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 211 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
2112.1.g.a	$2112$	$1$	2112.g	132.d	$2$	$1$	$1$	$1.054$	$\Q$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-33}) $	$\Q(\sqrt{3}) $	✓				528.1.g.a	$4$	$0$	$0$	$-1$	$0$	$0$		$1$		$q-q^{3}+q^{9}+q^{11}-2q^{23}+q^{25}+\cdots$
2112.1.g.b	$2112$	$1$	2112.g	132.d	$2$	$1$	$1$	$1.054$	$\Q$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-33}) $	$\Q(\sqrt{3}) $	✓				528.1.g.a	$4$	$0$	$0$	$1$	$0$	$0$		$1$		$q+q^{3}+q^{9}-q^{11}+2q^{23}+q^{25}+\cdots$
2112.1.g.c	$2112$	$1$	2112.g	132.d	$2$	$2$	$2$	$1.054$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-11}) $	None					528.1.g.c	$4$	$0$	$0$	$-1$	$0$	$0$		$1$		$q-\zeta_{6}q^{3}+(\zeta_{6}+\zeta_{6}^{2})q^{5}+\zeta_{6}^{2}q^{9}+\cdots$
2112.1.g.d	$2112$	$1$	2112.g	132.d	$2$	$2$	$2$	$1.054$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-11}) $	None					528.1.g.c	$4$	$0$	$0$	$1$	$0$	$0$		$1$		$q-\zeta_{6}^{2}q^{3}+(-\zeta_{6}-\zeta_{6}^{2})q^{5}-\zeta_{6}q^{9}+\cdots$
2112.1.p.a	$2112$	$1$	2112.p	264.p	$2$	$2$	$2$	$1.054$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-6}) $	$\Q(\sqrt{66}) $		✓			2112.1.p.a	$8$	$0$	$0$	$0$	$-4$	$0$		$1$		$q-i q^{3}-2 q^{5}-q^{9}+i q^{11}+2 i q^{15}+\cdots$
2112.1.p.b	$2112$	$1$	2112.p	264.p	$2$	$2$	$2$	$1.054$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-6}) $	$\Q(\sqrt{66}) $		✓			2112.1.p.a	$8$	$0$	$0$	$0$	$4$	$0$		$1$		$q-i q^{3}+2 q^{5}-q^{9}+i q^{11}-2 i q^{15}+\cdots$
2112.1.p.c	$2112$	$1$	2112.p	264.p	$2$	$4$	$4$	$1.054$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-11}) $	None		✓			2112.1.p.c	$8$	$0$	$0$	$0$	$-4$	$0$		$1$		$q-\zeta_{12}q^{3}-q^{5}+\zeta_{12}^{2}q^{9}-\zeta_{12}^{3}q^{11}+\cdots$
2112.1.p.d	$2112$	$1$	2112.p	264.p	$2$	$4$	$4$	$1.054$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-11}) $	None		✓			2112.1.p.c	$8$	$0$	$0$	$0$	$4$	$0$		$1$		$q-\zeta_{12}q^{3}+q^{5}+\zeta_{12}^{2}q^{9}-\zeta_{12}^{3}q^{11}+\cdots$
2112.1.bh.a	$2112$	$1$	2112.bh	264.r	$10$	$8$	$2$	$1.054$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-6}) $	None		✓			2112.1.bh.a	$8$	$0$	$0$	$0$	$-4$	$0$		$1$		$q-\zeta_{20}^{7}q^{3}+(\zeta_{20}^{4}+\zeta_{20}^{8})q^{5}+(-\zeta_{20}^{7}+\cdots)q^{7}+\cdots$
2112.1.bh.b	$2112$	$1$	2112.bh	264.r	$10$	$8$	$2$	$1.054$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-6}) $	None		✓			2112.1.bh.a	$8$	$0$	$0$	$0$	$4$	$0$		$1$		$q+\zeta_{20}^{7}q^{3}+(-\zeta_{20}^{4}-\zeta_{20}^{8})q^{5}+\cdots$
2112.1.bj.a	$2112$	$1$	2112.bj	264.t	$10$	$8$	$2$	$1.054$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-2}) $	None		✓			2112.1.bj.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{20}^{3}q^{3}+\zeta_{20}^{6}q^{9}+\zeta_{20}q^{11}+\cdots$
