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 145 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
2268.1.h.a	$2268$	$1$	2268.h	84.h	$2$	$8$	$8$	$1.132$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-7}) $	None		✓	✓	✓	2268.1.h.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}q^{2}+\zeta_{24}^{2}q^{4}+\zeta_{24}^{6}q^{7}-\zeta_{24}^{3}q^{8}+\cdots$
2268.1.m.a	$2268$	$1$	2268.m	63.n	$6$	$2$	$1$	$1.132$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None					84.1.p.a	$4$	$0$	$0$	$0$	$0$	$-1$		$1$		$q+\zeta_{6}^{2}q^{7}-\zeta_{6}^{2}q^{13}+\zeta_{6}q^{19}+q^{25}+\cdots$
2268.1.m.b	$2268$	$1$	2268.m	63.n	$6$	$2$	$1$	$1.132$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None					756.1.bk.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q+q^{7}+\zeta_{6}^{2}q^{13}+\zeta_{6}q^{19}+q^{25}+\cdots$
2268.1.p.a	$2268$	$1$	2268.p	63.k	$6$	$2$	$1$	$1.132$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None					756.1.z.a	$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-q^{7}+(1+\zeta_{6})q^{19}+q^{25}+(1+\zeta_{6}+\cdots)q^{31}+\cdots$
2268.1.p.b	$2268$	$1$	2268.p	63.k	$6$	$2$	$1$	$1.132$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None					252.1.z.a	$4$	$0$	$0$	$0$	$0$	$1$		$1$		$q+\zeta_{6}q^{7}+(1-\zeta_{6}^{2})q^{13}+(-1-\zeta_{6}+\cdots)q^{19}+\cdots$
2268.1.s.a	$2268$	$1$	2268.s	252.s	$6$	$2$	$1$	$1.132$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-21}) $	None					756.1.h.a	$4$	$0$	$-1$	$0$	$-1$	$1$		$1$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+\cdots$
2268.1.s.b	$2268$	$1$	2268.s	252.s	$6$	$2$	$1$	$1.132$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-21}) $	None					756.1.h.a	$4$	$0$	$-1$	$0$	$1$	$-1$		$1$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}+\cdots$
2268.1.s.c	$2268$	$1$	2268.s	252.s	$6$	$2$	$1$	$1.132$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-21}) $	None					756.1.h.a	$4$	$0$	$1$	$0$	$-1$	$-1$		$1$		$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}+\cdots$
2268.1.s.d	$2268$	$1$	2268.s	252.s	$6$	$2$	$1$	$1.132$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-21}) $	None					756.1.h.a	$4$	$0$	$1$	$0$	$1$	$1$		$1$		$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+\cdots$
2268.1.s.e	$2268$	$1$	2268.s	252.s	$6$	$8$	$4$	$1.132$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-7}) $	None		✓			2268.1.h.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{24}^{9}q^{2}-\zeta_{24}^{6}q^{4}-\zeta_{24}^{2}q^{7}+\cdots$
2268.1.s.f	$2268$	$1$	2268.s	252.s	$6$	$8$	$4$	$1.132$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-7}) $	None		✓			2268.1.h.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+\zeta_{24}^{2}q^{7}+\cdots$
2268.1.s.g	$2268$	$1$	2268.s	252.s	$6$	$8$	$4$	$1.132$	$\Q(\zeta_{24})$	$D_{4}$	$\Q(\sqrt{-7}) $	None					252.1.h.a	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{5}q^{2}+\zeta_{24}^{10}q^{4}-\zeta_{24}^{2}q^{7}+\cdots$
2268.1.bc.a	$2268$	$1$	2268.bc	63.l	$6$	$2$	$1$	$1.132$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{21}) $					756.1.d.a	$4$	$0$	$0$	$0$	$-3$	$1$		$1$		$q+(-1+\zeta_{6}^{2})q^{5}-\zeta_{6}^{2}q^{7}+(-\zeta_{6}+\cdots)q^{17}+\cdots$
