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 223 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
980.1.f.a	$980$	$1$	980.f	20.d	$2$	$1$	$1$	$0.489$	$\Q$	$D_{3}$	$\Q(\sqrt{-5}) $	None	✓				140.1.p.a	$2$	$0$	$-1$	$-1$	$-1$	$0$		$1$		$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots$
980.1.f.b	$980$	$1$	980.f	20.d	$2$	$1$	$1$	$0.489$	$\Q$	$D_{3}$	$\Q(\sqrt{-5}) $	None	✓				140.1.p.a	$2$	$0$	$-1$	$1$	$1$	$0$		$1$		$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots$
980.1.f.c	$980$	$1$	980.f	20.d	$2$	$1$	$1$	$0.489$	$\Q$	$D_{3}$	$\Q(\sqrt{-5}) $	None	✓				140.1.p.a	$2$	$0$	$1$	$-1$	$1$	$0$		$1$		$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots$
980.1.f.d	$980$	$1$	980.f	20.d	$2$	$1$	$1$	$0.489$	$\Q$	$D_{3}$	$\Q(\sqrt{-5}) $	None	✓				140.1.p.a	$2$	$0$	$1$	$1$	$-1$	$0$		$1$		$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots$
980.1.f.e	$980$	$1$	980.f	20.d	$2$	$4$	$4$	$0.489$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-1}) $	None		✓	✓		980.1.f.e	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}^{2}q^{2}-q^{4}-\zeta_{8}q^{5}-\zeta_{8}^{2}q^{8}+\cdots$
980.1.j.a	$980$	$1$	980.j	140.j	$4$	$8$	$4$	$0.489$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	980.1.j.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{16}^{2}q^{2}+\zeta_{16}^{4}q^{4}+\zeta_{16}^{5}q^{5}+\cdots$
980.1.l.a	$980$	$1$	980.l	5.c	$4$	$4$	$2$	$0.489$	$\Q(\zeta_{8})$	$S_{4}$	None	None		✓	✓	✓	980.1.l.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{3}+\zeta_{8}^{3}q^{5}-q^{11}-\zeta_{8}q^{13}+\cdots$
980.1.n.a	$980$	$1$	980.n	35.i	$6$	$2$	$1$	$0.489$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-35}) $	None					140.1.h.a	$4$	$0$	$0$	$-1$	$1$	$0$		$1$		$q-\zeta_{6}q^{3}-\zeta_{6}^{2}q^{5}+\zeta_{6}q^{11}+q^{13}+\cdots$
980.1.n.b	$980$	$1$	980.n	35.i	$6$	$2$	$1$	$0.489$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-35}) $	None					140.1.h.a	$4$	$0$	$0$	$1$	$-1$	$0$		$1$		$q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{11}-q^{13}+\cdots$
980.1.p.a	$980$	$1$	980.p	140.p	$6$	$2$	$1$	$0.489$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-5}) $	None					140.1.p.a	$4$	$0$	$-1$	$-1$	$1$	$0$		$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\cdots$
980.1.p.b	$980$	$1$	980.p	140.p	$6$	$2$	$1$	$0.489$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-5}) $	None					140.1.p.a	$4$	$0$	$1$	$1$	$1$	$0$		$1$		$q-\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\cdots$
980.1.p.c	$980$	$1$	980.p	140.p	$6$	$8$	$4$	$0.489$	$\Q(\zeta_{24})$	$D_{4}$	$\Q(\sqrt{-1}) $	None		✓	✓		980.1.f.e	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{10}q^{2}-\zeta_{24}^{8}q^{4}-\zeta_{24}^{7}q^{5}+\cdots$
