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 259 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
1920.1.i.a	$1920$	$1$	1920.i	120.i	$2$	$1$	$1$	$0.958$	$\Q$	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-30}) $	$\Q(\sqrt{6}) $	✓	✓			1920.1.i.a	$4$	$0$	$0$	$-1$	$-1$	$0$		$1$		$q-q^{3}-q^{5}+q^{9}+q^{15}-2q^{23}+q^{25}+\cdots$
1920.1.i.b	$1920$	$1$	1920.i	120.i	$2$	$1$	$1$	$0.958$	$\Q$	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-30}) $	$\Q(\sqrt{6}) $	✓	✓			1920.1.i.a	$4$	$0$	$0$	$-1$	$1$	$0$		$1$		$q-q^{3}+q^{5}+q^{9}-q^{15}+2q^{23}+q^{25}+\cdots$
1920.1.i.c	$1920$	$1$	1920.i	120.i	$2$	$1$	$1$	$0.958$	$\Q$	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-30}) $	$\Q(\sqrt{6}) $	✓	✓			1920.1.i.a	$4$	$0$	$0$	$1$	$-1$	$0$		$1$		$q+q^{3}-q^{5}+q^{9}-q^{15}+2q^{23}+q^{25}+\cdots$
1920.1.i.d	$1920$	$1$	1920.i	120.i	$2$	$1$	$1$	$0.958$	$\Q$	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-30}) $	$\Q(\sqrt{6}) $	✓	✓			1920.1.i.a	$4$	$0$	$0$	$1$	$1$	$0$		$1$		$q+q^{3}+q^{5}+q^{9}+q^{15}-2q^{23}+q^{25}+\cdots$
1920.1.i.e	$1920$	$1$	1920.i	120.i	$2$	$2$	$2$	$0.958$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-6}) $	$\Q(\sqrt{30}) $		✓			1920.1.i.e	$8$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-i q^{3}-q^{5}-2 i q^{7}-q^{9}+i q^{15}+\cdots$
1920.1.i.f	$1920$	$1$	1920.i	120.i	$2$	$2$	$2$	$0.958$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-6}) $	$\Q(\sqrt{30}) $		✓			1920.1.i.e	$8$	$0$	$0$	$0$	$2$	$0$		$1$		$q-i q^{3}+q^{5}+2 i q^{7}-q^{9}-i q^{15}+\cdots$
1920.1.u.a	$1920$	$1$	1920.u	120.q	$4$	$4$	$2$	$0.958$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-6}) $	None		✓			1920.1.u.a	$8$	$0$	$0$	$0$	$0$	$-4$		$1$		$q+\zeta_{8}q^{3}-\zeta_{8}^{3}q^{5}+(-1+\zeta_{8}^{2})q^{7}+\cdots$
1920.1.u.b	$1920$	$1$	1920.u	120.q	$4$	$4$	$2$	$0.958$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-6}) $	None		✓			1920.1.u.a	$8$	$0$	$0$	$0$	$0$	$4$		$1$		$q-\zeta_{8}q^{3}-\zeta_{8}^{3}q^{5}+(1-\zeta_{8}^{2})q^{7}+\zeta_{8}^{2}q^{9}+\cdots$
1920.1.bm.a	$1920$	$1$	1920.bm	240.am	$4$	$4$	$2$	$0.958$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-15}) $	None					240.1.bm.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}q^{3}+\zeta_{8}^{3}q^{5}+\zeta_{8}^{2}q^{9}-q^{15}+\cdots$
1920.1.bm.b	$1920$	$1$	1920.bm	240.am	$4$	$4$	$2$	$0.958$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-15}) $	None					240.1.bm.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{3}+\zeta_{8}^{3}q^{5}+\zeta_{8}^{2}q^{9}+q^{15}+\cdots$
1920.1.bu.a	$1920$	$1$	1920.bu	480.au	$8$	$8$	$2$	$0.958$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-15}) $	None			✓	✓	480.1.bu.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{16}^{5}q^{3}-\zeta_{16}^{7}q^{5}-\zeta_{16}^{2}q^{9}+\cdots$
