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 409 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
1008.1.f.a	$1008$	$1$	1008.f	7.b	$2$	$1$	$1$	$0.503$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-7}) $	$\Q(\sqrt{21}) $	✓		✓	✓	63.1.d.a	$4$	$0$	$0$	$0$	$0$	$1$		$1$		$q+q^{7}+q^{25}-2q^{37}+2q^{43}+q^{49}+\cdots$
1008.1.u.a	$1008$	$1$	1008.u	112.l	$4$	$2$	$1$	$0.503$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-7}) $	None		✓			1008.1.u.a	$4$	$0$	$-2$	$0$	$0$	$0$		$1$		$q-q^{2}+q^{4}+i q^{7}-q^{8}+(-i+1)q^{11}+\cdots$
1008.1.u.b	$1008$	$1$	1008.u	112.l	$4$	$2$	$1$	$0.503$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-7}) $	None					112.1.l.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+i q^{2}-q^{4}-i q^{7}-i q^{8}+(-i+1)q^{11}+\cdots$
1008.1.u.c	$1008$	$1$	1008.u	112.l	$4$	$2$	$1$	$0.503$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-7}) $	None		✓			1008.1.u.a	$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}+i q^{7}+q^{8}+(i-1)q^{11}+\cdots$
1008.1.y.a	$1008$	$1$	1008.y	336.v	$4$	$4$	$2$	$0.503$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-7}) $	None		✓			1008.1.y.a	$8$	$0$	$0$	$0$	$0$	$-4$		$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-q^{7}-\zeta_{8}^{3}q^{8}+\cdots$
1008.1.y.b	$1008$	$1$	1008.y	336.v	$4$	$4$	$2$	$0.503$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-7}) $	None		✓			1008.1.y.b	$8$	$0$	$0$	$0$	$0$	$4$		$1$		$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+q^{7}-\zeta_{8}q^{8}+\cdots$
1008.1.bw.a	$1008$	$1$	1008.bw	252.u	$6$	$4$	$2$	$0.503$	$\Q(\zeta_{12})$	$A_{4}$	None	None		✓	✓	✓	1008.1.bw.a	$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q-\zeta_{12}^{3}q^{3}+\zeta_{12}^{2}q^{5}-\zeta_{12}^{3}q^{7}+\cdots$
1008.1.cd.a	$1008$	$1$	1008.cd	28.g	$6$	$2$	$1$	$0.503$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			1008.1.cd.a	$4$	$0$	$0$	$0$	$0$	$-1$		$1$		$q+\zeta_{6}^{2}q^{7}+q^{13}+(1+\zeta_{6})q^{19}+\zeta_{6}q^{25}+\cdots$
1008.1.cd.b	$1008$	$1$	1008.cd	28.g	$6$	$2$	$1$	$0.503$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			1008.1.cd.a	$4$	$0$	$0$	$0$	$0$	$1$		$1$		$q-\zeta_{6}^{2}q^{7}+q^{13}+(-1-\zeta_{6})q^{19}+\cdots$
1008.1.cg.a	$1008$	$1$	1008.cg	7.d	$6$	$2$	$1$	$0.503$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None			✓	✓	252.1.z.a	$4$	$0$	$0$	$0$	$0$	$-1$		$1$		$q-\zeta_{6}q^{7}+(-\zeta_{6}-\zeta_{6}^{2})q^{13}+(1-\zeta_{6}^{2}+\cdots)q^{19}+\cdots$
1008.1.dc.a	$1008$	$1$	1008.dc	21.h	$6$	$4$	$2$	$0.503$	$\Q(\sqrt{-2}, \sqrt{-3})$	$S_{4}$	None	None			✓	✓	504.1.cu.a	$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q+\beta _{1}q^{5}+(-1+\beta _{2})q^{7}+(\beta _{1}-\beta _{3})q^{11}+\cdots$
1008.1.dd.a	$1008$	$1$	1008.dd	252.al	$6$	$4$	$2$	$0.503$	$\Q(\zeta_{12})$	$A_{4}$	None	None		✓	✓	✓	1008.1.bw.a	$4$	$0$	$0$	$0$	$-4$	$0$		$1$		$q+\zeta_{12}^{5}q^{3}-q^{5}+\zeta_{12}q^{7}-\zeta_{12}^{4}q^{9}+\cdots$