980.1.w.a	$980$	$1$	980.w	35.l	$12$	$8$	$2$	$0.489$	$\Q(\zeta_{24})$	$S_{4}$	None	None		✓	✓	✓	980.1.l.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{7}q^{3}+\zeta_{24}^{5}q^{5}+\zeta_{24}^{4}q^{11}+\cdots$
980.1.y.a	$980$	$1$	980.y	140.x	$12$	$16$	$4$	$0.489$	$\Q(\zeta_{48})$	$D_{8}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	980.1.j.a	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{48}^{2}q^{2}+\zeta_{48}^{4}q^{4}+\zeta_{48}^{5}q^{5}+\cdots$
980.1.ba.a	$980$	$1$	980.ba	980.aa	$14$	$6$	$1$	$0.489$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-5}) $	None		✓			980.1.ba.a	$4$	$0$	$-1$	$5$	$-1$	$-1$		$1$		$q-\zeta_{14}q^{2}+(1+\zeta_{14}^{6})q^{3}+\zeta_{14}^{2}q^{4}+\cdots$
980.1.ba.b	$980$	$1$	980.ba	980.aa	$14$	$6$	$1$	$0.489$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-5}) $	None		✓			980.1.ba.a	$4$	$0$	$1$	$-5$	$-1$	$1$		$1$		$q+\zeta_{14}q^{2}+(-1-\zeta_{14}^{6})q^{3}+\zeta_{14}^{2}q^{4}+\cdots$
980.1.bq.a	$980$	$1$	980.bq	980.aq	$42$	$12$	$1$	$0.489$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-5}) $	None		✓			980.1.bq.a	$4$	$0$	$-1$	$8$	$1$	$-1$		$1$		$q-\zeta_{42}^{4}q^{2}+(\zeta_{42}^{3}+\zeta_{42}^{7})q^{3}+\zeta_{42}^{8}q^{4}+\cdots$
980.1.bq.b	$980$	$1$	980.bq	980.aq	$42$	$12$	$1$	$0.489$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-5}) $	None		✓			980.1.bq.a	$4$	$0$	$1$	$-8$	$1$	$1$		$1$		$q+\zeta_{42}^{4}q^{2}+(-\zeta_{42}^{3}-\zeta_{42}^{7})q^{3}+\cdots$
980.2.a.a	$980$	$2$	980.a	1.a	$1$	$1$	$1$	$7.825$	$\Q$	$_{}$	None	None	✓				140.2.i.b	$1$	$0$	$0$	$-3$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-q^{5}+6q^{9}-2q^{11}-6q^{13}+\cdots$
980.2.a.b	$980$	$2$	980.a	1.a	$1$	$1$	$1$	$7.825$	$\Q$	$_{}$	None	None	✓				140.2.a.b	$1$	$0$	$0$	$-3$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+q^{5}+6q^{9}-5q^{11}+3q^{13}+\cdots$
980.2.a.c	$980$	$2$	980.a	1.a	$1$	$1$	$1$	$7.825$	$\Q$	$_{}$	None	None	✓				140.2.a.a	$1$	$1$	$0$	$-1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-2q^{9}+3q^{11}+q^{13}+\cdots$
980.2.a.d	$980$	$2$	980.a	1.a	$1$	$1$	$1$	$7.825$	$\Q$	$_{}$	None	None	✓	✓			980.2.a.d	$1$	$0$	$0$	$-1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-2q^{9}-q^{11}+5q^{13}+\cdots$
980.2.a.e	$980$	$2$	980.a	1.a	$1$	$1$	$1$	$7.825$	$\Q$	$_{}$	None	None	✓				140.2.i.a	$1$	$0$	$0$	$-1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-2q^{9}+6q^{11}-2q^{13}+\cdots$
980.2.a.f	$980$	$2$	980.a	1.a	$1$	$1$	$1$	$7.825$	$\Q$	$_{}$	None	None	✓	✓			980.2.a.d	$1$	$1$	$0$	$1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-2q^{9}-q^{11}-5q^{13}+\cdots$
980.2.a.g	$980$	$2$	980.a	1.a	$1$	$1$	$1$	$7.825$	$\Q$	$_{}$	None	None	✓				140.2.i.a	$1$	$0$	$0$	$1$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-2q^{9}+6q^{11}+2q^{13}+\cdots$
