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 187 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
416.1.h.a	$416$	$1$	416.h	104.h	$2$	$1$	$1$	$0.208$	$\Q$	$D_{3}$	$\Q(\sqrt{-26}) $	None	✓				104.1.h.a	$2$	$0$	$0$	$1$	$-1$	$1$		$1$		$q+q^{3}-q^{5}+q^{7}+q^{13}-q^{15}-q^{17}+\cdots$
416.1.h.b	$416$	$1$	416.h	104.h	$2$	$1$	$1$	$0.208$	$\Q$	$D_{3}$	$\Q(\sqrt{-26}) $	None	✓				104.1.h.a	$2$	$0$	$0$	$1$	$1$	$-1$		$1$		$q+q^{3}+q^{5}-q^{7}-q^{13}+q^{15}-q^{17}+\cdots$
416.1.t.a	$416$	$1$	416.t	13.d	$4$	$2$	$1$	$0.208$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	416.1.t.a	$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q+(1+i)q^{5}-q^{9}+iq^{13}-iq^{17}+\cdots$
416.1.bb.a	$416$	$1$	416.bb	52.j	$6$	$4$	$2$	$0.208$	$\Q(\zeta_{12})$	$A_{4}$	None	None		✓	✓	✓	416.1.bb.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}q^{3}-\zeta_{12}^{5}q^{7}-\zeta_{12}q^{11}+q^{13}+\cdots$
416.1.bl.a	$416$	$1$	416.bl	13.f	$12$	$4$	$1$	$0.208$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	416.1.bl.a	$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q+(\zeta_{12}^{4}+\zeta_{12}^{5})q^{5}+\zeta_{12}^{2}q^{9}+\zeta_{12}q^{13}+\cdots$
416.2.a.a	$416$	$2$	416.a	1.a	$1$	$1$	$1$	$3.322$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	416.2.a.a	$1$	$1$	$0$	$-1$	$1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-3q^{7}-2q^{9}-2q^{11}+\cdots$
416.2.a.b	$416$	$2$	416.a	1.a	$1$	$1$	$1$	$3.322$	$\Q$	$_{}$	None	None	✓	✓			416.2.a.a	$1$	$0$	$0$	$1$	$1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+3q^{7}-2q^{9}+2q^{11}+\cdots$
416.2.a.c	$416$	$2$	416.a	1.a	$1$	$2$	$2$	$3.322$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	✓	✓	✓	416.2.a.c	$1$	$1$	$0$	$-1$	$-3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(-2+\beta )q^{5}+(-2+\beta )q^{7}+\cdots$
416.2.a.d	$416$	$2$	416.a	1.a	$1$	$2$	$2$	$3.322$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓			416.2.a.d	$2$	$0$	$0$	$0$	$6$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{3}+3q^{5}-\beta q^{7}+2q^{9}+2\beta q^{11}+\cdots$
416.2.a.e	$416$	$2$	416.a	1.a	$1$	$2$	$2$	$3.322$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	✓			416.2.a.c	$1$	$0$	$0$	$1$	$-3$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(-2+\beta )q^{5}+(2-\beta )q^{7}+(1+\cdots)q^{9}+\cdots$
416.2.a.f	$416$	$2$	416.a	1.a	$1$	$4$	$4$	$3.322$	4.4.13448.1	$_{}$	None	None	✓	✓	✓		416.2.a.f	$2$	$0$	$0$	$0$	$-2$	$0$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+\beta _{3}q^{5}+(\beta _{1}-\beta _{2})q^{7}+(3+\cdots)q^{9}+\cdots$
416.2.b.a	$416$	$2$	416.b	8.b	$2$	$2$	$2$	$3.322$	$\Q(\sqrt{-1}) $	$_{}$	None	None					104.2.b.a	$2$	$0$	$0$	$0$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+3iq^{5}-3q^{7}+2q^{9}+iq^{13}+\cdots$