2268.1.bc.b	$2268$	$1$	2268.bc	63.l	$6$	$2$	$1$	$1.132$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None					756.1.d.b	$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-q^{7}+(1-\zeta_{6}^{2})q^{13}+(-\zeta_{6}-\zeta_{6}^{2}+\cdots)q^{19}+\cdots$
2268.1.bc.c	$2268$	$1$	2268.bc	63.l	$6$	$2$	$1$	$1.132$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None					756.1.d.b	$4$	$0$	$0$	$0$	$0$	$1$		$1$		$q+\zeta_{6}q^{7}+(-1+\zeta_{6}^{2})q^{13}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{19}+\cdots$
2268.1.bc.d	$2268$	$1$	2268.bc	63.l	$6$	$2$	$1$	$1.132$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{21}) $					756.1.d.a	$4$	$0$	$0$	$0$	$3$	$1$		$1$		$q+(1-\zeta_{6}^{2})q^{5}-\zeta_{6}^{2}q^{7}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{17}+\cdots$
2268.1.bd.a	$2268$	$1$	2268.bd	63.t	$6$	$2$	$1$	$1.132$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None					252.1.z.a	$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-q^{7}+(-1+\zeta_{6}^{2})q^{13}+(-1+\zeta_{6}^{2}+\cdots)q^{19}+\cdots$
2268.1.bd.b	$2268$	$1$	2268.bd	63.t	$6$	$2$	$1$	$1.132$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None					756.1.z.a	$4$	$0$	$0$	$0$	$0$	$1$		$1$		$q+\zeta_{6}q^{7}+(1-\zeta_{6}^{2})q^{19}-\zeta_{6}q^{25}+\cdots$
2268.1.bh.a	$2268$	$1$	2268.bh	63.j	$6$	$2$	$1$	$1.132$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None					756.1.bk.a	$4$	$0$	$0$	$0$	$0$	$-1$		$1$		$q+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{13}-\zeta_{6}^{2}q^{19}+\zeta_{6}^{2}q^{25}+\cdots$
2268.1.bh.b	$2268$	$1$	2268.bh	63.j	$6$	$2$	$1$	$1.132$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None					84.1.p.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q+q^{7}-\zeta_{6}^{2}q^{13}-\zeta_{6}^{2}q^{19}+\zeta_{6}^{2}q^{25}+\cdots$
2268.2.a.a	$2268$	$2$	2268.a	1.a	$1$	$1$	$1$	$18.110$	$\Q$	$_{}$	None	None	✓	✓			2268.2.a.a	$1$	$0$	$0$	$0$	$-2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-q^{7}-q^{11}+2q^{17}+2q^{19}+\cdots$
2268.2.a.b	$2268$	$2$	2268.a	1.a	$1$	$1$	$1$	$18.110$	$\Q$	$_{}$	None	None	✓	✓			2268.2.a.b	$1$	$1$	$0$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{7}-3q^{11}-4q^{13}+6q^{17}-4q^{19}+\cdots$
2268.2.a.c	$2268$	$2$	2268.a	1.a	$1$	$1$	$1$	$18.110$	$\Q$	$_{}$	None	None	✓	✓			2268.2.a.b	$1$	$1$	$0$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{7}+3q^{11}-4q^{13}-6q^{17}-4q^{19}+\cdots$
2268.2.a.d	$2268$	$2$	2268.a	1.a	$1$	$1$	$1$	$18.110$	$\Q$	$_{}$	None	None	✓	✓			2268.2.a.a	$1$	$0$	$0$	$0$	$2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-q^{7}+q^{11}-2q^{17}+2q^{19}+\cdots$
2268.2.a.e	$2268$	$2$	2268.a	1.a	$1$	$2$	$2$	$18.110$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	✓			2268.2.a.e	$2$	$0$	$0$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2\beta q^{5}+q^{7}+\beta q^{11}-4q^{13}+2\beta q^{17}+\cdots$
2268.2.a.f	$2268$	$2$	2268.a	1.a	$1$	$2$	$2$	$18.110$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	✓			2268.2.a.f	$2$	$0$	$0$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}+q^{7}+2\beta q^{11}+5q^{13}+\beta q^{17}+\cdots$
