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 77 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
2808.1.b.a	$2808$	$1$	2808.b	312.b	$2$	$1$	$1$	$1.401$	$\Q$	$D_{3}$	$\Q(\sqrt{-78}) $	None	✓	✓			2808.1.b.a	$2$	$0$	$-1$	$0$	$0$	$0$		$1$		$q-q^{2}+q^{4}-q^{8}-q^{13}+q^{16}+q^{19}+\cdots$
2808.1.b.b	$2808$	$1$	2808.b	312.b	$2$	$1$	$1$	$1.401$	$\Q$	$D_{3}$	$\Q(\sqrt{-78}) $	None	✓	✓			2808.1.b.a	$2$	$0$	$-1$	$0$	$0$	$0$		$1$		$q-q^{2}+q^{4}-q^{8}+q^{13}+q^{16}-q^{19}+\cdots$
2808.1.b.c	$2808$	$1$	2808.b	312.b	$2$	$1$	$1$	$1.401$	$\Q$	$D_{3}$	$\Q(\sqrt{-78}) $	None	✓	✓			2808.1.b.a	$2$	$0$	$1$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}+q^{8}-q^{13}+q^{16}+q^{19}+\cdots$
2808.1.b.d	$2808$	$1$	2808.b	312.b	$2$	$1$	$1$	$1.401$	$\Q$	$D_{3}$	$\Q(\sqrt{-78}) $	None	✓	✓			2808.1.b.a	$2$	$0$	$1$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}+q^{8}+q^{13}+q^{16}-q^{19}+\cdots$
2808.1.b.e	$2808$	$1$	2808.b	312.b	$2$	$8$	$8$	$1.401$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-39}) $	None		✓	✓		2808.1.b.e	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}q^{2}+\zeta_{24}^{2}q^{4}+(\zeta_{24}^{5}+\zeta_{24}^{7}+\cdots)q^{5}+\cdots$
2808.1.o.a	$2808$	$1$	2808.o	104.h	$2$	$8$	$8$	$1.401$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-39}) $	None		✓	✓	✓	2808.1.o.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}q^{2}+\zeta_{24}^{2}q^{4}+(-\zeta_{24}^{5}+\zeta_{24}^{7}+\cdots)q^{5}+\cdots$
2808.1.z.a	$2808$	$1$	2808.z	312.w	$4$	$4$	$2$	$1.401$	$\Q(\zeta_{8})$	$S_{4}$	None	None		✓			2808.1.z.a	$4$	$0$	$0$	$0$	$-4$	$0$		$1$		$q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-1+\zeta_{8}^{2})q^{5}+\cdots$
2808.1.z.b	$2808$	$1$	2808.z	312.w	$4$	$4$	$2$	$1.401$	$\Q(\zeta_{8})$	$S_{4}$	None	None		✓			2808.1.z.a	$4$	$0$	$0$	$0$	$4$	$0$		$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(1-\zeta_{8}^{2})q^{5}+\zeta_{8}^{3}q^{7}+\cdots$
2808.1.bf.a	$2808$	$1$	2808.bf	39.i	$6$	$4$	$2$	$1.401$	$\Q(\sqrt{-2}, \sqrt{-3})$	$S_{4}$	None	None		✓	✓	✓	2808.1.bf.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q+\beta _{3}q^{5}+\beta _{2}q^{7}+\beta _{1}q^{11}+(1-\beta _{2}+\cdots)q^{13}+\cdots$
2808.1.bs.a	$2808$	$1$	2808.bs	936.as	$6$	$6$	$3$	$1.401$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-26}) $	None					936.1.bs.a	$4$	$0$	$-3$	$0$	$0$	$0$		$3$		$q-\zeta_{18}^{3}q^{2}+\zeta_{18}^{6}q^{4}+(-\zeta_{18}+\zeta_{18}^{2}+\cdots)q^{5}+\cdots$
2808.1.bs.b	$2808$	$1$	2808.bs	936.as	$6$	$6$	$3$	$1.401$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-26}) $	None					936.1.bs.a	$4$	$0$	$3$	$0$	$0$	$0$		$3$		$q+\zeta_{18}^{3}q^{2}+\zeta_{18}^{6}q^{4}+(\zeta_{18}^{5}+\zeta_{18}^{7}+\cdots)q^{5}+\cdots$
2808.1.dd.a	$2808$	$1$	2808.dd	312.ah	$6$	$8$	$4$	$1.401$	$\Q(\zeta_{24})$	$S_{4}$	None	None		✓	✓	✓	2808.1.dd.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{5}q^{2}+\zeta_{24}^{10}q^{4}+\zeta_{24}^{3}q^{8}+\cdots$