980.2.a.h	$980$	$2$	980.a	1.a	$1$	$1$	$1$	$7.825$	$\Q$	$_{}$	None	None	✓				20.2.a.a	$1$	$0$	$0$	$2$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{5}+q^{9}-2q^{13}+2q^{15}+\cdots$
980.2.a.i	$980$	$2$	980.a	1.a	$1$	$1$	$1$	$7.825$	$\Q$	$_{}$	None	None	✓				140.2.i.b	$1$	$0$	$0$	$3$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+q^{5}+6q^{9}-2q^{11}+6q^{13}+\cdots$
980.2.a.j	$980$	$2$	980.a	1.a	$1$	$2$	$2$	$7.825$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓	✓	✓	980.2.a.j	$1$	$1$	$0$	$-2$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+q^{5}-2\beta q^{9}+(-1+\cdots)q^{11}+\cdots$
980.2.a.k	$980$	$2$	980.a	1.a	$1$	$2$	$2$	$7.825$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓	✓		980.2.a.j	$1$	$0$	$0$	$2$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}-q^{5}+2\beta q^{9}+(-1+2\beta )q^{11}+\cdots$
980.2.c.a	$980$	$2$	980.c	140.c	$2$	$8$	$8$	$7.825$	$\Q(\zeta_{16})$	$_{}$	$\Q(\sqrt{-1}) $	None		✓			980.2.c.a	$8$	$0$	$0$	$0$	$0$	$0$		$7^{4}$	$\mathrm{U}(1)[D_{2}]$	$q-\zeta_{16}^{2}q^{2}-2q^{4}-\zeta_{16}^{4}q^{5}+2\zeta_{16}^{2}q^{8}+\cdots$
980.2.c.b	$980$	$2$	980.c	140.c	$2$	$8$	$8$	$7.825$	8.0.3317760000.3	$_{}$	$\Q(\sqrt{-5}) $	None					140.2.s.a	$8$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{1}q^{2}+\beta _{3}q^{3}+2q^{4}+\beta _{6}q^{5}+(-\beta _{5}+\cdots)q^{6}+\cdots$
980.2.c.c	$980$	$2$	980.c	140.c	$2$	$16$	$16$	$7.825$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			980.2.c.c	$8$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}+(-\beta _{8}-\beta _{10}-\beta _{12})q^{3}+\cdots$
980.2.c.d	$980$	$2$	980.c	140.c	$2$	$32$	$32$	$7.825$		$_{}$	None	None					140.2.s.b	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
980.2.c.e	$980$	$2$	980.c	140.c	$2$	$48$	$48$	$7.825$		$_{}$	None	None		✓	✓		980.2.c.e	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
980.2.e.a	$980$	$2$	980.e	5.b	$2$	$2$	$2$	$7.825$	$\Q(\sqrt{-1}) $	$_{}$	None	None					140.2.e.b	$2$	$0$	$0$	$0$	$-2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-i)q^{5}+3q^{9}+2iq^{13}-2iq^{17}+\cdots$
980.2.e.b	$980$	$2$	980.e	5.b	$2$	$2$	$2$	$7.825$	$\Q(\sqrt{-1}) $	$_{}$	None	None					140.2.e.a	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3iq^{3}+(2+i)q^{5}-6q^{9}+3q^{11}+\cdots$
980.2.e.c	$980$	$2$	980.e	5.b	$2$	$4$	$4$	$7.825$	$\Q(\sqrt{-3}, \sqrt{-19})$	$_{}$	None	None					140.2.q.a	$2$	$0$	$0$	$0$	$-1$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{3}+\beta _{1}q^{5}+(-2-\beta _{1}-\beta _{3})q^{11}+\cdots$