416.2.b.b	$416$	$2$	416.b	8.b	$2$	$4$	$4$	$3.322$	$\Q(\zeta_{12})$	$_{}$	None	None					104.2.b.b	$2$	$0$	$0$	$0$	$0$	$12$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+2\zeta_{12}q^{3}-2\zeta_{12}^{2}q^{5}+(3-\zeta_{12}^{3})q^{7}+\cdots$
416.2.b.c	$416$	$2$	416.b	8.b	$2$	$6$	$6$	$3.322$	6.0.399424.1	$_{}$	None	None			✓		104.2.b.c	$2$	$0$	$0$	$0$	$0$	$-2$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{3}-\beta _{2}q^{5}+\beta _{1}q^{7}+(-2+\beta _{1}+\cdots)q^{9}+\cdots$
416.2.e.a	$416$	$2$	416.e	104.e	$2$	$2$	$2$	$3.322$	$\Q(\sqrt{-1}) $	$_{}$	None	None					104.2.e.a	$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}-q^{5}-3iq^{7}+2q^{9}+2q^{11}+\cdots$
416.2.e.b	$416$	$2$	416.e	104.e	$2$	$2$	$2$	$3.322$	$\Q(\sqrt{-1}) $	$_{}$	None	None					104.2.e.a	$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+q^{5}+3iq^{7}+2q^{9}-2q^{11}+\cdots$
416.2.e.c	$416$	$2$	416.e	104.e	$2$	$8$	$8$	$3.322$	8.0.4521217600.1	$_{}$	None	None			✓		104.2.e.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}+\beta _{4}q^{5}+\beta _{3}q^{7}+(-3-\beta _{5}+\cdots)q^{9}+\cdots$
416.2.f.a	$416$	$2$	416.f	13.b	$2$	$2$	$2$	$3.322$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			416.2.f.a	$2$	$1$	$0$	$-6$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-3q^{3}+3iq^{5}-iq^{7}+6q^{9}+4iq^{11}+\cdots$
416.2.f.b	$416$	$2$	416.f	13.b	$2$	$2$	$2$	$3.322$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		✓			416.2.f.b	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+2iq^{5}-3q^{9}+(-3+i)q^{13}-2q^{17}+\cdots$
416.2.f.c	$416$	$2$	416.f	13.b	$2$	$2$	$2$	$3.322$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			416.2.f.a	$2$	$0$	$0$	$6$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3q^{3}+3iq^{5}+iq^{7}+6q^{9}-4iq^{11}+\cdots$
416.2.f.d	$416$	$2$	416.f	13.b	$2$	$4$	$4$	$3.322$	$\Q(i, \sqrt{13})$	$_{}$	$\Q(\sqrt{-13}) $	None		✓			416.2.f.d	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{7}-3q^{9}+(\beta _{1}+\beta _{2})q^{11}-\beta _{3}q^{13}+\cdots$
416.2.f.e	$416$	$2$	416.f	13.b	$2$	$4$	$4$	$3.322$	$\Q(i, \sqrt{5})$	$_{}$	None	None		✓			416.2.f.e	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}-\beta _{1}q^{5}-\beta _{2}q^{7}+2q^{9}+(2+\cdots)q^{13}+\cdots$
416.2.i.a	$416$	$2$	416.i	13.c	$3$	$2$	$1$	$3.322$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			416.2.i.a	$2$	$0$	$0$	$-2$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{3}+q^{5}-\zeta_{6}q^{9}+(-4+\cdots)q^{11}+\cdots$
416.2.i.b	$416$	$2$	416.i	13.c	$3$	$2$	$1$	$3.322$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			416.2.i.a	$2$	$0$	$0$	$2$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{3}+q^{5}-\zeta_{6}q^{9}+(4-4\zeta_{6})q^{11}+\cdots$
416.2.i.c	$416$	$2$	416.i	13.c	$3$	$4$	$2$	$3.322$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		✓			416.2.i.c	$2$	$0$	$0$	$-2$	$0$	$6$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{1}-\beta _{2})q^{3}+2\beta _{3}q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$
