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 193 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
1296.1.g.a	$1296$	$1$	1296.g	4.b	$2$	$2$	$2$	$0.647$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-1}) $	None	✓	✓	✓	✓	1296.1.g.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta q^{5}+q^{13}+\beta q^{17}+2q^{25}+\beta q^{29}+\cdots$
1296.1.o.a	$1296$	$1$	1296.o	36.f	$6$	$2$	$1$	$0.647$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None					432.1.g.a	$4$	$0$	$0$	$0$	$0$	$-3$		$1$		$q+(-1+\zeta_{6}^{2})q^{7}+\zeta_{6}^{2}q^{13}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{19}+\cdots$
1296.1.o.b	$1296$	$1$	1296.o	36.f	$6$	$2$	$1$	$0.647$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-1}) $	$\Q(\sqrt{3}) $					144.1.g.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{6}^{2}q^{13}+\zeta_{6}q^{25}+q^{37}+\zeta_{6}^{2}q^{49}+\cdots$
1296.1.o.c	$1296$	$1$	1296.o	36.f	$6$	$2$	$1$	$0.647$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None					432.1.g.a	$4$	$0$	$0$	$0$	$0$	$3$		$1$		$q+(1-\zeta_{6}^{2})q^{7}+\zeta_{6}^{2}q^{13}+(-\zeta_{6}-\zeta_{6}^{2}+\cdots)q^{19}+\cdots$
1296.1.o.d	$1296$	$1$	1296.o	36.f	$6$	$4$	$2$	$0.647$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-1}) $	None		✓	✓		1296.1.g.a	$8$	$0$	$0$	$0$	$0$	$0$		$3$		$q+(\zeta_{12}+\zeta_{12}^{3})q^{5}-\zeta_{12}^{2}q^{13}+(\zeta_{12}+\cdots)q^{17}+\cdots$
1296.1.q.a	$1296$	$1$	1296.q	9.d	$6$	$2$	$1$	$0.647$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None			✓	✓	108.1.c.a	$4$	$0$	$0$	$0$	$0$	$-1$		$1$		$q-\zeta_{6}q^{7}-\zeta_{6}^{2}q^{13}+q^{19}-\zeta_{6}q^{25}+\cdots$
1296.1.x.a	$1296$	$1$	1296.x	144.w	$12$	$8$	$2$	$0.647$	$\Q(\zeta_{24})$	$S_{4}$	None	None			✓	✓	432.1.j.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}q^{2}+\zeta_{24}^{2}q^{4}+\zeta_{24}^{5}q^{5}-\zeta_{24}^{10}q^{7}+\cdots$
1296.2.a.a	$1296$	$2$	1296.a	1.a	$1$	$1$	$1$	$10.349$	$\Q$	$_{}$	None	None	✓				324.2.a.b	$1$	$0$	$0$	$0$	$-3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}-2q^{7}-6q^{11}+5q^{13}+3q^{17}+\cdots$
1296.2.a.b	$1296$	$2$	1296.a	1.a	$1$	$1$	$1$	$10.349$	$\Q$	$_{}$	None	None	✓				36.2.e.a	$1$	$1$	$0$	$0$	$-3$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}+q^{7}+3q^{11}-q^{13}-6q^{17}+\cdots$
1296.2.a.c	$1296$	$2$	1296.a	1.a	$1$	$1$	$1$	$10.349$	$\Q$	$_{}$	None	None	✓				162.2.a.a	$1$	$0$	$0$	$0$	$-3$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}+4q^{7}-q^{13}-3q^{17}+4q^{19}+\cdots$
1296.2.a.d	$1296$	$2$	1296.a	1.a	$1$	$1$	$1$	$10.349$	$\Q$	$_{}$	None	None	✓				648.2.a.b	$1$	$1$	$0$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+4q^{11}-5q^{13}-5q^{17}-8q^{19}+\cdots$
1296.2.a.e	$1296$	$2$	1296.a	1.a	$1$	$1$	$1$	$10.349$	$\Q$	$_{}$	None	None	✓				72.2.i.a	$1$	$1$	$0$	$0$	$-1$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+3q^{7}-5q^{11}-5q^{13}-2q^{17}+\cdots$
