}-q^{5}+(2-\beta )q^{7}+(3+4\beta )q^{9}+\cdots$
1360.2.a.p	$1360$	$2$	1360.a	1.a	$1$	$3$	$3$	$10.860$	3.3.940.1	$_{}$	None	None	✓		✓		680.2.a.h	$1$	$0$	$0$	$-3$	$3$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+q^{5}+(-1+\beta _{2})q^{7}+\cdots$
1360.2.a.q	$1360$	$2$	1360.a	1.a	$1$	$3$	$3$	$10.860$	3.3.1016.1	$_{}$	None	None	✓		✓		680.2.a.g	$1$	$1$	$0$	$-1$	$-3$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-q^{5}+(-2-\beta _{2})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots$
1360.2.a.r	$1360$	$2$	1360.a	1.a	$1$	$3$	$3$	$10.860$	3.3.229.1	$_{}$	None	None	✓		✓		680.2.a.f	$1$	$0$	$0$	$-1$	$-3$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}-q^{5}+(-\beta _{1}+\beta _{2})q^{7}+(1+\cdots)q^{9}+\cdots$
1360.2.a.s	$1360$	$2$	1360.a	1.a	$1$	$3$	$3$	$10.860$	3.3.404.1	$_{}$	None	None	✓		✓		340.2.a.b	$1$	$0$	$0$	$0$	$3$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+q^{5}+\beta _{2}q^{7}+(2-\beta _{1}+\beta _{2})q^{9}+\cdots$
1360.2.c.a	$1360$	$2$	1360.c	17.b	$2$	$2$	$2$	$10.860$	$\Q(\sqrt{-1}) $	$_{}$	None	None					170.2.b.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3 i q^{3}-i q^{5}-4 i q^{7}-6 q^{9}+\cdots$
1360.2.c.b	$1360$	$2$	1360.c	17.b	$2$	$2$	$2$	$10.860$	$\Q(\sqrt{-1}) $	$_{}$	None	None					170.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}-i q^{5}+2 q^{9}+6 i q^{11}+\cdots$
1360.2.c.c	$1360$	$2$	1360.c	17.b	$2$	$2$	$2$	$10.860$	$\Q(\sqrt{-1}) $	$_{}$	None	None					680.2.c.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+i q^{5}+4 i q^{7}+2 q^{9}-2 i q^{11}+\cdots$
1360.2.c.d	$1360$	$2$	1360.c	17.b	$2$	$2$	$2$	$10.860$	$\Q(\sqrt{-1}) $	$_{}$	None	None					170.2.b.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{5}+2 i q^{7}+3 q^{9}-4 i q^{11}+\cdots$
1360.2.c.e	$1360$	$2$	1360.c	17.b	$2$	$6$	$6$	$10.860$	6.0.37161216.1	$_{}$	None	None					340.2.c.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}-\beta _{4})q^{3}-\beta _{4}q^{5}+(\beta _{1}+\beta _{4})q^{7}+\cdots$
1360.2.c.f	$1360$	$2$	1360.c	17.b	$2$	$6$	$6$	$10.860$	6.0.350464.1	$_{}$	None	None					85.2.d.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{3}+\beta _{3}q^{5}+(2\beta _{4}-\beta _{5})q^{7}+(\beta _{1}+\cdots)q^{9}+\cdots$
1360.2.c.g	$1360$	$2$	1360.c	17.b	$2$	$8$	$8$	$10.860$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None					680.2.c.b	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{3}+\beta _{2}q^{5}+(-\beta _{2}-\beta _{3})q^{7}+\cdots$
1360.2.c.h	$1360$	$2$	1360.c	17.b	$2$	$8$	$8$	$10.860$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None					680.2.c.c	$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-\beta _{2}q^{5}+(-\beta _{1}+2\beta _{2})q^{7}+\cdots$
1360.2.e.a	$1360$	$2$	1360.e	5.b	$2$	$2$	$2$	$10.860$	$\Q(\sqrt{-1}) $	$_{}$	None	None					680.2.e.a	$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+(-2 i-1)q^{5}-4 i q^{7}+\cdots$
1360.2.e.b	$1360$	$2$	1360.e	5.b	$2$	$2$	$2$	$10.860$	$\Q(\sqrt{-1}) $	$_{}$	None	None					170.2.c.a	$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+(-2 i+1)q^{5}+2 q^{9}+6 q^{11}+\cdots$
1360.2.e.c	$1360$	$2$	1360.e	5.b	$2$	$6$	$6$	$10.860$	6.0.5161984.1	$_{}$	None	None					170.2.c.b	$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}+\beta _{2}+\beta _{5})q^{3}+(-\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots$
