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 85 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
2640.1.l.a	$2640$	$1$	2640.l	660.g	$2$	$1$	$1$	$1.318$	$\Q$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-165}) $	$\Q(\sqrt{15}) $	✓	✓			2640.1.l.a	$4$	$0$	$0$	$-1$	$-1$	$0$		$1$		$q-q^{3}-q^{5}+q^{9}-q^{11}+q^{15}+q^{25}+\cdots$
2640.1.l.b	$2640$	$1$	2640.l	660.g	$2$	$1$	$1$	$1.318$	$\Q$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-165}) $	$\Q(\sqrt{15}) $	✓	✓			2640.1.l.a	$4$	$0$	$0$	$-1$	$1$	$0$		$1$		$q-q^{3}+q^{5}+q^{9}+q^{11}-q^{15}+q^{25}+\cdots$
2640.1.l.c	$2640$	$1$	2640.l	660.g	$2$	$1$	$1$	$1.318$	$\Q$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-165}) $	$\Q(\sqrt{15}) $	✓	✓			2640.1.l.a	$4$	$0$	$0$	$1$	$-1$	$0$		$1$		$q+q^{3}-q^{5}+q^{9}+q^{11}-q^{15}+q^{25}+\cdots$
2640.1.l.d	$2640$	$1$	2640.l	660.g	$2$	$1$	$1$	$1.318$	$\Q$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-165}) $	$\Q(\sqrt{15}) $	✓	✓			2640.1.l.a	$4$	$0$	$0$	$1$	$1$	$0$		$1$		$q+q^{3}+q^{5}+q^{9}-q^{11}+q^{15}+q^{25}+\cdots$
2640.1.l.e	$2640$	$1$	2640.l	660.g	$2$	$2$	$2$	$1.318$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-11}) $	None		✓			2640.1.l.e	$4$	$0$	$0$	$-1$	$-1$	$0$		$1$		$q-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{9}-q^{11}+\cdots$
2640.1.l.f	$2640$	$1$	2640.l	660.g	$2$	$2$	$2$	$1.318$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-11}) $	None		✓			2640.1.l.e	$4$	$0$	$0$	$-1$	$1$	$0$		$1$		$q+\zeta_{6}^{2}q^{3}-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{9}+q^{11}+\cdots$
2640.1.l.g	$2640$	$1$	2640.l	660.g	$2$	$2$	$2$	$1.318$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-11}) $	None		✓			2640.1.l.e	$4$	$0$	$0$	$1$	$-1$	$0$		$1$		$q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{9}+q^{11}+\cdots$
2640.1.l.h	$2640$	$1$	2640.l	660.g	$2$	$2$	$2$	$1.318$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-11}) $	None		✓			2640.1.l.e	$4$	$0$	$0$	$1$	$1$	$0$		$1$		$q-\zeta_{6}^{2}q^{3}-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{9}-q^{11}+\cdots$
2640.1.ch.a	$2640$	$1$	2640.ch	165.l	$4$	$2$	$1$	$1.318$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-11}) $	None					165.1.l.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{3}+i q^{5}-q^{9}+i q^{11}+q^{15}+\cdots$
2640.1.ch.b	$2640$	$1$	2640.ch	165.l	$4$	$2$	$1$	$1.318$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-11}) $	None					165.1.l.a	$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q+q^{3}-i q^{5}+q^{9}-i q^{11}-i q^{15}+\cdots$
2640.1.ch.c	$2640$	$1$	2640.ch	165.l	$4$	$4$	$2$	$1.318$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-11}) $	None					660.1.v.a	$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q-\zeta_{12}^{2}q^{3}-\zeta_{12}^{5}q^{5}+\zeta_{12}^{4}q^{9}+\cdots$