1296.2.a.f	$1296$	$2$	1296.a	1.a	$1$	$1$	$1$	$10.349$	$\Q$	$_{}$	None	None	✓				18.2.c.a	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}-3q^{11}+2q^{13}+3q^{17}+q^{19}+\cdots$
1296.2.a.g	$1296$	$2$	1296.a	1.a	$1$	$1$	$1$	$10.349$	$\Q$	$_{}$	None	None	✓				18.2.c.a	$1$	$0$	$0$	$0$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}+3q^{11}+2q^{13}-3q^{17}+q^{19}+\cdots$
1296.2.a.h	$1296$	$2$	1296.a	1.a	$1$	$1$	$1$	$10.349$	$\Q$	$_{}$	None	None	✓				648.2.a.b	$1$	$1$	$0$	$0$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-4q^{11}-5q^{13}+5q^{17}-8q^{19}+\cdots$
1296.2.a.i	$1296$	$2$	1296.a	1.a	$1$	$1$	$1$	$10.349$	$\Q$	$_{}$	None	None	✓				72.2.i.a	$1$	$0$	$0$	$0$	$1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+3q^{7}+5q^{11}-5q^{13}+2q^{17}+\cdots$
1296.2.a.j	$1296$	$2$	1296.a	1.a	$1$	$1$	$1$	$10.349$	$\Q$	$_{}$	None	None	✓				324.2.a.b	$1$	$0$	$0$	$0$	$3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}-2q^{7}+6q^{11}+5q^{13}-3q^{17}+\cdots$
1296.2.a.k	$1296$	$2$	1296.a	1.a	$1$	$1$	$1$	$10.349$	$\Q$	$_{}$	None	None	✓				36.2.e.a	$1$	$0$	$0$	$0$	$3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}+q^{7}-3q^{11}-q^{13}+6q^{17}+\cdots$
1296.2.a.l	$1296$	$2$	1296.a	1.a	$1$	$1$	$1$	$10.349$	$\Q$	$_{}$	None	None	✓				162.2.a.a	$1$	$0$	$0$	$0$	$3$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}+4q^{7}-q^{13}+3q^{17}+4q^{19}+\cdots$
1296.2.a.m	$1296$	$2$	1296.a	1.a	$1$	$2$	$2$	$10.349$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				648.2.a.e	$1$	$0$	$0$	$0$	$-4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-2+\beta )q^{5}+2\beta q^{7}+2q^{11}+(1+\cdots)q^{13}+\cdots$
1296.2.a.n	$1296$	$2$	1296.a	1.a	$1$	$2$	$2$	$10.349$	$\Q(\sqrt{33}) $	$_{}$	None	None	✓		✓		72.2.i.b	$1$	$1$	$0$	$0$	$-1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{5}+(-2+\beta )q^{7}-q^{11}+(2+\beta )q^{13}+\cdots$
1296.2.a.o	$1296$	$2$	1296.a	1.a	$1$	$2$	$2$	$10.349$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓		✓		81.2.a.a	$2$	$1$	$0$	$0$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}-2q^{7}-2\beta q^{11}-q^{13}-3\beta q^{17}+\cdots$
1296.2.a.p	$1296$	$2$	1296.a	1.a	$1$	$2$	$2$	$10.349$	$\Q(\sqrt{33}) $	$_{}$	None	None	✓				72.2.i.b	$1$	$0$	$0$	$0$	$1$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}+(-2+\beta )q^{7}+q^{11}+(2+\beta )q^{13}+\cdots$
1296.2.a.q	$1296$	$2$	1296.a	1.a	$1$	$2$	$2$	$10.349$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				648.2.a.e	$1$	$0$	$0$	$0$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(2+\beta )q^{5}-2\beta q^{7}-2q^{11}+(1-2\beta )q^{13}+\cdots$
1296.2.c.a	$1296$	$2$	1296.c	12.b	$2$	$2$	$2$	$10.349$	$\Q(\sqrt{-3}) $	$_{}$	None	None					144.2.s.b	$2$	$1$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{5}-\beta q^{7}-3 q^{11}-5 q^{13}+4\beta q^{17}+\cdots$
1296.2.c.b	$1296$	$2$	1296.c	12.b	$2$	$2$	$2$	$10.349$	$\Q(\sqrt{-3}) $	$_{}$	None	None					144.2.s.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-2\beta q^{5}-2\beta q^{7}-3 q^{11}+4 q^{13}+\cdots$