416.2.i.d	$416$	$2$	416.i	13.c	$3$	$4$	$2$	$3.322$	$\Q(\sqrt{-3}, \sqrt{11})$	$_{}$	None	None		✓			416.2.i.d	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{7}+8\beta _{2}q^{9}+\cdots$
416.2.i.e	$416$	$2$	416.i	13.c	$3$	$4$	$2$	$3.322$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-1}) $	None		✓			416.2.i.e	$4$	$0$	$0$	$0$	$4$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{3}]$	$q+(1-2\zeta_{12}+\zeta_{12}^{3})q^{5}+3\zeta_{12}^{2}q^{9}+\cdots$
416.2.i.f	$416$	$2$	416.i	13.c	$3$	$4$	$2$	$3.322$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		✓			416.2.i.c	$2$	$0$	$0$	$2$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{1}+\beta _{2})q^{3}-2\beta _{3}q^{5}+(\beta _{1}+3\beta _{2}+\cdots)q^{7}+\cdots$
416.2.i.g	$416$	$2$	416.i	13.c	$3$	$8$	$4$	$3.322$	8.0.6927565824.3	$_{}$	None	None		✓	✓		416.2.i.g	$4$	$0$	$0$	$0$	$-4$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{2}-\beta _{7})q^{3}+(-1+\beta _{3})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$
416.2.k.a	$416$	$2$	416.k	52.f	$4$	$2$	$1$	$3.322$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			416.2.k.a	$2$	$0$	$0$	$0$	$-2$	$-2$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-2iq^{3}+(-1-i)q^{5}+(-1-i)q^{7}+\cdots$
416.2.k.b	$416$	$2$	416.k	52.f	$4$	$2$	$1$	$3.322$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			416.2.k.a	$2$	$0$	$0$	$0$	$-2$	$2$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+2iq^{3}+(-1-i)q^{5}+(1+i)q^{7}+\cdots$
416.2.k.c	$416$	$2$	416.k	52.f	$4$	$4$	$2$	$3.322$	$\Q(i, \sqrt{10})$	$_{}$	None	None		✓			416.2.k.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{2}q^{3}+\beta _{1}q^{5}-\beta _{1}q^{7}+2q^{9}+(-1+\cdots)q^{11}+\cdots$
416.2.k.d	$416$	$2$	416.k	52.f	$4$	$4$	$2$	$3.322$	$\Q(i, \sqrt{10})$	$_{}$	None	None		✓			416.2.k.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{2}q^{3}+\beta _{1}q^{5}+\beta _{1}q^{7}+2q^{9}+(1+\cdots)q^{11}+\cdots$
416.2.k.e	$416$	$2$	416.k	52.f	$4$	$8$	$4$	$3.322$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None		✓			416.2.k.e	$2$	$0$	$0$	$0$	$0$	$-2$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{4}q^{3}+\beta _{7}q^{5}+(-\beta _{3}+\beta _{7})q^{7}+\cdots$
416.2.k.f	$416$	$2$	416.k	52.f	$4$	$8$	$4$	$3.322$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None		✓			416.2.k.e	$2$	$0$	$0$	$0$	$0$	$2$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{4}q^{3}-\beta _{6}q^{5}+(-\beta _{2}+\beta _{6})q^{7}+\cdots$
416.2.u.a	$416$	$2$	416.u	104.m	$4$	$4$	$2$	$3.322$	$\Q(i, \sqrt{26})$	$_{}$	None	None					104.2.m.a	$4$	$0$	$0$	$4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+q^{3}+\beta _{1}q^{5}-\beta _{3}q^{7}-2q^{9}+(-1+\cdots)q^{11}+\cdots$