2112.1.bj.b	$2112$	$1$	2112.bj	264.t	$10$	$8$	$2$	$1.054$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-2}) $	None		✓			2112.1.bj.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{20}^{9}q^{3}-\zeta_{20}^{8}q^{9}-\zeta_{20}q^{11}+\cdots$
2112.2.a.a	$2112$	$2$	2112.a	1.a	$1$	$1$	$1$	$16.864$	$\Q$	$_{}$	None	None	✓				264.2.a.d	$1$	$0$	$0$	$-1$	$-4$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-4q^{5}-2q^{7}+q^{9}+q^{11}+4q^{15}+\cdots$
2112.2.a.b	$2112$	$2$	2112.a	1.a	$1$	$1$	$1$	$16.864$	$\Q$	$_{}$	None	None	✓				132.2.a.a	$1$	$0$	$0$	$-1$	$-2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}-2q^{7}+q^{9}-q^{11}-6q^{13}+\cdots$
2112.2.a.c	$2112$	$2$	2112.a	1.a	$1$	$1$	$1$	$16.864$	$\Q$	$_{}$	None	None	✓				132.2.a.b	$1$	$1$	$0$	$-1$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}-2q^{7}+q^{9}-q^{11}+2q^{13}+\cdots$
2112.2.a.d	$2112$	$2$	2112.a	1.a	$1$	$1$	$1$	$16.864$	$\Q$	$_{}$	None	None	✓				264.2.a.a	$1$	$1$	$0$	$-1$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}+q^{9}+q^{11}-2q^{13}+\cdots$
2112.2.a.e	$2112$	$2$	2112.a	1.a	$1$	$1$	$1$	$16.864$	$\Q$	$_{}$	None	None	✓				66.2.a.b	$1$	$0$	$0$	$-1$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}+4q^{7}+q^{9}-q^{11}+6q^{13}+\cdots$
2112.2.a.f	$2112$	$2$	2112.a	1.a	$1$	$1$	$1$	$16.864$	$\Q$	$_{}$	None	None	✓				1056.2.a.e	$1$	$0$	$0$	$-1$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}+4q^{7}+q^{9}+q^{11}+2q^{13}+\cdots$
2112.2.a.g	$2112$	$2$	2112.a	1.a	$1$	$1$	$1$	$16.864$	$\Q$	$_{}$	None	None	✓				1056.2.a.d	$1$	$1$	$0$	$-1$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{7}+q^{9}-q^{11}-4q^{13}+\cdots$
2112.2.a.h	$2112$	$2$	2112.a	1.a	$1$	$1$	$1$	$16.864$	$\Q$	$_{}$	None	None	✓				264.2.a.c	$1$	$1$	$0$	$-1$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{7}+q^{9}-q^{11}-2q^{17}+\cdots$
2112.2.a.i	$2112$	$2$	2112.a	1.a	$1$	$1$	$1$	$16.864$	$\Q$	$_{}$	None	None	✓				66.2.a.a	$1$	$0$	$0$	$-1$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{7}+q^{9}+q^{11}+4q^{13}+\cdots$
2112.2.a.j	$2112$	$2$	2112.a	1.a	$1$	$1$	$1$	$16.864$	$\Q$	$_{}$	None	None	✓				33.2.a.a	$1$	$1$	$0$	$-1$	$2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}-4q^{7}+q^{9}+q^{11}+2q^{13}+\cdots$
2112.2.a.k	$2112$	$2$	2112.a	1.a	$1$	$1$	$1$	$16.864$	$\Q$	$_{}$	None	None	✓				1056.2.a.c	$1$	$0$	$0$	$-1$	$2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}-2q^{7}+q^{9}-q^{11}+2q^{13}+\cdots$
2112.2.a.l	$2112$	$2$	2112.a	1.a	$1$	$1$	$1$	$16.864$	$\Q$	$_{}$	None	None	✓				1056.2.a.b	$1$	$0$	$0$	$-1$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}+q^{9}+q^{11}+6q^{13}+\cdots$