1296.2.c.c	$1296$	$2$	1296.c	12.b	$2$	$2$	$2$	$10.349$	$\Q(\sqrt{-3}) $	$_{}$	None	None					144.2.s.b	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{5}+\beta q^{7}+3 q^{11}-5 q^{13}+4\beta q^{17}+\cdots$
1296.2.c.d	$1296$	$2$	1296.c	12.b	$2$	$2$	$2$	$10.349$	$\Q(\sqrt{-3}) $	$_{}$	None	None					144.2.s.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-2\beta q^{5}+2\beta q^{7}+3 q^{11}+4 q^{13}+\cdots$
1296.2.c.e	$1296$	$2$	1296.c	12.b	$2$	$4$	$4$	$10.349$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	$\Q(\sqrt{-1}) $	None		✓			1296.2.c.e	$4$	$0$	$0$	$0$	$0$	$0$		$3^{3}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{5}+(-2+\beta _{3})q^{13}+(\beta _{1}-\beta _{2}+\cdots)q^{17}+\cdots$
1296.2.c.f	$1296$	$2$	1296.c	12.b	$2$	$4$	$4$	$10.349$	$\Q(\zeta_{12})$	$_{}$	None	None					144.2.s.e	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_{2} q^{5}-\beta_1 q^{7}-\beta_{3} q^{11}+q^{13}+\cdots$
1296.2.c.g	$1296$	$2$	1296.c	12.b	$2$	$8$	$8$	$10.349$	$\Q(\zeta_{24})$	$_{}$	None	None		✓	✓		1296.2.c.g	$4$	$0$	$0$	$0$	$0$	$0$		$2^{6}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_{3} q^{5}-\beta_{4} q^{7}-\beta_{2} q^{11}+q^{13}+\cdots$
1296.2.i.a	$1296$	$2$	1296.i	9.c	$3$	$2$	$1$	$10.349$	$\Q(\sqrt{-3}) $	$_{}$	None	None					216.2.a.a	$2$	$1$	$0$	$0$	$-4$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-4\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+(4-4\zeta_{6})q^{11}+\cdots$
1296.2.i.b	$1296$	$2$	1296.i	9.c	$3$	$2$	$1$	$10.349$	$\Q(\sqrt{-3}) $	$_{}$	None	None					162.2.a.a	$2$	$0$	$0$	$0$	$-3$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-3\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{7}+\zeta_{6}q^{13}+\cdots$
1296.2.i.c	$1296$	$2$	1296.i	9.c	$3$	$2$	$1$	$10.349$	$\Q(\sqrt{-3}) $	$_{}$	None	None					54.2.a.a	$2$	$0$	$0$	$0$	$-3$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-3\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+(-3+3\zeta_{6})q^{11}+\cdots$
1296.2.i.d	$1296$	$2$	1296.i	9.c	$3$	$2$	$1$	$10.349$	$\Q(\sqrt{-3}) $	$_{}$	None	None					324.2.a.b	$2$	$1$	$0$	$0$	$-3$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-3\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+(-6+6\zeta_{6})q^{11}+\cdots$
1296.2.i.e	$1296$	$2$	1296.i	9.c	$3$	$2$	$1$	$10.349$	$\Q(\sqrt{-3}) $	$_{}$	None	None					24.2.a.a	$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-2\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{11}+2\zeta_{6}q^{13}+\cdots$
1296.2.i.f	$1296$	$2$	1296.i	9.c	$3$	$2$	$1$	$10.349$	$\Q(\sqrt{-3}) $	$_{}$	None	None					648.2.a.b	$2$	$0$	$0$	$0$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{5}+(4-4\zeta_{6})q^{11}+5\zeta_{6}q^{13}+\cdots$
1296.2.i.g	$1296$	$2$	1296.i	9.c	$3$	$2$	$1$	$10.349$	$\Q(\sqrt{-3}) $	$_{}$	None	None					216.2.a.b	$2$	$0$	$0$	$0$	$-1$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+(-5+5\zeta_{6})q^{11}+\cdots$