1008.1.dt.a	$1008$	$1$	1008.dt	112.u	$12$	$8$	$2$	$0.503$	$\Q(\zeta_{24})$	$S_{4}$	None	None		✓	✓	✓	1008.1.dt.a	$8$	$0$	$0$	$0$	$0$	$-4$		$1$		$q-\zeta_{24}^{11}q^{2}-\zeta_{24}^{10}q^{4}+\zeta_{24}^{11}q^{5}+\cdots$
1008.1.ed.a	$1008$	$1$	1008.ed	336.at	$12$	$8$	$2$	$0.503$	$\Q(\zeta_{24})$	$S_{4}$	None	None		✓	✓	✓	1008.1.ed.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+\zeta_{24}q^{5}+\zeta_{24}^{2}q^{7}+\cdots$
1008.2.a.a	$1008$	$2$	1008.a	1.a	$1$	$1$	$1$	$8.049$	$\Q$	$_{}$	None	None	✓				84.2.a.a	$1$	$0$	$0$	$0$	$-4$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}+q^{7}+2q^{11}-6q^{13}+4q^{17}+\cdots$
1008.2.a.b	$1008$	$2$	1008.a	1.a	$1$	$1$	$1$	$8.049$	$\Q$	$_{}$	None	None	✓				168.2.a.a	$1$	$0$	$0$	$0$	$-2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-q^{7}+6q^{13}+2q^{17}-4q^{19}+\cdots$
1008.2.a.c	$1008$	$2$	1008.a	1.a	$1$	$1$	$1$	$8.049$	$\Q$	$_{}$	None	None	✓				504.2.a.d	$1$	$1$	$0$	$0$	$-2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-q^{7}+6q^{11}-6q^{13}+2q^{17}+\cdots$
1008.2.a.d	$1008$	$2$	1008.a	1.a	$1$	$1$	$1$	$8.049$	$\Q$	$_{}$	None	None	✓				56.2.a.a	$1$	$1$	$0$	$0$	$-2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+q^{7}-4q^{11}+2q^{13}+6q^{17}+\cdots$
1008.2.a.e	$1008$	$2$	1008.a	1.a	$1$	$1$	$1$	$8.049$	$\Q$	$_{}$	None	None	✓				168.2.a.b	$1$	$1$	$0$	$0$	$-2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+q^{7}-2q^{13}-6q^{17}+4q^{19}+\cdots$
1008.2.a.f	$1008$	$2$	1008.a	1.a	$1$	$1$	$1$	$8.049$	$\Q$	$_{}$	None	None	✓				504.2.a.a	$1$	$0$	$0$	$0$	$-2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+q^{7}+2q^{11}+2q^{13}-6q^{17}+\cdots$
1008.2.a.g	$1008$	$2$	1008.a	1.a	$1$	$1$	$1$	$8.049$	$\Q$	$_{}$	None	None	✓				84.2.a.b	$1$	$1$	$0$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{7}-6q^{11}+2q^{13}+4q^{19}-6q^{23}+\cdots$
1008.2.a.h	$1008$	$2$	1008.a	1.a	$1$	$1$	$1$	$8.049$	$\Q$	$_{}$	None	None	✓				14.2.a.a	$1$	$1$	$0$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{7}-4q^{13}-6q^{17}-2q^{19}-5q^{25}+\cdots$
1008.2.a.i	$1008$	$2$	1008.a	1.a	$1$	$1$	$1$	$8.049$	$\Q$	$_{}$	None	None	✓				504.2.a.d	$1$	$1$	$0$	$0$	$2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-q^{7}-6q^{11}-6q^{13}-2q^{17}+\cdots$
1008.2.a.j	$1008$	$2$	1008.a	1.a	$1$	$1$	$1$	$8.049$	$\Q$	$_{}$	None	None	✓				42.2.a.a	$1$	$0$	$0$	$0$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+q^{7}-4q^{11}+6q^{13}-2q^{17}+\cdots$
1008.2.a.k	$1008$	$2$	1008.a	1.a	$1$	$1$	$1$	$8.049$	$\Q$	$_{}$	None	None	✓				504.2.a.a	$1$	$0$	$0$	$0$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+q^{7}-2q^{11}+2q^{13}+6q^{17}+\cdots$
1008.2.a.l	$1008$	$2$	1008.a	1.a	$1$	$1$	$1$	$8.049$	$\Q$	$_{}$	None	None	✓				21.2.a.a	$1$	$0$	$0$	$0$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+q^{7}+4q^{11}-2q^{13}+6q^{17}+\cdots$
