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 365 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
960.1.c.a	$960$	$1$	960.c	15.d	$2$	$4$	$4$	$0.479$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-5}) $	None			✓	✓	480.1.c.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}^{3}q^{3}+\zeta_{8}^{2}q^{5}+(\zeta_{8}+\zeta_{8}^{3})q^{7}+\cdots$
960.1.u.a	$960$	$1$	960.u	120.q	$4$	$4$	$2$	$0.479$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-6}) $	None		✓			960.1.u.a	$8$	$0$	$0$	$0$	$0$	$-4$		$1$		$q-\zeta_{8}^{3}q^{3}-\zeta_{8}^{3}q^{5}+(-1-\zeta_{8}^{2})q^{7}+\cdots$
960.1.u.b	$960$	$1$	960.u	120.q	$4$	$4$	$2$	$0.479$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-6}) $	None		✓			960.1.u.a	$8$	$0$	$0$	$0$	$0$	$4$		$1$		$q-\zeta_{8}^{3}q^{3}+\zeta_{8}^{3}q^{5}+(1+\zeta_{8}^{2})q^{7}+\cdots$
960.1.bm.a	$960$	$1$	960.bm	240.am	$4$	$4$	$2$	$0.479$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-15}) $	None			✓	✓	240.1.bm.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}q^{3}-\zeta_{8}^{3}q^{5}+\zeta_{8}^{2}q^{9}+q^{15}+\cdots$
960.1.cl.a	$960$	$1$	960.cl	960.bl	$16$	$16$	$2$	$0.479$	$\Q(\zeta_{32})$	$D_{16}$	$\Q(\sqrt{-15}) $	None		✓	✓	✓	960.1.cl.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{32}^{13}q^{2}+\zeta_{32}q^{3}-\zeta_{32}^{10}q^{4}+\cdots$
960.2.a.a	$960$	$2$	960.a	1.a	$1$	$1$	$1$	$7.666$	$\Q$	$_{}$	None	None	✓				15.2.a.a	$1$	$0$	$0$	$-1$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots$
960.2.a.b	$960$	$2$	960.a	1.a	$1$	$1$	$1$	$7.666$	$\Q$	$_{}$	None	None	✓				480.2.a.d	$1$	$1$	$0$	$-1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{9}-2q^{13}+q^{15}+6q^{17}+\cdots$
960.2.a.c	$960$	$2$	960.a	1.a	$1$	$1$	$1$	$7.666$	$\Q$	$_{}$	None	None	✓				120.2.a.b	$1$	$1$	$0$	$-1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{9}+4q^{11}-6q^{13}+\cdots$
960.2.a.d	$960$	$2$	960.a	1.a	$1$	$1$	$1$	$7.666$	$\Q$	$_{}$	None	None	✓				480.2.a.c	$1$	$0$	$0$	$-1$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+4q^{7}+q^{9}+2q^{13}+q^{15}+\cdots$
960.2.a.e	$960$	$2$	960.a	1.a	$1$	$1$	$1$	$7.666$	$\Q$	$_{}$	None	None	✓				30.2.a.a	$1$	$0$	$0$	$-1$	$1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-4q^{7}+q^{9}-2q^{13}-q^{15}+\cdots$
960.2.a.f	$960$	$2$	960.a	1.a	$1$	$1$	$1$	$7.666$	$\Q$	$_{}$	None	None	✓		✓	✓	480.2.a.b	$1$	$1$	$0$	$-1$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots$
960.2.a.g	$960$	$2$	960.a	1.a	$1$	$1$	$1$	$7.666$	$\Q$	$_{}$	None	None	✓				120.2.a.a	$1$	$0$	$0$	$-1$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+4q^{7}+q^{9}+6q^{13}-q^{15}+\cdots$
960.2.a.h	$960$	$2$	960.a	1.a	$1$	$1$	$1$	$7.666$	$\Q$	$_{}$	None	None	✓				480.2.a.a	$1$	$0$	$0$	$-1$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+4q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots$
960.2.a.i	$960$	$2$	960.a	1.a	$1$	$1$	$1$	$7.666$	$\Q$	$_{}$	None	None	✓				480.2.a.c	$1$	$1$	$0$	$1$	$-1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-4q^{7}+q^{9}+2q^{13}-q^{15}+\cdots$
960.2.a.j	$960$	$2$	960.a	1.a	$1$	$1$	$1$	$7.666$	$\Q$	$_{}$	None	None	✓				120.2.a.b	$1$	$1$	$0$	$1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{9}-4q^{11}-6q^{13}+\cdots$
960.2.a.k	$960$	$2$	960.a	1.a	$1$	$1$	$1$	$7.666$	$\Q$	$_{}$	None	None	✓				480.2.a.d	$1$	$0$	$0$	$1$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{9}-2q^{13}-q^{15}+6q^{17}+\cdots$
960.2.a.l	$960$	$2$	960.a	1.a	$1$	$1$	$1$	$7.666$	$\Q$	$_{}$	None	None	✓				15.2.a.a	$1$	$0$	$0$	$1$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots$