1296.2.i.h	$1296$	$2$	1296.i	9.c	$3$	$2$	$1$	$10.349$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None					36.2.a.a	$4$	$1$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{U}(1)[D_{3}]$	$q+(-4+4\zeta_{6})q^{7}-2\zeta_{6}q^{13}-8q^{19}+\cdots$
1296.2.i.i	$1296$	$2$	1296.i	9.c	$3$	$2$	$1$	$10.349$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None					27.2.a.a	$4$	$0$	$0$	$0$	$0$	$-1$		$1$	$\mathrm{U}(1)[D_{3}]$	$q+(-1+\zeta_{6})q^{7}-5\zeta_{6}q^{13}+7q^{19}+\cdots$
1296.2.i.j	$1296$	$2$	1296.i	9.c	$3$	$2$	$1$	$10.349$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None					108.2.a.a	$4$	$0$	$0$	$0$	$0$	$5$		$1$	$\mathrm{U}(1)[D_{3}]$	$q+(5-5\zeta_{6})q^{7}+7\zeta_{6}q^{13}+q^{19}+(5+\cdots)q^{25}+\cdots$
1296.2.i.k	$1296$	$2$	1296.i	9.c	$3$	$2$	$1$	$10.349$	$\Q(\sqrt{-3}) $	$_{}$	None	None					648.2.a.b	$2$	$0$	$0$	$0$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{11}+5\zeta_{6}q^{13}+\cdots$
1296.2.i.l	$1296$	$2$	1296.i	9.c	$3$	$2$	$1$	$10.349$	$\Q(\sqrt{-3}) $	$_{}$	None	None					216.2.a.b	$2$	$0$	$0$	$0$	$1$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+(5-5\zeta_{6})q^{11}+\cdots$
1296.2.i.m	$1296$	$2$	1296.i	9.c	$3$	$2$	$1$	$10.349$	$\Q(\sqrt{-3}) $	$_{}$	None	None					24.2.a.a	$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+2\zeta_{6}q^{5}+(4-4\zeta_{6})q^{11}+2\zeta_{6}q^{13}+\cdots$
1296.2.i.n	$1296$	$2$	1296.i	9.c	$3$	$2$	$1$	$10.349$	$\Q(\sqrt{-3}) $	$_{}$	None	None					162.2.a.a	$2$	$0$	$0$	$0$	$3$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+3\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{7}+\zeta_{6}q^{13}+\cdots$
1296.2.i.o	$1296$	$2$	1296.i	9.c	$3$	$2$	$1$	$10.349$	$\Q(\sqrt{-3}) $	$_{}$	None	None					54.2.a.a	$2$	$0$	$0$	$0$	$3$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+3\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+(3-3\zeta_{6})q^{11}+\cdots$
1296.2.i.p	$1296$	$2$	1296.i	9.c	$3$	$2$	$1$	$10.349$	$\Q(\sqrt{-3}) $	$_{}$	None	None					324.2.a.b	$2$	$0$	$0$	$0$	$3$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+3\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+(6-6\zeta_{6})q^{11}+\cdots$
1296.2.i.q	$1296$	$2$	1296.i	9.c	$3$	$2$	$1$	$10.349$	$\Q(\sqrt{-3}) $	$_{}$	None	None					216.2.a.a	$2$	$0$	$0$	$0$	$4$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+4\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+(-4+4\zeta_{6})q^{11}+\cdots$
1296.2.i.r	$1296$	$2$	1296.i	9.c	$3$	$4$	$2$	$10.349$	$\Q(\zeta_{12})$	$_{}$	None	None					648.2.a.e	$2$	$0$	$0$	$0$	$-4$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta_{2}-2\beta_1)q^{5}+(-2\beta_{3}+2\beta_{2})q^{7}+\cdots$
1296.2.i.s	$1296$	$2$	1296.i	9.c	$3$	$4$	$2$	$10.349$	$\Q(\zeta_{12})$	$_{}$	None	None					81.2.a.a	$4$	$0$	$0$	$0$	$0$	$4$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta_{2} q^{5}+(-2\beta_1+2)q^{7}+(2\beta_{3}-2\beta_{2})q^{11}+\cdots$

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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.