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 61 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
2912.1.f.a	$2912$	$1$	2912.f	91.b	$2$	$4$	$4$	$1.453$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-13}) $	None		✓	✓	✓	2912.1.f.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{7}+q^{9}+(\zeta_{8}+\zeta_{8}^{3})q^{11}-\zeta_{8}^{2}q^{13}+\cdots$
2912.1.l.a	$2912$	$1$	2912.l	728.l	$2$	$1$	$1$	$1.453$	$\Q$	$D_{3}$	$\Q(\sqrt{-182}) $	None	✓				728.1.l.a	$2$	$0$	$0$	$-1$	$0$	$-1$		$1$		$q-q^{3}-q^{7}-q^{11}-q^{13}+q^{21}+q^{23}+\cdots$
2912.1.l.b	$2912$	$1$	2912.l	728.l	$2$	$1$	$1$	$1.453$	$\Q$	$D_{3}$	$\Q(\sqrt{-182}) $	None	✓				728.1.l.a	$2$	$0$	$0$	$-1$	$0$	$1$		$1$		$q-q^{3}+q^{7}+q^{11}-q^{13}-q^{21}+q^{23}+\cdots$
2912.1.l.c	$2912$	$1$	2912.l	728.l	$2$	$1$	$1$	$1.453$	$\Q$	$D_{3}$	$\Q(\sqrt{-182}) $	None	✓				728.1.l.a	$2$	$0$	$0$	$1$	$0$	$-1$		$1$		$q+q^{3}-q^{7}+q^{11}+q^{13}-q^{21}+q^{23}+\cdots$
2912.1.l.d	$2912$	$1$	2912.l	728.l	$2$	$1$	$1$	$1.453$	$\Q$	$D_{3}$	$\Q(\sqrt{-182}) $	None	✓				728.1.l.a	$2$	$0$	$0$	$1$	$0$	$1$		$1$		$q+q^{3}+q^{7}-q^{11}+q^{13}+q^{21}+q^{23}+\cdots$
2912.1.l.e	$2912$	$1$	2912.l	728.l	$2$	$4$	$4$	$1.453$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-14}) $	None			✓		728.1.l.e	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{8}-\zeta_{8}^{3})q^{3}+(-\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots$
2912.1.bs.a	$2912$	$1$	2912.bs	364.q	$6$	$4$	$2$	$1.453$	$\Q(\zeta_{12})$	$A_{4}$	None	None		✓	✓	✓	2912.1.bs.a	$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q+\zeta_{12}^{2}q^{5}-\zeta_{12}^{3}q^{7}+q^{9}-q^{13}+\cdots$
2912.1.cb.a	$2912$	$1$	2912.cb	728.al	$6$	$8$	$4$	$1.453$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-14}) $	None			✓	✓	728.1.bl.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{24}^{9}+\zeta_{24}^{11})q^{3}+(\zeta_{24}^{5}+\zeta_{24}^{7}+\cdots)q^{5}+\cdots$
2912.1.ci.a	$2912$	$1$	2912.ci	728.as	$6$	$6$	$3$	$1.453$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-26}) $	None					728.1.bs.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{18}^{2}-\zeta_{18}^{4})q^{3}+(\zeta_{18}-\zeta_{18}^{2}+\cdots)q^{5}+\cdots$
2912.1.ci.b	$2912$	$1$	2912.ci	728.as	$6$	$6$	$3$	$1.453$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-26}) $	None					728.1.bs.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{18}^{7}-\zeta_{18}^{8})q^{3}+(\zeta_{18}^{4}+\zeta_{18}^{8}+\cdots)q^{5}+\cdots$
2912.1.cn.a	$2912$	$1$	2912.cn	728.ax	$6$	$4$	$2$	$1.453$	$\Q(\zeta_{12})$	$A_{4}$	None	None			✓	✓	728.1.bx.a	$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q+\zeta_{12}^{2}q^{3}+\zeta_{12}^{5}q^{5}-\zeta_{12}^{3}q^{7}+\cdots$