2112.2.a.m	$2112$	$2$	2112.a	1.a	$1$	$1$	$1$	$16.864$	$\Q$	$_{}$	None	None	✓				264.2.a.b	$1$	$0$	$0$	$-1$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}+4q^{7}+q^{9}+q^{11}-6q^{13}+\cdots$
2112.2.a.n	$2112$	$2$	2112.a	1.a	$1$	$1$	$1$	$16.864$	$\Q$	$_{}$	None	None	✓				66.2.a.c	$1$	$1$	$0$	$-1$	$4$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+4q^{5}-2q^{7}+q^{9}-q^{11}-4q^{13}+\cdots$
2112.2.a.o	$2112$	$2$	2112.a	1.a	$1$	$1$	$1$	$16.864$	$\Q$	$_{}$	None	None	✓				1056.2.a.a	$1$	$0$	$0$	$-1$	$4$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+4q^{5}-2q^{7}+q^{9}+q^{11}-4q^{13}+\cdots$
2112.2.a.p	$2112$	$2$	2112.a	1.a	$1$	$1$	$1$	$16.864$	$\Q$	$_{}$	None	None	✓				264.2.a.d	$1$	$1$	$0$	$1$	$-4$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{5}+2q^{7}+q^{9}-q^{11}-4q^{15}+\cdots$
2112.2.a.q	$2112$	$2$	2112.a	1.a	$1$	$1$	$1$	$16.864$	$\Q$	$_{}$	None	None	✓				1056.2.a.e	$1$	$0$	$0$	$1$	$-2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}-4q^{7}+q^{9}-q^{11}+2q^{13}+\cdots$
2112.2.a.r	$2112$	$2$	2112.a	1.a	$1$	$1$	$1$	$16.864$	$\Q$	$_{}$	None	None	✓				66.2.a.b	$1$	$1$	$0$	$1$	$-2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}-4q^{7}+q^{9}+q^{11}+6q^{13}+\cdots$
2112.2.a.s	$2112$	$2$	2112.a	1.a	$1$	$1$	$1$	$16.864$	$\Q$	$_{}$	None	None	✓				264.2.a.a	$1$	$0$	$0$	$1$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}+q^{9}-q^{11}-2q^{13}+\cdots$
2112.2.a.t	$2112$	$2$	2112.a	1.a	$1$	$1$	$1$	$16.864$	$\Q$	$_{}$	None	None	✓				132.2.a.a	$1$	$1$	$0$	$1$	$-2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}+2q^{7}+q^{9}+q^{11}-6q^{13}+\cdots$
2112.2.a.u	$2112$	$2$	2112.a	1.a	$1$	$1$	$1$	$16.864$	$\Q$	$_{}$	None	None	✓				132.2.a.b	$1$	$0$	$0$	$1$	$-2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}+2q^{7}+q^{9}+q^{11}+2q^{13}+\cdots$
2112.2.a.v	$2112$	$2$	2112.a	1.a	$1$	$1$	$1$	$16.864$	$\Q$	$_{}$	None	None	✓				66.2.a.a	$1$	$1$	$0$	$1$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{7}+q^{9}-q^{11}+4q^{13}+\cdots$
2112.2.a.w	$2112$	$2$	2112.a	1.a	$1$	$1$	$1$	$16.864$	$\Q$	$_{}$	None	None	✓				1056.2.a.d	$1$	$1$	$0$	$1$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{7}+q^{9}+q^{11}-4q^{13}+\cdots$
2112.2.a.x	$2112$	$2$	2112.a	1.a	$1$	$1$	$1$	$16.864$	$\Q$	$_{}$	None	None	✓				264.2.a.c	$1$	$0$	$0$	$1$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{7}+q^{9}+q^{11}-2q^{17}+\cdots$
2112.2.a.y	$2112$	$2$	2112.a	1.a	$1$	$1$	$1$	$16.864$	$\Q$	$_{}$	None	None	✓				264.2.a.b	$1$	$1$	$0$	$1$	$2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}-4q^{7}+q^{9}-q^{11}-6q^{13}+\cdots$
2112.2.a.z	$2112$	$2$	2112.a	1.a	$1$	$1$	$1$	$16.864$	$\Q$	$_{}$	None	None	✓				1056.2.a.b	$1$	$0$	$0$	$1$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}+q^{9}-q^{11}+6q^{13}+\cdots$