416.2.u.b	$416$	$2$	416.u	104.m	$4$	$20$	$10$	$3.322$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None			✓		104.2.m.b	$4$	$0$	$0$	$4$	$0$	$0$		$2^{16}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{2}q^{3}+\beta _{15}q^{5}+(\beta _{4}-\beta _{9})q^{7}+(1+\cdots)q^{9}+\cdots$
416.2.w.a	$416$	$2$	416.w	13.e	$6$	$4$	$2$	$3.322$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			416.2.w.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(-2+4\zeta_{12}^{2}+\cdots)q^{5}+\cdots$
416.2.w.b	$416$	$2$	416.w	13.e	$6$	$4$	$2$	$3.322$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-1}) $	None		✓			416.2.w.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{6}]$	$q+(-1+2\zeta_{12}^{2}+\zeta_{12}^{3})q^{5}+(3-3\zeta_{12}^{2}+\cdots)q^{9}+\cdots$
416.2.w.c	$416$	$2$	416.w	13.e	$6$	$8$	$4$	$3.322$	8.0.56070144.2	$_{}$	None	None		✓			416.2.w.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{6}q^{3}+(-\beta _{4}+\beta _{5})q^{5}+\beta _{3}q^{7}+\cdots$
416.2.w.d	$416$	$2$	416.w	13.e	$6$	$12$	$6$	$3.322$	12.0.$\cdots$.1	$_{}$	None	None		✓	✓		416.2.w.d	$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{9}q^{3}+(-2\beta _{4}-\beta _{5}+\beta _{6})q^{5}-\beta _{3}q^{7}+\cdots$
416.2.z.a	$416$	$2$	416.z	104.r	$6$	$24$	$12$	$3.322$		$_{}$	None	None			✓	✓	104.2.r.a	$4$	$0$	$0$	$0$	$0$	$2$			$\mathrm{SU}(2)[C_{6}]$
416.2.ba.a	$416$	$2$	416.ba	104.s	$6$	$4$	$2$	$3.322$	$\Q(\zeta_{12})$	$_{}$	None	None					104.2.s.a	$2$	$0$	$0$	$-6$	$8$	$12$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+\zeta_{12}-\zeta_{12}^{2})q^{3}+(2+2\zeta_{12}+\cdots)q^{5}+\cdots$
416.2.ba.b	$416$	$2$	416.ba	104.s	$6$	$4$	$2$	$3.322$	$\Q(\zeta_{12})$	$_{}$	None	None					104.2.s.a	$2$	$0$	$0$	$6$	$-8$	$12$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(2-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+(-2+\cdots)q^{5}+\cdots$
416.2.ba.c	$416$	$2$	416.ba	104.s	$6$	$16$	$8$	$3.322$	16.0.$\cdots$.2	$_{}$	None	None			✓		104.2.s.c	$4$	$0$	$0$	$0$	$0$	$-18$		$2^{8}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{1}+\beta _{8}+\beta _{12})q^{3}+(-\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots$
416.2.bd.a	$416$	$2$	416.bd	416.ad	$8$	$216$	$54$	$3.322$		$_{}$	None	None		✓	✓	✓	416.2.bd.a	$2$	$0$	$-4$	$-8$	$-4$	$0$			$\mathrm{SU}(2)[C_{8}]$
416.2.bf.a	$416$	$2$	416.bf	32.g	$8$	$192$	$48$	$3.322$		$_{}$	None	None		✓	✓	✓	416.2.bf.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
416.2.bg.a	$416$	$2$	416.bg	416.ag	$8$	$216$	$54$	$3.322$		$_{}$	None	None		✓	✓	✓	416.2.bg.a	$4$	$0$	$0$	$-8$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
416.2.bi.a	$416$	$2$	416.bi	416.ai	$8$	$216$	$54$	$3.322$		$_{}$	None	None		✓	✓	✓	416.2.bd.a	$2$	$0$	$-4$	$-8$	$-4$	$-8$			$\mathrm{SU}(2)[C_{8}]$
416.2.bk.a	$416$	$2$	416.bk	104.u	$12$	$48$	$12$	$3.322$		$_{}$	None	None			✓	✓	104.2.u.a	$4$	$0$	$0$	$4$	$0$	$0$			$\mathrm{SU}(2)[C_{12}]$

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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.