2268.2.a.g	$2268$	$2$	2268.a	1.a	$1$	$3$	$3$	$18.110$	3.3.321.1	$_{}$	None	None	✓		✓		252.2.j.b	$1$	$1$	$0$	$0$	$-3$	$3$	$+$	$3$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{5}+q^{7}+(-2-\beta _{1})q^{11}+\cdots$
2268.2.a.h	$2268$	$2$	2268.a	1.a	$1$	$3$	$3$	$18.110$	3.3.321.1	$_{}$	None	None	✓				252.2.j.a	$1$	$1$	$0$	$0$	$-1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{5}-q^{7}+(-1-\beta _{1}-2\beta _{2})q^{11}+\cdots$
2268.2.a.i	$2268$	$2$	2268.a	1.a	$1$	$3$	$3$	$18.110$	3.3.321.1	$_{}$	None	None	✓		✓		252.2.j.a	$1$	$0$	$0$	$0$	$1$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{5}-q^{7}+(1+\beta _{1}+2\beta _{2})q^{11}+\cdots$
2268.2.a.j	$2268$	$2$	2268.a	1.a	$1$	$3$	$3$	$18.110$	3.3.321.1	$_{}$	None	None	✓		✓		252.2.j.b	$1$	$0$	$0$	$0$	$3$	$3$	$-$	$3$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{5}+q^{7}+(2+\beta _{1})q^{11}-q^{13}+\cdots$
2268.2.a.k	$2268$	$2$	2268.a	1.a	$1$	$4$	$4$	$18.110$	$\Q(\sqrt{3}, \sqrt{19})$	$_{}$	None	None	✓	✓	✓		2268.2.a.k	$2$	$1$	$0$	$0$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{5}-q^{7}+(-\beta _{1}-\beta _{2})q^{11}+(-2+\cdots)q^{13}+\cdots$
2268.2.f.a	$2268$	$2$	2268.f	21.c	$2$	$16$	$16$	$18.110$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			2268.2.f.a	$4$	$0$	$0$	$0$	$0$	$-4$		$2^{8}\cdot 3^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{5}+\beta _{10}q^{7}-\beta _{4}q^{11}+\beta _{13}q^{13}+\cdots$
2268.2.f.b	$2268$	$2$	2268.f	21.c	$2$	$16$	$16$	$18.110$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None					252.2.x.a	$4$	$0$	$0$	$0$	$0$	$2$		$2^{8}\cdot 3^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{15}q^{5}+\beta _{9}q^{7}+\beta _{1}q^{11}+\beta _{7}q^{13}+\cdots$
2268.2.i.a	$2268$	$2$	2268.i	63.h	$3$	$2$	$1$	$18.110$	$\Q(\sqrt{-3}) $	$_{}$	None	None					28.2.e.a	$2$	$1$	$0$	$0$	$-3$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-3+3\zeta_{6})q^{5}+(1-3\zeta_{6})q^{7}+3\zeta_{6}q^{11}+\cdots$
2268.2.i.b	$2268$	$2$	2268.i	63.h	$3$	$2$	$1$	$18.110$	$\Q(\sqrt{-3}) $	$_{}$	None	None					84.2.i.a	$2$	$0$	$0$	$0$	$-2$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{5}+(1+2\zeta_{6})q^{7}+2\zeta_{6}q^{11}+\cdots$
2268.2.i.c	$2268$	$2$	2268.i	63.h	$3$	$2$	$1$	$18.110$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None					252.2.k.b	$4$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{U}(1)[D_{3}]$	$q+(-3+2\zeta_{6})q^{7}-5\zeta_{6}q^{13}+\zeta_{6}q^{19}+\cdots$
2268.2.i.d	$2268$	$2$	2268.i	63.h	$3$	$2$	$1$	$18.110$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None					756.2.k.c	$4$	$0$	$0$	$0$	$0$	$-1$		$1$	$\mathrm{U}(1)[D_{3}]$	$q+(-2+3\zeta_{6})q^{7}-2\zeta_{6}q^{13}+\zeta_{6}q^{19}+\cdots$
2268.2.i.e	$2268$	$2$	2268.i	63.h	$3$	$2$	$1$	$18.110$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None					756.2.k.a	$4$	$0$	$0$	$0$	$0$	$-1$		$1$	$\mathrm{U}(1)[D_{3}]$	$q+(1-3\zeta_{6})q^{7}+7\zeta_{6}q^{13}-8\zeta_{6}q^{19}+\cdots$