2640.1.ch.d	$2640$	$1$	2640.ch	165.l	$4$	$4$	$2$	$1.318$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-11}) $	None					660.1.v.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{5}q^{3}-\zeta_{12}q^{5}-\zeta_{12}^{4}q^{9}+\zeta_{12}^{3}q^{11}+\cdots$
2640.2.a.a	$2640$	$2$	2640.a	1.a	$1$	$1$	$1$	$21.081$	$\Q$	$_{}$	None	None	✓				1320.2.a.l	$1$	$1$	$0$	$-1$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-2q^{7}+q^{9}-q^{11}+q^{15}+\cdots$
2640.2.a.b	$2640$	$2$	2640.a	1.a	$1$	$1$	$1$	$21.081$	$\Q$	$_{}$	None	None	✓		✓	✓	660.2.a.d	$1$	$0$	$0$	$-1$	$-1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-2q^{7}+q^{9}-q^{11}+2q^{13}+\cdots$
2640.2.a.c	$2640$	$2$	2640.a	1.a	$1$	$1$	$1$	$21.081$	$\Q$	$_{}$	None	None	✓				1320.2.a.k	$1$	$1$	$0$	$-1$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+2q^{7}+q^{9}-q^{11}+q^{15}+\cdots$
2640.2.a.d	$2640$	$2$	2640.a	1.a	$1$	$1$	$1$	$21.081$	$\Q$	$_{}$	None	None	✓				1320.2.a.i	$1$	$0$	$0$	$-1$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+2q^{7}+q^{9}+q^{11}-4q^{13}+\cdots$
2640.2.a.e	$2640$	$2$	2640.a	1.a	$1$	$1$	$1$	$21.081$	$\Q$	$_{}$	None	None	✓				1320.2.a.j	$1$	$0$	$0$	$-1$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+2q^{7}+q^{9}+q^{11}+q^{15}+\cdots$
2640.2.a.f	$2640$	$2$	2640.a	1.a	$1$	$1$	$1$	$21.081$	$\Q$	$_{}$	None	None	✓				660.2.a.c	$1$	$1$	$0$	$-1$	$-1$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+4q^{7}+q^{9}+q^{11}-4q^{13}+\cdots$
2640.2.a.g	$2640$	$2$	2640.a	1.a	$1$	$1$	$1$	$21.081$	$\Q$	$_{}$	None	None	✓		✓	✓	1320.2.a.n	$1$	$1$	$0$	$-1$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{9}+q^{11}-2q^{13}-q^{15}+\cdots$
2640.2.a.h	$2640$	$2$	2640.a	1.a	$1$	$1$	$1$	$21.081$	$\Q$	$_{}$	None	None	✓				330.2.a.e	$1$	$0$	$0$	$-1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{9}+q^{11}-2q^{13}-q^{15}+\cdots$
2640.2.a.i	$2640$	$2$	2640.a	1.a	$1$	$1$	$1$	$21.081$	$\Q$	$_{}$	None	None	✓				1320.2.a.m	$1$	$0$	$0$	$-1$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+4q^{7}+q^{9}-q^{11}-6q^{13}+\cdots$
2640.2.a.j	$2640$	$2$	2640.a	1.a	$1$	$1$	$1$	$21.081$	$\Q$	$_{}$	None	None	✓				330.2.a.c	$1$	$0$	$0$	$1$	$-1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-4q^{7}+q^{9}+q^{11}+2q^{13}+\cdots$
2640.2.a.k	$2640$	$2$	2640.a	1.a	$1$	$1$	$1$	$21.081$	$\Q$	$_{}$	None	None	✓				1320.2.a.d	$1$	$1$	$0$	$1$	$-1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-4q^{7}+q^{9}+q^{11}+2q^{13}+\cdots$
2640.2.a.l	$2640$	$2$	2640.a	1.a	$1$	$1$	$1$	$21.081$	$\Q$	$_{}$	None	None	✓				1320.2.a.c	$1$	$1$	$0$	$1$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-2q^{7}+q^{9}+q^{11}-4q^{13}+\cdots$
2640.2.a.m	$2640$	$2$	2640.a	1.a	$1$	$1$	$1$	$21.081$	$\Q$	$_{}$	None	None	✓				660.2.a.b	$1$	$1$	$0$	$1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{9}-q^{11}-4q^{13}-q^{15}+\cdots$