960.2.a.m	$960$	$2$	960.a	1.a	$1$	$1$	$1$	$7.666$	$\Q$	$_{}$	None	None	✓		✓	✓	480.2.a.a	$1$	$1$	$0$	$1$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-4q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots$
960.2.a.n	$960$	$2$	960.a	1.a	$1$	$1$	$1$	$7.666$	$\Q$	$_{}$	None	None	✓				120.2.a.a	$1$	$0$	$0$	$1$	$1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-4q^{7}+q^{9}+6q^{13}+q^{15}+\cdots$
960.2.a.o	$960$	$2$	960.a	1.a	$1$	$1$	$1$	$7.666$	$\Q$	$_{}$	None	None	✓				480.2.a.b	$1$	$0$	$0$	$1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots$
960.2.a.p	$960$	$2$	960.a	1.a	$1$	$1$	$1$	$7.666$	$\Q$	$_{}$	None	None	✓				30.2.a.a	$1$	$0$	$0$	$1$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+4q^{7}+q^{9}-2q^{13}+q^{15}+\cdots$
960.2.b.a	$960$	$2$	960.b	24.f	$2$	$4$	$4$	$7.666$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			960.2.b.a	$4$	$0$	$0$	$0$	$-4$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{8}q^{3}-q^{5}+(\zeta_{8}-\zeta_{8}^{2})q^{7}+(1-\zeta_{8}^{3})q^{9}+\cdots$
960.2.b.b	$960$	$2$	960.b	24.f	$2$	$4$	$4$	$7.666$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			960.2.b.a	$4$	$0$	$0$	$0$	$4$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{8}^{2}q^{3}+q^{5}+(-\zeta_{8}+\zeta_{8}^{2})q^{7}+\cdots$
960.2.b.c	$960$	$2$	960.b	24.f	$2$	$12$	$12$	$7.666$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓			960.2.b.c	$4$	$0$	$0$	$0$	$-12$	$0$		$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{3}-q^{5}+(-\beta _{4}+\beta _{5}+\beta _{6})q^{7}+\cdots$
960.2.b.d	$960$	$2$	960.b	24.f	$2$	$12$	$12$	$7.666$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓			960.2.b.c	$4$	$0$	$0$	$0$	$12$	$0$		$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{3}+q^{5}+(-\beta _{4}+\beta _{5}+\beta _{6})q^{7}+\cdots$
960.2.d.a	$960$	$2$	960.d	40.f	$2$	$2$	$2$	$7.666$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			960.2.d.a	$2$	$1$	$0$	$-2$	$-2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+(-1-i)q^{5}+iq^{7}+q^{9}-iq^{11}+\cdots$
960.2.d.b	$960$	$2$	960.d	40.f	$2$	$2$	$2$	$7.666$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			960.2.d.a	$2$	$0$	$0$	$-2$	$2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+(1-i)q^{5}+iq^{7}+q^{9}+iq^{11}+\cdots$
960.2.d.c	$960$	$2$	960.d	40.f	$2$	$2$	$2$	$7.666$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			960.2.d.a	$2$	$0$	$0$	$2$	$-2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+(-1+i)q^{5}+iq^{7}+q^{9}-iq^{11}+\cdots$
960.2.d.d	$960$	$2$	960.d	40.f	$2$	$2$	$2$	$7.666$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			960.2.d.a	$2$	$0$	$0$	$2$	$2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+(1+i)q^{5}+iq^{7}+q^{9}+iq^{11}+\cdots$
960.2.d.e	$960$	$2$	960.d	40.f	$2$	$8$	$8$	$7.666$	8.0.49787136.1	$_{}$	None	None		✓			960.2.d.e	$4$	$0$	$0$	$-8$	$0$	$0$		$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}-\beta _{4}q^{5}+(-\beta _{4}+\beta _{5})q^{7}+q^{9}+\cdots$
960.2.d.f	$960$	$2$	960.d	40.f	$2$	$8$	$8$	$7.666$	8.0.49787136.1	$_{}$	None	None		✓			960.2.d.e	$4$	$0$	$0$	$8$	$0$	$0$		$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+\beta _{4}q^{5}+(-\beta _{4}+\beta _{5})q^{7}+q^{9}+\cdots$
960.2.f.a	$960$	$2$	960.f	5.b	$2$	$2$	$2$	$7.666$	$\Q(\sqrt{-1}) $	$_{}$	None	None					120.2.f.a	$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{3}+(-2+i)q^{5}+2iq^{7}-q^{9}+\cdots$
960.2.f.b	$960$	$2$	960.f	5.b	$2$	$2$	$2$	$7.666$	$\Q(\sqrt{-1}) $	$_{}$	None	None					120.2.f.a	$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{3}+(-2-i)q^{5}+2iq^{7}-q^{9}+\cdots$