2912.1.cu.a	$2912$	$1$	2912.cu	728.be	$6$	$2$	$1$	$1.453$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-14}) $	None					728.1.ce.a	$4$	$0$	$0$	$-1$	$-2$	$1$		$1$		$q+\zeta_{6}^{2}q^{3}-q^{5}+\zeta_{6}q^{7}-\zeta_{6}q^{13}+\cdots$
2912.1.cu.b	$2912$	$1$	2912.cu	728.be	$6$	$2$	$1$	$1.453$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-14}) $	None					728.1.ce.a	$4$	$0$	$0$	$1$	$2$	$1$		$1$		$q-\zeta_{6}^{2}q^{3}+q^{5}+\zeta_{6}q^{7}+\zeta_{6}q^{13}+\cdots$
2912.1.cu.c	$2912$	$1$	2912.cu	728.be	$6$	$4$	$2$	$1.453$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-14}) $	None			✓		728.1.ce.c	$8$	$0$	$0$	$0$	$0$	$-2$		$1$		$q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(-\zeta_{12}+\zeta_{12}^{5}+\cdots)q^{5}+\cdots$
2912.1.de.a	$2912$	$1$	2912.de	91.s	$6$	$8$	$4$	$1.453$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-13}) $	None		✓	✓	✓	2912.1.de.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{7}q^{7}-\zeta_{24}^{4}q^{9}+(\zeta_{24}^{7}-\zeta_{24}^{9}+\cdots)q^{11}+\cdots$
2912.1.dg.a	$2912$	$1$	2912.dg	364.ai	$6$	$4$	$2$	$1.453$	$\Q(\zeta_{12})$	$A_{4}$	None	None		✓	✓	✓	2912.1.bs.a	$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q-\zeta_{12}^{4}q^{5}+\zeta_{12}^{5}q^{7}-\zeta_{12}^{2}q^{9}+\cdots$
2912.1.dj.a	$2912$	$1$	2912.dj	364.al	$6$	$4$	$2$	$1.453$	$\Q(\zeta_{12})$	$A_{4}$	None	None		✓			2912.1.dj.a	$4$	$0$	$0$	$0$	$0$	$-4$		$1$		$q-\zeta_{12}q^{3}-\zeta_{12}^{5}q^{5}-q^{7}+\zeta_{12}^{4}q^{11}+\cdots$
2912.1.dj.b	$2912$	$1$	2912.dj	364.al	$6$	$4$	$2$	$1.453$	$\Q(\zeta_{12})$	$A_{4}$	None	None		✓			2912.1.dj.b	$4$	$0$	$0$	$0$	$0$	$-4$		$1$		$q+\zeta_{12}q^{3}-\zeta_{12}^{5}q^{5}-q^{7}+\zeta_{12}^{4}q^{11}+\cdots$
2912.1.dj.c	$2912$	$1$	2912.dj	364.al	$6$	$4$	$2$	$1.453$	$\Q(\zeta_{12})$	$A_{4}$	None	None		✓			2912.1.dj.a	$4$	$0$	$0$	$0$	$0$	$4$		$1$		$q+\zeta_{12}q^{3}-\zeta_{12}^{5}q^{5}+q^{7}-\zeta_{12}^{4}q^{11}+\cdots$
2912.1.dj.d	$2912$	$1$	2912.dj	364.al	$6$	$4$	$2$	$1.453$	$\Q(\zeta_{12})$	$A_{4}$	None	None		✓			2912.1.dj.b	$4$	$0$	$0$	$0$	$0$	$4$		$1$		$q-\zeta_{12}q^{3}-\zeta_{12}^{5}q^{5}+q^{7}-\zeta_{12}^{4}q^{11}+\cdots$
2912.1.dy.a	$2912$	$1$	2912.dy	728.ci	$6$	$4$	$2$	$1.453$	$\Q(\zeta_{12})$	$A_{4}$	None	None			✓	✓	728.1.bx.a	$4$	$0$	$0$	$-4$	$0$	$0$		$1$		$q-q^{3}+\zeta_{12}^{5}q^{5}+\zeta_{12}^{5}q^{7}-q^{11}+\cdots$
2912.2.a.a	$2912$	$2$	2912.a	1.a	$1$	$1$	$1$	$23.252$	$\Q$	$_{}$	None	None	✓	✓			2912.2.a.a	$1$	$1$	$0$	$-1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}-2q^{9}+q^{11}+q^{13}+4q^{17}+\cdots$
2912.2.a.b	$2912$	$2$	2912.a	1.a	$1$	$1$	$1$	$23.252$	$\Q$	$_{}$	None	None	✓	✓			2912.2.a.b	$1$	$1$	$0$	$-1$	$4$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+4q^{5}-q^{7}-2q^{9}-5q^{11}+\cdots$
2912.2.a.c	$2912$	$2$	2912.a	1.a	$1$	$1$	$1$	$23.252$	$\Q$	$_{}$	None	None	✓	✓			2912.2.a.c	$1$	$0$	$0$	$0$	$-2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-q^{7}-3q^{9}-4q^{11}+q^{13}+\cdots$