2808.1.dp.a	$2808$	$1$	2808.dp	117.y	$12$	$4$	$1$	$1.401$	$\Q(\zeta_{12})$	$S_{4}$	None	None					936.1.dm.b	$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q+(-\zeta_{12}^{2}-\zeta_{12}^{5})q^{5}-\zeta_{12}^{2}q^{13}+\cdots$
2808.1.dp.b	$2808$	$1$	2808.dp	117.y	$12$	$4$	$1$	$1.401$	$\Q(\zeta_{12})$	$S_{4}$	None	None					936.1.dm.a	$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q+(\zeta_{12}+\zeta_{12}^{4})q^{7}+(-\zeta_{12}-\zeta_{12}^{4}+\cdots)q^{11}+\cdots$
2808.1.fi.a	$2808$	$1$	2808.fi	2808.ei	$18$	$18$	$3$	$1.401$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-26}) $	None		✓			2808.1.fi.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{54}^{24}q^{2}-\zeta_{54}^{7}q^{3}-\zeta_{54}^{21}q^{4}+\cdots$
2808.1.fi.b	$2808$	$1$	2808.fi	2808.ei	$18$	$18$	$3$	$1.401$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-26}) $	None		✓			2808.1.fi.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{54}^{24}q^{2}-\zeta_{54}^{7}q^{3}-\zeta_{54}^{21}q^{4}+\cdots$
2808.2.a.a	$2808$	$2$	2808.a	1.a	$1$	$1$	$1$	$22.422$	$\Q$	$_{}$	None	None	✓	✓			2808.2.a.a	$1$	$1$	$0$	$0$	$-3$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}+2q^{7}+4q^{11}-q^{13}-6q^{17}+\cdots$
2808.2.a.b	$2808$	$2$	2808.a	1.a	$1$	$1$	$1$	$22.422$	$\Q$	$_{}$	None	None	✓	✓			2808.2.a.b	$1$	$0$	$0$	$0$	$-2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-4q^{7}+2q^{11}-q^{13}+q^{19}+\cdots$
2808.2.a.c	$2808$	$2$	2808.a	1.a	$1$	$1$	$1$	$22.422$	$\Q$	$_{}$	None	None	✓	✓			2808.2.a.c	$1$	$0$	$0$	$0$	$-2$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-3q^{7}+q^{11}-q^{13}-4q^{17}+\cdots$
2808.2.a.d	$2808$	$2$	2808.a	1.a	$1$	$1$	$1$	$22.422$	$\Q$	$_{}$	None	None	✓	✓			2808.2.a.d	$1$	$1$	$0$	$0$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{7}+q^{13}+4q^{17}+2q^{19}+\cdots$
2808.2.a.e	$2808$	$2$	2808.a	1.a	$1$	$1$	$1$	$22.422$	$\Q$	$_{}$	None	None	✓	✓			2808.2.a.e	$1$	$0$	$0$	$0$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{7}+4q^{11}-q^{13}+6q^{17}+\cdots$
2808.2.a.f	$2808$	$2$	2808.a	1.a	$1$	$1$	$1$	$22.422$	$\Q$	$_{}$	None	None	✓	✓			2808.2.a.f	$1$	$0$	$0$	$0$	$-1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+3q^{7}+3q^{11}+q^{13}+2q^{17}+\cdots$
2808.2.a.g	$2808$	$2$	2808.a	1.a	$1$	$1$	$1$	$22.422$	$\Q$	$_{}$	None	None	✓	✓			2808.2.a.g	$1$	$0$	$0$	$0$	$0$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{7}-3q^{11}-q^{13}+2q^{17}+6q^{19}+\cdots$
2808.2.a.h	$2808$	$2$	2808.a	1.a	$1$	$1$	$1$	$22.422$	$\Q$	$_{}$	None	None	✓	✓			2808.2.a.g	$1$	$1$	$0$	$0$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{7}+3q^{11}-q^{13}-2q^{17}+6q^{19}+\cdots$
2808.2.a.i	$2808$	$2$	2808.a	1.a	$1$	$1$	$1$	$22.422$	$\Q$	$_{}$	None	None	✓	✓			2808.2.a.d	$1$	$0$	$0$	$0$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{7}+q^{13}-4q^{17}+2q^{19}+\cdots$