1008.2.a.m	$1008$	$2$	1008.a	1.a	$1$	$1$	$1$	$8.049$	$\Q$	$_{}$	None	None	✓				56.2.a.b	$1$	$0$	$0$	$0$	$4$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}-q^{7}+2q^{17}+2q^{19}+8q^{23}+\cdots$
1008.2.a.n	$1008$	$2$	1008.a	1.a	$1$	$2$	$2$	$8.049$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓		✓	✓	63.2.a.b	$2$	$0$	$0$	$0$	$0$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{5}-q^{7}+\beta q^{11}+2q^{13}-\beta q^{17}+\cdots$
1008.2.b.a	$1008$	$2$	1008.b	28.d	$2$	$2$	$2$	$8.049$	$\Q(\sqrt{-3}) $	$_{}$	None	None					336.2.b.a	$2$	$0$	$0$	$0$	$0$	$-4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta-2)q^{7}-2\beta q^{11}-4\beta q^{17}-4 q^{19}+\cdots$
1008.2.b.b	$1008$	$2$	1008.b	28.d	$2$	$2$	$2$	$8.049$	$\Q(\sqrt{-3}) $	$_{}$	None	None					112.2.f.a	$2$	$0$	$0$	$0$	$0$	$-4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-2\beta q^{5}+(-\beta-2)q^{7}+2\beta q^{11}+\cdots$
1008.2.b.c	$1008$	$2$	1008.b	28.d	$2$	$2$	$2$	$8.049$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		✓			1008.2.b.c	$4$	$0$	$0$	$0$	$0$	$-4$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+(\beta-2)q^{7}-4\beta q^{13}+8 q^{19}+5 q^{25}+\cdots$
1008.2.b.d	$1008$	$2$	1008.b	28.d	$2$	$2$	$2$	$8.049$	$\Q(\sqrt{-6}) $	$_{}$	None	None					336.2.b.b	$2$	$0$	$0$	$0$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{5}+(-1-\beta )q^{7}-\beta q^{11}-2\beta q^{13}+\cdots$
1008.2.b.e	$1008$	$2$	1008.b	28.d	$2$	$2$	$2$	$8.049$	$\Q(\sqrt{-6}) $	$_{}$	None	None					336.2.b.b	$2$	$0$	$0$	$0$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{5}+(1+\beta )q^{7}+\beta q^{11}-2\beta q^{13}+\cdots$
1008.2.b.f	$1008$	$2$	1008.b	28.d	$2$	$2$	$2$	$8.049$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		✓			1008.2.b.c	$4$	$0$	$0$	$0$	$0$	$4$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+(-\beta+2)q^{7}-4\beta q^{13}-8 q^{19}+\cdots$
1008.2.b.g	$1008$	$2$	1008.b	28.d	$2$	$2$	$2$	$8.049$	$\Q(\sqrt{-3}) $	$_{}$	None	None					112.2.f.a	$2$	$0$	$0$	$0$	$0$	$4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-2\beta q^{5}+(\beta+2)q^{7}-2\beta q^{11}-2\beta q^{13}+\cdots$
1008.2.b.h	$1008$	$2$	1008.b	28.d	$2$	$2$	$2$	$8.049$	$\Q(\sqrt{-3}) $	$_{}$	None	None					336.2.b.a	$2$	$0$	$0$	$0$	$0$	$4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta+2)q^{7}-2\beta q^{11}+4\beta q^{17}+4 q^{19}+\cdots$
1008.2.b.i	$1008$	$2$	1008.b	28.d	$2$	$4$	$4$	$8.049$	$\Q(\sqrt{-6}, \sqrt{7})$	$_{}$	$\Q(\sqrt{-21}) $	None		✓	✓		1008.2.b.i	$8$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{1}q^{5}-\beta _{3}q^{7}-\beta _{2}q^{11}+3\beta _{1}q^{17}+\cdots$
1008.2.h.a	$1008$	$2$	1008.h	12.b	$2$	$4$	$4$	$8.049$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			1008.2.h.a	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_{2} q^{5}+\beta_1 q^{7}+4\beta_{3} q^{11}-4 q^{13}+\cdots$