960.2.f.c	$960$	$2$	960.f	5.b	$2$	$2$	$2$	$7.666$	$\Q(\sqrt{-1}) $	$_{}$	None	None					60.2.d.a	$2$	$1$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+(-1-2i)q^{5}+4iq^{7}-q^{9}+\cdots$
960.2.f.d	$960$	$2$	960.f	5.b	$2$	$2$	$2$	$7.666$	$\Q(\sqrt{-1}) $	$_{}$	None	None					480.2.f.c	$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{3}+(-1-2i)q^{5}+4iq^{7}-q^{9}+\cdots$
960.2.f.e	$960$	$2$	960.f	5.b	$2$	$2$	$2$	$7.666$	$\Q(\sqrt{-1}) $	$_{}$	None	None					480.2.f.c	$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{3}+(-1+2i)q^{5}+4iq^{7}-q^{9}+\cdots$
960.2.f.f	$960$	$2$	960.f	5.b	$2$	$2$	$2$	$7.666$	$\Q(\sqrt{-1}) $	$_{}$	None	None					60.2.d.a	$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+(-1+2i)q^{5}+4iq^{7}-q^{9}+\cdots$
960.2.f.g	$960$	$2$	960.f	5.b	$2$	$2$	$2$	$7.666$	$\Q(\sqrt{-1}) $	$_{}$	None	None					480.2.f.a	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+(2-i)q^{5}+2iq^{7}-q^{9}-6q^{11}+\cdots$
960.2.f.h	$960$	$2$	960.f	5.b	$2$	$2$	$2$	$7.666$	$\Q(\sqrt{-1}) $	$_{}$	None	None					30.2.c.a	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{3}+(2+i)q^{5}+2iq^{7}-q^{9}-2q^{11}+\cdots$
960.2.f.i	$960$	$2$	960.f	5.b	$2$	$2$	$2$	$7.666$	$\Q(\sqrt{-1}) $	$_{}$	None	None					30.2.c.a	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{3}+(2-i)q^{5}+2iq^{7}-q^{9}+2q^{11}+\cdots$
960.2.f.j	$960$	$2$	960.f	5.b	$2$	$2$	$2$	$7.666$	$\Q(\sqrt{-1}) $	$_{}$	None	None					480.2.f.a	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+(2+i)q^{5}+2iq^{7}-q^{9}+6q^{11}+\cdots$
960.2.f.k	$960$	$2$	960.f	5.b	$2$	$4$	$4$	$7.666$	$\Q(i, \sqrt{5})$	$_{}$	None	None			✓		480.2.f.e	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-\beta _{2}q^{5}+2\beta _{1}q^{7}-q^{9}+2\beta _{3}q^{11}+\cdots$
960.2.h.a	$960$	$2$	960.h	12.b	$2$	$4$	$4$	$7.666$	$\Q(\zeta_{8})$	$_{}$	None	None					480.2.h.a	$2$	$1$	$0$	$-4$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\zeta_{8}^{2})q^{3}-\zeta_{8}q^{5}+(2\zeta_{8}+2\zeta_{8}^{2}+\cdots)q^{7}+\cdots$
960.2.h.b	$960$	$2$	960.h	12.b	$2$	$4$	$4$	$7.666$	$\Q(\zeta_{8})$	$_{}$	None	None					480.2.h.b	$2$	$0$	$0$	$-4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{5}+\cdots$
960.2.h.c	$960$	$2$	960.h	12.b	$2$	$4$	$4$	$7.666$	$\Q(i, \sqrt{6})$	$_{}$	None	None					240.2.h.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+\beta _{2}q^{5}+(\beta _{1}+\beta _{3})q^{7}+3\beta _{2}q^{9}+\cdots$
960.2.h.d	$960$	$2$	960.h	12.b	$2$	$4$	$4$	$7.666$	$\Q(\zeta_{12})$	$_{}$	None	None					240.2.h.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{12}^{3}q^{3}-\zeta_{12}q^{5}-2\zeta_{12}^{2}q^{7}+\cdots$
960.2.h.e	$960$	$2$	960.h	12.b	$2$	$4$	$4$	$7.666$	$\Q(\zeta_{8})$	$_{}$	None	None					480.2.h.a	$2$	$0$	$0$	$4$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\zeta_{8}^{2})q^{3}+\zeta_{8}q^{5}+(2\zeta_{8}+2\zeta_{8}^{2}+\cdots)q^{7}+\cdots$
960.2.h.f	$960$	$2$	960.h	12.b	$2$	$4$	$4$	$7.666$	$\Q(\zeta_{8})$	$_{}$	None	None					480.2.h.b	$2$	$0$	$0$	$4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\zeta_{8}-\zeta_{8}^{2})q^{3}+\zeta_{8}^{2}q^{5}+(-\zeta_{8}+\cdots)q^{7}+\cdots$
960.2.h.g	$960$	$2$	960.h	12.b	$2$	$8$	$8$	$7.666$	8.0.342102016.5	$_{}$	None	None			✓		60.2.e.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{3}-\beta _{1}q^{5}+(\beta _{3}+\beta _{4})q^{7}+\beta _{6}q^{9}+\cdots$
960.2.k.a	$960$	$2$	960.k	8.b	$2$	$2$	$2$	$7.666$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			960.2.k.a	$2$	$1$	$0$	$0$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{3}-iq^{5}-4q^{7}-q^{9}-4iq^{11}+\cdots$

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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.