2640.2.a.n	$2640$	$2$	2640.a	1.a	$1$	$1$	$1$	$21.081$	$\Q$	$_{}$	None	None	✓				330.2.a.a	$1$	$1$	$0$	$1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{9}-q^{11}+2q^{13}-q^{15}+\cdots$
2640.2.a.o	$2640$	$2$	2640.a	1.a	$1$	$1$	$1$	$21.081$	$\Q$	$_{}$	None	None	✓				1320.2.a.b	$1$	$0$	$0$	$1$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+2q^{7}+q^{9}-q^{11}+4q^{13}+\cdots$
2640.2.a.p	$2640$	$2$	2640.a	1.a	$1$	$1$	$1$	$21.081$	$\Q$	$_{}$	None	None	✓				1320.2.a.a	$1$	$1$	$0$	$1$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+2q^{7}+q^{9}+q^{11}-4q^{13}+\cdots$
2640.2.a.q	$2640$	$2$	2640.a	1.a	$1$	$1$	$1$	$21.081$	$\Q$	$_{}$	None	None	✓				660.2.a.a	$1$	$0$	$0$	$1$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+2q^{7}+q^{9}+q^{11}+2q^{13}+\cdots$
2640.2.a.r	$2640$	$2$	2640.a	1.a	$1$	$1$	$1$	$21.081$	$\Q$	$_{}$	None	None	✓				1320.2.a.h	$1$	$1$	$0$	$1$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-4q^{7}+q^{9}-q^{11}+2q^{13}+\cdots$
2640.2.a.s	$2640$	$2$	2640.a	1.a	$1$	$1$	$1$	$21.081$	$\Q$	$_{}$	None	None	✓				1320.2.a.g	$1$	$1$	$0$	$1$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{9}-q^{11}-6q^{13}+q^{15}+\cdots$
2640.2.a.t	$2640$	$2$	2640.a	1.a	$1$	$1$	$1$	$21.081$	$\Q$	$_{}$	None	None	✓				330.2.a.d	$1$	$0$	$0$	$1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{9}-q^{11}+6q^{13}+q^{15}+\cdots$
2640.2.a.u	$2640$	$2$	2640.a	1.a	$1$	$1$	$1$	$21.081$	$\Q$	$_{}$	None	None	✓				1320.2.a.f	$1$	$0$	$0$	$1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{9}+q^{11}-2q^{13}+q^{15}+\cdots$
2640.2.a.v	$2640$	$2$	2640.a	1.a	$1$	$1$	$1$	$21.081$	$\Q$	$_{}$	None	None	✓				330.2.a.b	$1$	$0$	$0$	$1$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+4q^{7}+q^{9}-q^{11}-2q^{13}+\cdots$
2640.2.a.w	$2640$	$2$	2640.a	1.a	$1$	$1$	$1$	$21.081$	$\Q$	$_{}$	None	None	✓				1320.2.a.e	$1$	$0$	$0$	$1$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+4q^{7}+q^{9}+q^{11}+2q^{13}+\cdots$
2640.2.a.x	$2640$	$2$	2640.a	1.a	$1$	$2$	$2$	$21.081$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓		✓		165.2.a.b	$1$	$1$	$0$	$-2$	$-2$	$-4$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-2q^{7}+q^{9}+q^{11}+(2+\cdots)q^{13}+\cdots$
2640.2.a.y	$2640$	$2$	2640.a	1.a	$1$	$2$	$2$	$21.081$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓		✓		660.2.a.f	$1$	$0$	$0$	$-2$	$2$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+(-1-\beta )q^{7}+q^{9}+q^{11}+\cdots$
2640.2.a.z	$2640$	$2$	2640.a	1.a	$1$	$2$	$2$	$21.081$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓		✓		1320.2.a.q	$1$	$0$	$0$	$-2$	$2$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+\beta q^{7}+q^{9}-q^{11}+(2+\cdots)q^{13}+\cdots$