1360.2.e.d	$1360$	$2$	1360.e	5.b	$2$	$8$	$8$	$10.860$	8.0.619810816.2	$_{}$	None	None					85.2.b.a	$2$	$0$	$0$	$0$	$-2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{2}-\beta _{3}+\beta _{4}-\beta _{5}+\beta _{6})q^{3}+\cdots$
1360.2.e.e	$1360$	$2$	1360.e	5.b	$2$	$8$	$8$	$10.860$	8.0.2058981376.2	$_{}$	None	None					340.2.e.a	$2$	$0$	$0$	$0$	$-2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{6}q^{3}+(-\beta _{2}+\beta _{5}-\beta _{7})q^{5}+(\beta _{5}+\cdots)q^{7}+\cdots$
1360.2.e.f	$1360$	$2$	1360.e	5.b	$2$	$10$	$10$	$10.860$	10.0.$\cdots$.1	$_{}$	None	None					680.2.e.b	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{3}+(\beta _{6}-\beta _{8})q^{5}+(\beta _{5}+\beta _{7})q^{7}+\cdots$
1360.2.e.g	$1360$	$2$	1360.e	5.b	$2$	$12$	$12$	$10.860$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None			✓		680.2.e.c	$2$	$0$	$0$	$0$	$2$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}+\beta _{3})q^{3}-\beta _{6}q^{5}+(-\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots$
1360.2.o.a	$1360$	$2$	1360.o	85.c	$2$	$2$	$2$	$10.860$	$\Q(\sqrt{-1}) $	$_{}$	None	None					170.2.d.a	$2$	$0$	$0$	$-2$	$4$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+(-i+2)q^{5}-2 q^{7}-2 q^{9}+\cdots$
1360.2.o.b	$1360$	$2$	1360.o	85.c	$2$	$2$	$2$	$10.860$	$\Q(\sqrt{-1}) $	$_{}$	None	None					170.2.d.a	$2$	$0$	$0$	$2$	$-4$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+(-i-2)q^{5}+2 q^{7}-2 q^{9}+\cdots$
1360.2.o.c	$1360$	$2$	1360.o	85.c	$2$	$4$	$4$	$10.860$	$\Q(\zeta_{8})$	$_{}$	None	None					680.2.o.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-2\zeta_{8}+2\zeta_{8}^{3})q^{3}+(\zeta_{8}-2\zeta_{8}^{3})q^{5}+\cdots$
1360.2.o.d	$1360$	$2$	1360.o	85.c	$2$	$4$	$4$	$10.860$	$\Q(\zeta_{8})$	$_{}$	None	None					170.2.d.c	$4$	$0$	$0$	$0$	$0$	$0$		$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+2\beta_{3} q^{3}+(-\beta_{3}+\beta_{2})q^{5}-3\beta_{3} q^{7}+\cdots$
1360.2.o.e	$1360$	$2$	1360.o	85.c	$2$	$8$	$8$	$10.860$	8.0.$\cdots$.4	$_{}$	None	None					340.2.g.a	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{6}q^{3}+\beta _{1}q^{5}+\beta _{2}q^{7}-\beta _{3}q^{9}+\cdots$
1360.2.o.f	$1360$	$2$	1360.o	85.c	$2$	$8$	$8$	$10.860$	8.0.$\cdots$.11	$_{}$	None	None					85.2.c.a	$4$	$0$	$0$	$0$	$0$	$0$		$2\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{3}+(\beta _{2}-\beta _{4})q^{5}+(\beta _{2}-\beta _{4}-\beta _{5}+\cdots)q^{7}+\cdots$
1360.2.o.g	$1360$	$2$	1360.o	85.c	$2$	$24$	$24$	$10.860$		$_{}$	None	None			✓		680.2.o.b	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1360.2.bn.a	$1360$	$2$	1360.bn	20.e	$4$	$32$	$16$	$10.860$		$_{}$	None	None		✓			1360.2.bn.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
1360.2.bn.b	$1360$	$2$	1360.bn	20.e	$4$	$64$	$32$	$10.860$		$_{}$	None	None		✓	✓		1360.2.bn.b	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
1360.2.bt.a	$1360$	$2$	1360.bt	17.c	$4$	$4$	$2$	$10.860$	$\Q(\zeta_{8})$	$_{}$	None	None					170.2.h.a	$2$	$0$	$0$	$-4$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+\zeta_{8}^{3}q^{5}+\cdots$

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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.