980.2.e.d	$980$	$2$	980.e	5.b	$2$	$4$	$4$	$7.825$	$\Q(\sqrt{-5}, \sqrt{-21})$	$_{}$	$\Q(\sqrt{-35}) $	None		✓			980.2.e.d	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{3}+\beta _{2}q^{5}+(-4+\beta _{3})q^{9}+(1+\cdots)q^{11}+\cdots$
980.2.e.e	$980$	$2$	980.e	5.b	$2$	$4$	$4$	$7.825$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		✓			980.2.e.e	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{3}+(\beta _{1}+\beta _{2})q^{5}-q^{11}-\beta _{2}q^{13}+\cdots$
980.2.e.f	$980$	$2$	980.e	5.b	$2$	$4$	$4$	$7.825$	$\Q(\sqrt{-3}, \sqrt{-19})$	$_{}$	None	None					140.2.q.a	$2$	$0$	$0$	$0$	$1$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{3}-\beta _{3}q^{5}+(-2-\beta _{1}-\beta _{3})q^{11}+\cdots$
980.2.g.a	$980$	$2$	980.g	28.d	$2$	$32$	$32$	$7.825$		$_{}$	None	None					140.2.o.a	$4$	$0$	$-4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
980.2.g.b	$980$	$2$	980.g	28.d	$2$	$48$	$48$	$7.825$		$_{}$	None	None		✓	✓		980.2.g.b	$4$	$0$	$8$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
980.2.i.a	$980$	$2$	980.i	7.c	$3$	$2$	$1$	$7.825$	$\Q(\sqrt{-3}) $	$_{}$	None	None					140.2.i.b	$2$	$0$	$0$	$-3$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-3+3\zeta_{6})q^{3}-\zeta_{6}q^{5}-6\zeta_{6}q^{9}+\cdots$
980.2.i.b	$980$	$2$	980.i	7.c	$3$	$2$	$1$	$7.825$	$\Q(\sqrt{-3}) $	$_{}$	None	None					140.2.a.b	$2$	$0$	$0$	$-3$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-3+3\zeta_{6})q^{3}+\zeta_{6}q^{5}-6\zeta_{6}q^{9}+\cdots$
980.2.i.c	$980$	$2$	980.i	7.c	$3$	$2$	$1$	$7.825$	$\Q(\sqrt{-3}) $	$_{}$	None	None					20.2.a.a	$2$	$1$	$0$	$-2$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots$
980.2.i.d	$980$	$2$	980.i	7.c	$3$	$2$	$1$	$7.825$	$\Q(\sqrt{-3}) $	$_{}$	None	None					140.2.a.a	$2$	$0$	$0$	$-1$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+2\zeta_{6}q^{9}+\cdots$
980.2.i.e	$980$	$2$	980.i	7.c	$3$	$2$	$1$	$7.825$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			980.2.a.d	$2$	$0$	$0$	$-1$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{5}+2\zeta_{6}q^{9}+\cdots$
980.2.i.f	$980$	$2$	980.i	7.c	$3$	$2$	$1$	$7.825$	$\Q(\sqrt{-3}) $	$_{}$	None	None					140.2.i.a	$2$	$0$	$0$	$1$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+2\zeta_{6}q^{9}+(-6+\cdots)q^{11}+\cdots$
980.2.i.g	$980$	$2$	980.i	7.c	$3$	$2$	$1$	$7.825$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			980.2.a.d	$2$	$0$	$0$	$1$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+2\zeta_{6}q^{9}+(1+\cdots)q^{11}+\cdots$
980.2.i.h	$980$	$2$	980.i	7.c	$3$	$2$	$1$	$7.825$	$\Q(\sqrt{-3}) $	$_{}$	None	None					140.2.a.a	$2$	$0$	$0$	$1$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+2\zeta_{6}q^{9}+(-3+\cdots)q^{11}+\cdots$

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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.