2640.2.a.ba	$2640$	$2$	2640.a	1.a	$1$	$2$	$2$	$21.081$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓		✓		1320.2.a.o	$1$	$0$	$0$	$2$	$-2$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+(1+\beta )q^{7}+q^{9}-q^{11}+\cdots$
2640.2.a.bb	$2640$	$2$	2640.a	1.a	$1$	$2$	$2$	$21.081$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓		✓		165.2.a.a	$1$	$0$	$0$	$2$	$-2$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+(2+\beta )q^{7}+q^{9}+q^{11}+\cdots$
2640.2.a.bc	$2640$	$2$	2640.a	1.a	$1$	$2$	$2$	$21.081$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓		✓		660.2.a.e	$1$	$0$	$0$	$2$	$2$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+(-1-\beta )q^{7}+q^{9}-q^{11}+\cdots$
2640.2.a.bd	$2640$	$2$	2640.a	1.a	$1$	$2$	$2$	$21.081$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓		✓		1320.2.a.p	$1$	$0$	$0$	$2$	$2$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+\beta q^{7}+q^{9}+q^{11}+(2+\cdots)q^{13}+\cdots$
2640.2.a.be	$2640$	$2$	2640.a	1.a	$1$	$3$	$3$	$21.081$	3.3.148.1	$_{}$	None	None	✓		✓	✓	165.2.a.c	$1$	$1$	$0$	$-3$	$3$	$0$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-\beta _{2}q^{7}+q^{9}-q^{11}+(-1+\cdots)q^{13}+\cdots$
2640.2.d.a	$2640$	$2$	2640.d	5.b	$2$	$2$	$2$	$21.081$	$\Q(\sqrt{-1}) $	$_{}$	None	None					660.2.c.a	$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+(-2 i-1)q^{5}+2 i q^{7}+\cdots$
2640.2.d.b	$2640$	$2$	2640.d	5.b	$2$	$2$	$2$	$21.081$	$\Q(\sqrt{-1}) $	$_{}$	None	None					660.2.c.b	$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{3}+(-2 i+1)q^{5}-q^{9}-q^{11}+\cdots$
2640.2.d.c	$2640$	$2$	2640.d	5.b	$2$	$4$	$4$	$21.081$	$\Q(i, \sqrt{10})$	$_{}$	None	None					330.2.c.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{3}+\beta _{1}q^{5}+(-\beta _{1}+2\beta _{2}-\beta _{3})q^{7}+\cdots$
2640.2.d.d	$2640$	$2$	2640.d	5.b	$2$	$4$	$4$	$21.081$	$\Q(i, \sqrt{5})$	$_{}$	None	None					660.2.c.c	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}-\beta _{3}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots$
2640.2.d.e	$2640$	$2$	2640.d	5.b	$2$	$4$	$4$	$21.081$	$\Q(\zeta_{8})$	$_{}$	None	None					330.2.c.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{8}^{2}q^{3}+(\zeta_{8}+2\zeta_{8}^{3})q^{5}+(-\zeta_{8}+\cdots)q^{7}+\cdots$
2640.2.d.f	$2640$	$2$	2640.d	5.b	$2$	$6$	$6$	$21.081$	6.0.350464.1	$_{}$	None	None					1320.2.d.b	$2$	$0$	$0$	$0$	$-2$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{3}+(-\beta _{1}+\beta _{3})q^{5}+(\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots$
2640.2.d.g	$2640$	$2$	2640.d	5.b	$2$	$6$	$6$	$21.081$	6.0.350464.1	$_{}$	None	None					1320.2.d.a	$2$	$0$	$0$	$0$	$-2$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{3}+(\beta _{1}+\beta _{5})q^{5}+(\beta _{1}+\beta _{4})q^{7}+\cdots$

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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.