2912.2.a.d	$2912$	$2$	2912.a	1.a	$1$	$1$	$1$	$23.252$	$\Q$	$_{}$	None	None	✓	✓			2912.2.a.c	$1$	$0$	$0$	$0$	$-2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+q^{7}-3q^{9}+4q^{11}+q^{13}+\cdots$
2912.2.a.e	$2912$	$2$	2912.a	1.a	$1$	$1$	$1$	$23.252$	$\Q$	$_{}$	None	None	✓	✓			2912.2.a.a	$1$	$0$	$0$	$1$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}-2q^{9}-q^{11}+q^{13}+4q^{17}+\cdots$
2912.2.a.f	$2912$	$2$	2912.a	1.a	$1$	$1$	$1$	$23.252$	$\Q$	$_{}$	None	None	✓	✓			2912.2.a.b	$1$	$0$	$0$	$1$	$4$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+4q^{5}+q^{7}-2q^{9}+5q^{11}+\cdots$
2912.2.a.g	$2912$	$2$	2912.a	1.a	$1$	$3$	$3$	$23.252$	3.3.564.1	$_{}$	None	None	✓	✓			2912.2.a.g	$1$	$1$	$0$	$-2$	$1$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(1-\beta _{1}+\beta _{2})q^{5}+\cdots$
2912.2.a.h	$2912$	$2$	2912.a	1.a	$1$	$3$	$3$	$23.252$	3.3.148.1	$_{}$	None	None	✓	✓			2912.2.a.h	$1$	$1$	$0$	$0$	$-5$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+(-2+\beta _{1})q^{5}-q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots$
2912.2.a.i	$2912$	$2$	2912.a	1.a	$1$	$3$	$3$	$23.252$	3.3.148.1	$_{}$	None	None	✓	✓			2912.2.a.h	$1$	$1$	$0$	$0$	$-5$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+(-2+\beta _{1})q^{5}+q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots$
2912.2.a.j	$2912$	$2$	2912.a	1.a	$1$	$3$	$3$	$23.252$	3.3.148.1	$_{}$	None	None	✓	✓			2912.2.a.j	$1$	$1$	$0$	$0$	$1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+\beta _{1}q^{5}-q^{7}+(-\beta _{1}-\beta _{2})q^{9}+\cdots$
2912.2.a.k	$2912$	$2$	2912.a	1.a	$1$	$3$	$3$	$23.252$	3.3.148.1	$_{}$	None	None	✓	✓			2912.2.a.j	$1$	$1$	$0$	$0$	$1$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+\beta _{1}q^{5}+q^{7}+(-\beta _{1}-\beta _{2})q^{9}+\cdots$
2912.2.a.l	$2912$	$2$	2912.a	1.a	$1$	$3$	$3$	$23.252$	3.3.564.1	$_{}$	None	None	✓	✓			2912.2.a.g	$1$	$0$	$0$	$2$	$1$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(1-\beta _{1}+\beta _{2})q^{5}-q^{7}+\cdots$
2912.2.a.m	$2912$	$2$	2912.a	1.a	$1$	$4$	$4$	$23.252$	4.4.11348.1	$_{}$	None	None	✓	✓	✓		2912.2.a.m	$1$	$1$	$0$	$-2$	$-1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{3}-\beta _{1}q^{5}-q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots$
2912.2.a.n	$2912$	$2$	2912.a	1.a	$1$	$4$	$4$	$23.252$	4.4.33844.1	$_{}$	None	None	✓	✓	✓		2912.2.a.n	$1$	$1$	$0$	$-1$	$-1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+\beta _{3}q^{5}-q^{7}+(\beta _{1}+\beta _{2})q^{9}+\cdots$
2912.2.a.o	$2912$	$2$	2912.a	1.a	$1$	$4$	$4$	$23.252$	4.4.33844.1	$_{}$	None	None	✓	✓			2912.2.a.n	$1$	$0$	$0$	$1$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+\beta _{3}q^{5}+q^{7}+(\beta _{1}+\beta _{2})q^{9}+\cdots$