2808.2.a.j	$2808$	$2$	2808.a	1.a	$1$	$1$	$1$	$22.422$	$\Q$	$_{}$	None	None	✓	✓			2808.2.a.e	$1$	$1$	$0$	$0$	$1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+2q^{7}-4q^{11}-q^{13}-6q^{17}+\cdots$
2808.2.a.k	$2808$	$2$	2808.a	1.a	$1$	$1$	$1$	$22.422$	$\Q$	$_{}$	None	None	✓	✓			2808.2.a.f	$1$	$0$	$0$	$0$	$1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+3q^{7}-3q^{11}+q^{13}-2q^{17}+\cdots$
2808.2.a.l	$2808$	$2$	2808.a	1.a	$1$	$1$	$1$	$22.422$	$\Q$	$_{}$	None	None	✓	✓			2808.2.a.b	$1$	$0$	$0$	$0$	$2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-4q^{7}-2q^{11}-q^{13}+q^{19}+\cdots$
2808.2.a.m	$2808$	$2$	2808.a	1.a	$1$	$1$	$1$	$22.422$	$\Q$	$_{}$	None	None	✓	✓			2808.2.a.c	$1$	$1$	$0$	$0$	$2$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-3q^{7}-q^{11}-q^{13}+4q^{17}+\cdots$
2808.2.a.n	$2808$	$2$	2808.a	1.a	$1$	$1$	$1$	$22.422$	$\Q$	$_{}$	None	None	✓	✓			2808.2.a.a	$1$	$0$	$0$	$0$	$3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}+2q^{7}-4q^{11}-q^{13}+6q^{17}+\cdots$
2808.2.a.o	$2808$	$2$	2808.a	1.a	$1$	$2$	$2$	$22.422$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓			2808.2.a.o	$1$	$1$	$0$	$0$	$-3$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{5}+(-1-2\beta )q^{7}+(2+\beta )q^{11}+\cdots$
2808.2.a.p	$2808$	$2$	2808.a	1.a	$1$	$2$	$2$	$22.422$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	✓			2808.2.a.p	$1$	$1$	$0$	$0$	$-3$	$5$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{5}+(2+\beta )q^{7}+(-4+\beta )q^{11}+\cdots$
2808.2.a.q	$2808$	$2$	2808.a	1.a	$1$	$2$	$2$	$22.422$	$\Q(\sqrt{6}) $	$_{}$	None	None	✓	✓			2808.2.a.q	$1$	$1$	$0$	$0$	$-2$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{5}+2q^{7}-2q^{11}-q^{13}+\cdots$
2808.2.a.r	$2808$	$2$	2808.a	1.a	$1$	$2$	$2$	$22.422$	$\Q(\sqrt{37}) $	$_{}$	None	None	✓	✓			2808.2.a.r	$1$	$0$	$0$	$0$	$-1$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{5}+3q^{7}+(-3-\beta )q^{11}-q^{13}+\cdots$
2808.2.a.s	$2808$	$2$	2808.a	1.a	$1$	$2$	$2$	$22.422$	$\Q(\sqrt{37}) $	$_{}$	None	None	✓	✓	✓		2808.2.a.r	$1$	$0$	$0$	$0$	$1$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}+3q^{7}+(3+\beta )q^{11}-q^{13}+\cdots$
2808.2.a.t	$2808$	$2$	2808.a	1.a	$1$	$2$	$2$	$22.422$	$\Q(\sqrt{6}) $	$_{}$	None	None	✓	✓			2808.2.a.q	$1$	$0$	$0$	$0$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{5}+2q^{7}+2q^{11}-q^{13}+\cdots$
2808.2.a.u	$2808$	$2$	2808.a	1.a	$1$	$2$	$2$	$22.422$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓			2808.2.a.o	$1$	$1$	$0$	$0$	$3$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{5}+(-1-2\beta )q^{7}+(-2-\beta )q^{11}+\cdots$
2808.2.a.v	$2808$	$2$	2808.a	1.a	$1$	$2$	$2$	$22.422$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	✓			2808.2.a.p	$1$	$0$	$0$	$0$	$3$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{5}+(2+\beta )q^{7}+(4-\beta )q^{11}+\cdots$