2268.2.i.f	$2268$	$2$	2268.i	63.h	$3$	$2$	$1$	$18.110$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None					756.2.k.b	$4$	$0$	$0$	$0$	$0$	$5$		$1$	$\mathrm{U}(1)[D_{3}]$	$q+(3-\zeta_{6})q^{7}-5\zeta_{6}q^{13}-8\zeta_{6}q^{19}+\cdots$
2268.2.i.g	$2268$	$2$	2268.i	63.h	$3$	$2$	$1$	$18.110$	$\Q(\sqrt{-3}) $	$_{}$	None	None					84.2.i.a	$2$	$0$	$0$	$0$	$2$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{5}+(1+2\zeta_{6})q^{7}-2\zeta_{6}q^{11}+\cdots$
2268.2.i.h	$2268$	$2$	2268.i	63.h	$3$	$2$	$1$	$18.110$	$\Q(\sqrt{-3}) $	$_{}$	None	None					28.2.e.a	$2$	$0$	$0$	$0$	$3$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(3-3\zeta_{6})q^{5}+(1-3\zeta_{6})q^{7}-3\zeta_{6}q^{11}+\cdots$
2268.2.i.i	$2268$	$2$	2268.i	63.h	$3$	$4$	$2$	$18.110$	$\Q(\sqrt{-3}, \sqrt{10})$	$_{}$	None	None					756.2.k.d	$4$	$0$	$0$	$0$	$0$	$-10$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{5}+(-2+\beta _{2})q^{7}+(-2\beta _{1}-2\beta _{3})q^{11}+\cdots$
2268.2.i.j	$2268$	$2$	2268.i	63.h	$3$	$6$	$3$	$18.110$	6.0.309123.1	$_{}$	None	None					756.2.k.e	$2$	$0$	$0$	$0$	$-1$	$2$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}+\beta _{2}+\beta _{4}-\beta _{5})q^{5}+(1+\beta _{3}+\cdots)q^{7}+\cdots$
2268.2.i.k	$2268$	$2$	2268.i	63.h	$3$	$6$	$3$	$18.110$	6.0.309123.1	$_{}$	None	None					756.2.k.e	$2$	$0$	$0$	$0$	$1$	$2$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}-\beta _{2}-\beta _{4}+\beta _{5})q^{5}+(1+\beta _{3}+\cdots)q^{7}+\cdots$
2268.2.i.l	$2268$	$2$	2268.i	63.h	$3$	$8$	$4$	$18.110$	8.0.310217769.2	$_{}$	None	None		✓			2268.2.k.c	$2$	$0$	$0$	$0$	$-2$	$1$		$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}+\beta _{2})q^{5}+\beta _{5}q^{7}+(1-\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots$
2268.2.i.m	$2268$	$2$	2268.i	63.h	$3$	$8$	$4$	$18.110$	8.0.310217769.2	$_{}$	None	None		✓			2268.2.k.c	$2$	$0$	$0$	$0$	$2$	$1$		$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}-\beta _{2})q^{5}+\beta _{5}q^{7}+(-1+\beta _{1}+\cdots)q^{11}+\cdots$
2268.2.i.n	$2268$	$2$	2268.i	63.h	$3$	$16$	$8$	$18.110$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓	✓		2268.2.k.g	$4$	$0$	$0$	$0$	$0$	$-6$		$3^{7}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{13}q^{5}+\beta _{3}q^{7}-\beta _{12}q^{11}+(2-2\beta _{4}+\cdots)q^{13}+\cdots$
2268.2.j.a	$2268$	$2$	2268.j	9.c	$3$	$2$	$1$	$18.110$	$\Q(\sqrt{-3}) $	$_{}$	None	None					84.2.a.a	$2$	$0$	$0$	$0$	$-4$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-4\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots$
2268.2.j.b	$2268$	$2$	2268.j	9.c	$3$	$2$	$1$	$18.110$	$\Q(\sqrt{-3}) $	$_{}$	None	None					756.2.a.a	$2$	$0$	$0$	$0$	$-3$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-3\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+(-3+3\zeta_{6})q^{11}+\cdots$
2268.2.j.c	$2268$	$2$	2268.j	9.c	$3$	$2$	$1$	$18.110$	$\Q(\sqrt{-3}) $	$_{}$	None	None					756.2.a.b	$2$	$1$	$0$	$0$	$-3$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-3\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}-2\zeta_{6}q^{13}+\cdots$

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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.