2112.2.a.ba	$2112$	$2$	2112.a	1.a	$1$	$1$	$1$	$16.864$	$\Q$	$_{}$	None	None	✓				1056.2.a.c	$1$	$0$	$0$	$1$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}+2q^{7}+q^{9}+q^{11}+2q^{13}+\cdots$
2112.2.a.bb	$2112$	$2$	2112.a	1.a	$1$	$1$	$1$	$16.864$	$\Q$	$_{}$	None	None	✓				33.2.a.a	$1$	$0$	$0$	$1$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}+4q^{7}+q^{9}-q^{11}+2q^{13}+\cdots$
2112.2.a.bc	$2112$	$2$	2112.a	1.a	$1$	$1$	$1$	$16.864$	$\Q$	$_{}$	None	None	✓				1056.2.a.a	$1$	$0$	$0$	$1$	$4$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+4q^{5}+2q^{7}+q^{9}-q^{11}-4q^{13}+\cdots$
2112.2.a.bd	$2112$	$2$	2112.a	1.a	$1$	$1$	$1$	$16.864$	$\Q$	$_{}$	None	None	✓				66.2.a.c	$1$	$0$	$0$	$1$	$4$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+4q^{5}+2q^{7}+q^{9}+q^{11}-4q^{13}+\cdots$
2112.2.a.be	$2112$	$2$	2112.a	1.a	$1$	$2$	$2$	$16.864$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓		✓		1056.2.a.k	$1$	$1$	$0$	$-2$	$-2$	$2$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+(-1-\beta )q^{5}+(1-\beta )q^{7}+q^{9}+\cdots$
2112.2.a.bf	$2112$	$2$	2112.a	1.a	$1$	$2$	$2$	$16.864$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓		✓		1056.2.a.k	$1$	$1$	$0$	$2$	$-2$	$-2$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+(-1-\beta )q^{5}+(-1+\beta )q^{7}+\cdots$
2112.2.a.bg	$2112$	$2$	2112.a	1.a	$1$	$3$	$3$	$16.864$	3.3.229.1	$_{}$	None	None	✓		✓		1056.2.a.m	$1$	$0$	$0$	$-3$	$0$	$4$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{3}+\beta _{1}q^{5}+(1+\beta _{2})q^{7}+q^{9}-q^{11}+\cdots$
2112.2.a.bh	$2112$	$2$	2112.a	1.a	$1$	$3$	$3$	$16.864$	3.3.229.1	$_{}$	None	None	✓		✓		1056.2.a.m	$1$	$0$	$0$	$3$	$0$	$-4$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{3}+\beta _{1}q^{5}+(-1-\beta _{2})q^{7}+q^{9}+\cdots$
2112.2.b.a	$2112$	$2$	2112.b	33.d	$2$	$2$	$2$	$16.864$	$\Q(\sqrt{-2}) $	$_{}$	None	None					1056.2.b.a	$2$	$1$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta )q^{3}+\beta q^{5}+\beta q^{7}+(-1+\cdots)q^{9}+\cdots$
2112.2.b.b	$2112$	$2$	2112.b	33.d	$2$	$2$	$2$	$16.864$	$\Q(\sqrt{-2}) $	$_{}$	None	None					66.2.b.a	$2$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\beta )q^{3}+\beta q^{5}-3\beta q^{7}+(-1+\cdots)q^{9}+\cdots$
2112.2.b.c	$2112$	$2$	2112.b	33.d	$2$	$2$	$2$	$16.864$	$\Q(\sqrt{-2}) $	$_{}$	None	None					1056.2.b.a	$2$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta )q^{3}+\beta q^{5}-\beta q^{7}+(-1+\cdots)q^{9}+\cdots$
2112.2.b.d	$2112$	$2$	2112.b	33.d	$2$	$2$	$2$	$16.864$	$\Q(\sqrt{-2}) $	$_{}$	None	None					66.2.b.a	$2$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\beta )q^{3}+\beta q^{5}+3\beta q^{7}+(-1+\cdots)q^{9}+\cdots$

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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.