2912.2.a.p	$2912$	$2$	2912.a	1.a	$1$	$4$	$4$	$23.252$	4.4.11348.1	$_{}$	None	None	✓	✓			2912.2.a.m	$1$	$0$	$0$	$2$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{3}-\beta _{1}q^{5}+q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots$
2912.2.a.q	$2912$	$2$	2912.a	1.a	$1$	$5$	$5$	$23.252$	5.5.1025428.1	$_{}$	None	None	✓	✓	✓		2912.2.a.q	$1$	$1$	$0$	$-5$	$-3$	$5$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{3}+(-1+\beta _{4})q^{5}+q^{7}+\cdots$
2912.2.a.r	$2912$	$2$	2912.a	1.a	$1$	$5$	$5$	$23.252$	5.5.6329476.1	$_{}$	None	None	✓	✓	✓		2912.2.a.r	$1$	$0$	$0$	$0$	$3$	$-5$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(1-\beta _{3})q^{5}-q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots$
2912.2.a.s	$2912$	$2$	2912.a	1.a	$1$	$5$	$5$	$23.252$	5.5.6329476.1	$_{}$	None	None	✓	✓	✓		2912.2.a.r	$1$	$0$	$0$	$0$	$3$	$5$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(1-\beta _{3})q^{5}+q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots$
2912.2.a.t	$2912$	$2$	2912.a	1.a	$1$	$5$	$5$	$23.252$	5.5.1025428.1	$_{}$	None	None	✓	✓			2912.2.a.q	$1$	$0$	$0$	$5$	$-3$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{3}+(-1+\beta _{4})q^{5}-q^{7}+\cdots$
2912.2.a.u	$2912$	$2$	2912.a	1.a	$1$	$6$	$6$	$23.252$	6.6.153499364.1	$_{}$	None	None	✓	✓	✓		2912.2.a.u	$1$	$0$	$0$	$-4$	$3$	$-6$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}-\beta _{5}q^{5}-q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots$
2912.2.a.v	$2912$	$2$	2912.a	1.a	$1$	$6$	$6$	$23.252$	6.6.153499364.1	$_{}$	None	None	✓	✓	✓		2912.2.a.u	$1$	$0$	$0$	$4$	$3$	$6$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}-\beta _{5}q^{5}+q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots$
2912.2.c.a	$2912$	$2$	2912.c	8.b	$2$	$34$	$34$	$23.252$		$_{}$	None	None					728.2.c.a	$2$	$0$	$0$	$0$	$0$	$34$			$\mathrm{SU}(2)[C_{2}]$
2912.2.c.b	$2912$	$2$	2912.c	8.b	$2$	$38$	$38$	$23.252$		$_{}$	None	None			✓		728.2.c.b	$2$	$0$	$0$	$0$	$0$	$-38$			$\mathrm{SU}(2)[C_{2}]$
2912.2.h.a	$2912$	$2$	2912.h	56.e	$2$	$48$	$48$	$23.252$		$_{}$	None	None					728.2.h.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
2912.2.h.b	$2912$	$2$	2912.h	56.e	$2$	$48$	$48$	$23.252$		$_{}$	None	None					728.2.h.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
2912.2.i.a	$2912$	$2$	2912.i	104.e	$2$	$84$	$84$	$23.252$		$_{}$	None	None			✓	✓	728.2.i.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
2912.2.j.a	$2912$	$2$	2912.j	28.d	$2$	$48$	$48$	$23.252$		$_{}$	None	None		✓			2912.2.j.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
2912.2.j.b	$2912$	$2$	2912.j	28.d	$2$	$48$	$48$	$23.252$		$_{}$	None	None		✓			2912.2.j.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$

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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.