1008.2.h.b	$1008$	$2$	1008.h	12.b	$2$	$8$	$8$	$8.049$	$\Q(\zeta_{24})$	$_{}$	None	None		✓	✓		1008.2.h.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta_{7}-\beta_{2})q^{5}-\beta_1 q^{7}+(-2\beta_{6}-\beta_{3})q^{11}+\cdots$
1008.2.k.a	$1008$	$2$	1008.k	21.c	$2$	$4$	$4$	$8.049$	$\Q(\sqrt{-2}, \sqrt{7})$	$_{}$	$\Q(\sqrt{-7}) $	None					63.2.c.a	$4$	$0$	$0$	$0$	$0$	$0$		$2\cdot 3$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{2}q^{7}+(\beta _{1}-\beta _{3})q^{11}+(\beta _{1}+\beta _{3})q^{23}+\cdots$
1008.2.k.b	$1008$	$2$	1008.k	21.c	$2$	$4$	$4$	$8.049$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	None	None					252.2.f.a	$4$	$0$	$0$	$0$	$0$	$4$		$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{5}+(1+\beta _{1})q^{7}-\beta _{2}q^{11}-2\beta _{1}q^{13}+\cdots$
1008.2.k.c	$1008$	$2$	1008.k	21.c	$2$	$8$	$8$	$8.049$	$\Q(\zeta_{16})$	$_{}$	None	None			✓		504.2.k.a	$4$	$0$	$0$	$0$	$0$	$-8$		$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_{7} q^{5}+(-\beta_{6}-1)q^{7}+(\beta_{2}+\beta_1)q^{11}+\cdots$
1008.2.q.a	$1008$	$2$	1008.q	63.h	$3$	$2$	$1$	$8.049$	$\Q(\sqrt{-3}) $	$_{}$	None	None					126.2.e.a	$2$	$0$	$0$	$0$	$-3$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-2\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+(1+\cdots)q^{7}+\cdots$
1008.2.q.b	$1008$	$2$	1008.q	63.h	$3$	$2$	$1$	$8.049$	$\Q(\sqrt{-3}) $	$_{}$	None	None					504.2.q.a	$2$	$1$	$0$	$0$	$-1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{5}+(-1+\cdots)q^{7}+\cdots$
1008.2.q.c	$1008$	$2$	1008.q	63.h	$3$	$2$	$1$	$8.049$	$\Q(\sqrt{-3}) $	$_{}$	None	None					63.2.g.a	$2$	$0$	$0$	$0$	$1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+(-3+2\zeta_{6})q^{7}+\cdots$
1008.2.q.d	$1008$	$2$	1008.q	63.h	$3$	$2$	$1$	$8.049$	$\Q(\sqrt{-3}) $	$_{}$	None	None					504.2.q.b	$2$	$0$	$0$	$0$	$1$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+(3-2\zeta_{6})q^{7}+\cdots$
1008.2.q.e	$1008$	$2$	1008.q	63.h	$3$	$2$	$1$	$8.049$	$\Q(\sqrt{-3}) $	$_{}$	None	None					126.2.e.b	$2$	$0$	$0$	$0$	$3$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-2\zeta_{6})q^{3}+(3-3\zeta_{6})q^{5}+(3-2\zeta_{6})q^{7}+\cdots$
1008.2.q.f	$1008$	$2$	1008.q	63.h	$3$	$2$	$1$	$8.049$	$\Q(\sqrt{-3}) $	$_{}$	None	None					252.2.i.a	$2$	$0$	$0$	$3$	$-2$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{5}+(2+\zeta_{6})q^{7}+\cdots$
1008.2.q.g	$1008$	$2$	1008.q	63.h	$3$	$6$	$3$	$8.049$	6.0.309123.1	$_{}$	None	None					126.2.e.c	$2$	$0$	$0$	$-2$	$1$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{2}+\beta _{4})q^{3}+(1-\beta _{1}+\beta _{3}-\beta _{4}+\cdots)q^{5}+\cdots$
1008.2.q.h	$1008$	$2$	1008.q	63.h	$3$	$6$	$3$	$8.049$	6.0.309123.1	$_{}$	None	None					126.2.e.d	$2$	$0$	$0$	$2$	$-5$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{3}+\beta _{4}+\beta _{5})q^{3}+(\beta _{1}+2\beta _{4}+\cdots)q^{5}+\cdots$

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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.