2808.2.a.w	$2808$	$2$	2808.a	1.a	$1$	$3$	$3$	$22.422$	3.3.2213.1	$_{}$	None	None	✓	✓	✓		2808.2.a.w	$1$	$0$	$0$	$0$	$-5$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-2+\beta _{1})q^{5}+\beta _{2}q^{7}+(2+\beta _{1}+\beta _{2})q^{11}+\cdots$
2808.2.a.x	$2808$	$2$	2808.a	1.a	$1$	$3$	$3$	$22.422$	3.3.1101.1	$_{}$	None	None	✓	✓	✓		2808.2.a.x	$1$	$1$	$0$	$0$	$-2$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{5}-q^{7}+(2-\beta _{1}+\beta _{2})q^{11}+\cdots$
2808.2.a.y	$2808$	$2$	2808.a	1.a	$1$	$3$	$3$	$22.422$	3.3.1016.1	$_{}$	None	None	✓	✓	✓		2808.2.a.y	$1$	$1$	$0$	$0$	$-2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{5}+(-\beta _{1}-\beta _{2})q^{7}+(\beta _{1}+\cdots)q^{11}+\cdots$
2808.2.a.z	$2808$	$2$	2808.a	1.a	$1$	$3$	$3$	$22.422$	3.3.1101.1	$_{}$	None	None	✓	✓	✓		2808.2.a.x	$1$	$1$	$0$	$0$	$2$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{5}-q^{7}+(-2+\beta _{1}-\beta _{2})q^{11}+\cdots$
2808.2.a.ba	$2808$	$2$	2808.a	1.a	$1$	$3$	$3$	$22.422$	3.3.1016.1	$_{}$	None	None	✓	✓			2808.2.a.y	$1$	$0$	$0$	$0$	$2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{5}+(-\beta _{1}-\beta _{2})q^{7}+(-\beta _{1}+\cdots)q^{11}+\cdots$
2808.2.a.bb	$2808$	$2$	2808.a	1.a	$1$	$3$	$3$	$22.422$	3.3.2213.1	$_{}$	None	None	✓	✓			2808.2.a.w	$1$	$0$	$0$	$0$	$5$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(2-\beta _{1})q^{5}+\beta _{2}q^{7}+(-2-\beta _{1}-\beta _{2})q^{11}+\cdots$
2808.2.c.a	$2808$	$2$	2808.c	13.b	$2$	$2$	$2$	$22.422$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			2808.2.c.a	$2$	$1$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3 i q^{5}+4 i q^{7}-4 i q^{11}+(-2 i-3)q^{13}+\cdots$
2808.2.c.b	$2808$	$2$	2808.c	13.b	$2$	$2$	$2$	$22.422$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			2808.2.c.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3 i q^{5}-4 i q^{7}-4 i q^{11}+(2 i-3)q^{13}+\cdots$
2808.2.c.c	$2808$	$2$	2808.c	13.b	$2$	$4$	$4$	$22.422$	$\Q(i, \sqrt{17})$	$_{}$	None	None		✓			2808.2.c.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}+(-\beta _{1}-\beta _{2})q^{7}+(\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots$
2808.2.c.d	$2808$	$2$	2808.c	13.b	$2$	$4$	$4$	$22.422$	$\Q(i, \sqrt{17})$	$_{}$	None	None		✓			2808.2.c.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}+(\beta _{1}+\beta _{2})q^{7}+(\beta _{1}+\beta _{2})q^{11}+\cdots$
2808.2.c.e	$2808$	$2$	2808.c	13.b	$2$	$14$	$14$	$22.422$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	$_{}$	None	None		✓			2808.2.c.e	$2$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}-\beta _{4}q^{7}+\beta _{7}q^{11}-\beta _{13}q^{13}+\cdots$
2808.2.c.f	$2808$	$2$	2808.c	13.b	$2$	$14$	$14$	$22.422$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	$_{}$	None	None		✓			2808.2.c.e	$2$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}+\beta _{4}q^{7}+\beta _{7}q^{11}-\beta _{10}q^{13}+\cdots$

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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.