1920.1.db.a	$1920$	$1$	1920.db	1920.cb	$32$	$32$	$2$	$0.958$	$\Q(\zeta_{64})$	$D_{32}$	$\Q(\sqrt{-15}) $	None		✓	✓	✓	1920.1.db.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{64}^{27}q^{2}-\zeta_{64}^{23}q^{3}-\zeta_{64}^{22}q^{4}+\cdots$
1920.2.a.a	$1920$	$2$	1920.a	1.a	$1$	$1$	$1$	$15.331$	$\Q$	$_{}$	None	None	✓	✓			1920.2.a.a	$1$	$0$	$0$	$-1$	$-1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-4q^{7}+q^{9}+2q^{11}+q^{15}+\cdots$
1920.2.a.b	$1920$	$2$	1920.a	1.a	$1$	$1$	$1$	$15.331$	$\Q$	$_{}$	None	None	✓	✓			1920.2.a.b	$1$	$0$	$0$	$-1$	$-1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-2q^{7}+q^{9}-6q^{11}-2q^{13}+\cdots$
1920.2.a.c	$1920$	$2$	1920.a	1.a	$1$	$1$	$1$	$15.331$	$\Q$	$_{}$	None	None	✓	✓			1920.2.a.c	$1$	$1$	$0$	$-1$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-2q^{7}+q^{9}+2q^{11}+6q^{13}+\cdots$
1920.2.a.d	$1920$	$2$	1920.a	1.a	$1$	$1$	$1$	$15.331$	$\Q$	$_{}$	None	None	✓	✓			1920.2.a.d	$1$	$0$	$0$	$-1$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{9}+2q^{11}-4q^{13}+\cdots$
1920.2.a.e	$1920$	$2$	1920.a	1.a	$1$	$1$	$1$	$15.331$	$\Q$	$_{}$	None	None	✓	✓			1920.2.a.e	$1$	$1$	$0$	$-1$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+2q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots$
1920.2.a.f	$1920$	$2$	1920.a	1.a	$1$	$1$	$1$	$15.331$	$\Q$	$_{}$	None	None	✓	✓			1920.2.a.f	$1$	$0$	$0$	$-1$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+4q^{7}+q^{9}+6q^{11}+4q^{13}+\cdots$
1920.2.a.g	$1920$	$2$	1920.a	1.a	$1$	$1$	$1$	$15.331$	$\Q$	$_{}$	None	None	✓	✓			1920.2.a.f	$1$	$1$	$0$	$-1$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-4q^{7}+q^{9}+6q^{11}-4q^{13}+\cdots$
1920.2.a.h	$1920$	$2$	1920.a	1.a	$1$	$1$	$1$	$15.331$	$\Q$	$_{}$	None	None	✓	✓			1920.2.a.e	$1$	$1$	$0$	$-1$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-2q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots$
1920.2.a.i	$1920$	$2$	1920.a	1.a	$1$	$1$	$1$	$15.331$	$\Q$	$_{}$	None	None	✓	✓			1920.2.a.d	$1$	$0$	$0$	$-1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{9}+2q^{11}+4q^{13}+\cdots$
1920.2.a.j	$1920$	$2$	1920.a	1.a	$1$	$1$	$1$	$15.331$	$\Q$	$_{}$	None	None	✓	✓			1920.2.a.b	$1$	$1$	$0$	$-1$	$1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+2q^{7}+q^{9}-6q^{11}+2q^{13}+\cdots$
1920.2.a.k	$1920$	$2$	1920.a	1.a	$1$	$1$	$1$	$15.331$	$\Q$	$_{}$	None	None	✓	✓			1920.2.a.c	$1$	$1$	$0$	$-1$	$1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+2q^{7}+q^{9}+2q^{11}-6q^{13}+\cdots$
1920.2.a.l	$1920$	$2$	1920.a	1.a	$1$	$1$	$1$	$15.331$	$\Q$	$_{}$	None	None	✓	✓			1920.2.a.a	$1$	$0$	$0$	$-1$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+4q^{7}+q^{9}+2q^{11}-q^{15}+\cdots$
1920.2.a.m	$1920$	$2$	1920.a	1.a	$1$	$1$	$1$	$15.331$	$\Q$	$_{}$	None	None	✓	✓			1920.2.a.f	$1$	$0$	$0$	$1$	$-1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-4q^{7}+q^{9}-6q^{11}+4q^{13}+\cdots$
1920.2.a.n	$1920$	$2$	1920.a	1.a	$1$	$1$	$1$	$15.331$	$\Q$	$_{}$	None	None	✓	✓			1920.2.a.e	$1$	$1$	$0$	$1$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-2q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots$
1920.2.a.o	$1920$	$2$	1920.a	1.a	$1$	$1$	$1$	$15.331$	$\Q$	$_{}$	None	None	✓	✓			1920.2.a.d	$1$	$1$	$0$	$1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{9}-2q^{11}-4q^{13}+\cdots$
1920.2.a.p	$1920$	$2$	1920.a	1.a	$1$	$1$	$1$	$15.331$	$\Q$	$_{}$	None	None	✓	✓			1920.2.a.c	$1$	$0$	$0$	$1$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+2q^{7}+q^{9}-2q^{11}+6q^{13}+\cdots$
1920.2.a.q	$1920$	$2$	1920.a	1.a	$1$	$1$	$1$	$15.331$	$\Q$	$_{}$	None	None	✓	✓			1920.2.a.b	$1$	$0$	$0$	$1$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+2q^{7}+q^{9}+6q^{11}-2q^{13}+\cdots$
1920.2.a.r	$1920$	$2$	1920.a	1.a	$1$	$1$	$1$	$15.331$	$\Q$	$_{}$	None	None	✓	✓			1920.2.a.a	$1$	$0$	$0$	$1$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+4q^{7}+q^{9}-2q^{11}-q^{15}+\cdots$
1920.2.a.s	$1920$	$2$	1920.a	1.a	$1$	$1$	$1$	$15.331$	$\Q$	$_{}$	None	None	✓	✓			1920.2.a.a	$1$	$1$	$0$	$1$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-4q^{7}+q^{9}-2q^{11}+q^{15}+\cdots$
1920.2.a.t	$1920$	$2$	1920.a	1.a	$1$	$1$	$1$	$15.331$	$\Q$	$_{}$	None	None	✓	✓			1920.2.a.c	$1$	$1$	$0$	$1$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-2q^{7}+q^{9}-2q^{11}-6q^{13}+\cdots$
1920.2.a.u	$1920$	$2$	1920.a	1.a	$1$	$1$	$1$	$15.331$	$\Q$	$_{}$	None	None	✓	✓			1920.2.a.b	$1$	$0$	$0$	$1$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-2q^{7}+q^{9}+6q^{11}+2q^{13}+\cdots$
1920.2.a.v	$1920$	$2$	1920.a	1.a	$1$	$1$	$1$	$15.331$	$\Q$	$_{}$	None	None	✓	✓			1920.2.a.d	$1$	$0$	$0$	$1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{9}-2q^{11}+4q^{13}+\cdots$
1920.2.a.w	$1920$	$2$	1920.a	1.a	$1$	$1$	$1$	$15.331$	$\Q$	$_{}$	None	None	✓	✓			1920.2.a.e	$1$	$0$	$0$	$1$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+2q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots$
1920.2.a.x	$1920$	$2$	1920.a	1.a	$1$	$1$	$1$	$15.331$	$\Q$	$_{}$	None	None	✓	✓			1920.2.a.f	$1$	$0$	$0$	$1$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+4q^{7}+q^{9}-6q^{11}-4q^{13}+\cdots$
1920.2.a.y	$1920$	$2$	1920.a	1.a	$1$	$2$	$2$	$15.331$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	✓	✓		1920.2.a.y	$1$	$1$	$0$	$-2$	$-2$	$2$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+(1+\beta )q^{7}+q^{9}-2q^{11}+\cdots$
1920.2.a.z	$1920$	$2$	1920.a	1.a	$1$	$2$	$2$	$15.331$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	✓	✓		1920.2.a.y	$1$	$0$	$0$	$-2$	$2$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+(-1-\beta )q^{7}+q^{9}-2q^{11}+\cdots$
1920.2.a.ba	$1920$	$2$	1920.a	1.a	$1$	$2$	$2$	$15.331$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	✓	✓		1920.2.a.y	$1$	$0$	$0$	$2$	$-2$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+(-1-\beta )q^{7}+q^{9}+2q^{11}+\cdots$
1920.2.a.bb	$1920$	$2$	1920.a	1.a	$1$	$2$	$2$	$15.331$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	✓	✓		1920.2.a.y	$1$	$0$	$0$	$2$	$2$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+(1+\beta )q^{7}+q^{9}+2q^{11}+\cdots$
1920.2.b.a	$1920$	$2$	1920.b	24.f	$2$	$8$	$8$	$15.331$	8.0.619810816.2	$_{}$	None	None		✓			1920.2.b.a	$2$	$0$	$0$	$-2$	$-8$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}-q^{5}+(\beta _{2}-\beta _{7})q^{7}+(-1+\cdots)q^{9}+\cdots$
1920.2.b.b	$1920$	$2$	1920.b	24.f	$2$	$8$	$8$	$15.331$	8.0.619810816.2	$_{}$	None	None		✓			1920.2.b.a	$2$	$0$	$0$	$-2$	$8$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+q^{5}+(\beta _{2}-\beta _{7})q^{7}+(-1+\cdots)q^{9}+\cdots$
1920.2.b.c	$1920$	$2$	1920.b	24.f	$2$	$8$	$8$	$15.331$	8.0.$\cdots$.11	$_{}$	None	None		✓			1920.2.b.c	$4$	$0$	$0$	$0$	$-8$	$0$		$2^{5}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-q^{5}-\beta _{3}q^{7}+\beta _{2}q^{9}+(-\beta _{5}+\cdots)q^{13}+\cdots$
1920.2.b.d	$1920$	$2$	1920.b	24.f	$2$	$8$	$8$	$15.331$	8.0.3288334336.2	$_{}$	None	None		✓			1920.2.b.d	$4$	$0$	$0$	$0$	$-8$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{6}q^{3}-q^{5}-\beta _{1}q^{7}+(1+\beta _{5}-\beta _{7})q^{9}+\cdots$
1920.2.b.e	$1920$	$2$	1920.b	24.f	$2$	$8$	$8$	$15.331$	8.0.$\cdots$.11	$_{}$	None	None		✓			1920.2.b.c	$4$	$0$	$0$	$0$	$8$	$0$		$2^{5}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+q^{5}-\beta _{3}q^{7}+\beta _{2}q^{9}+(\beta _{5}+\cdots)q^{13}+\cdots$
1920.2.b.f	$1920$	$2$	1920.b	24.f	$2$	$8$	$8$	$15.331$	8.0.3288334336.2	$_{}$	None	None		✓			1920.2.b.d	$4$	$0$	$0$	$0$	$8$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{6}q^{3}+q^{5}-\beta _{1}q^{7}+(1+\beta _{5}-\beta _{7})q^{9}+\cdots$
1920.2.b.g	$1920$	$2$	1920.b	24.f	$2$	$8$	$8$	$15.331$	8.0.619810816.2	$_{}$	None	None		✓			1920.2.b.a	$2$	$0$	$0$	$2$	$-8$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}-q^{5}+(\beta _{2}-\beta _{7})q^{7}+(-1+\cdots)q^{9}+\cdots$
1920.2.b.h	$1920$	$2$	1920.b	24.f	$2$	$8$	$8$	$15.331$	8.0.619810816.2	$_{}$	None	None		✓			1920.2.b.a	$2$	$0$	$0$	$2$	$8$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{3}+q^{5}+(\beta _{2}-\beta _{7})q^{7}+(-1+\cdots)q^{9}+\cdots$
1920.2.d.a	$1920$	$2$	1920.d	40.f	$2$	$4$	$4$	$15.331$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	None	None		✓			1920.2.d.a	$4$	$0$	$0$	$-4$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}-\beta _{1}q^{5}+q^{9}+(-\beta _{1}-\beta _{2})q^{13}+\cdots$
1920.2.d.b	$1920$	$2$	1920.d	40.f	$2$	$4$	$4$	$15.331$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	None	None		✓			1920.2.d.a	$4$	$0$	$0$	$4$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+\beta _{1}q^{5}+q^{9}+(\beta _{1}+\beta _{2})q^{13}+\cdots$

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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.