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 116 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
3168.1.e.a	$3168$	$1$	3168.e	88.b	$2$	$1$	$1$	$1.581$	$\Q$	$D_{2}$	$\Q(\sqrt{-6}) $, $\Q(\sqrt{-22}) $	$\Q(\sqrt{33}) $	✓				792.1.e.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-q^{11}+q^{25}+2q^{29}+2q^{31}+q^{49}+\cdots$
3168.1.e.b	$3168$	$1$	3168.e	88.b	$2$	$1$	$1$	$1.581$	$\Q$	$D_{2}$	$\Q(\sqrt{-6}) $, $\Q(\sqrt{-22}) $	$\Q(\sqrt{33}) $	✓				792.1.e.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{11}+q^{25}-2q^{29}+2q^{31}+q^{49}+\cdots$
3168.1.j.a	$3168$	$1$	3168.j	11.b	$2$	$2$	$2$	$1.581$	$\Q(\sqrt{-2}) $	$D_{4}$	$\Q(\sqrt{-33}) $	None		✓			3168.1.j.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta q^{7}-q^{11}+\beta q^{17}-\beta q^{19}+2q^{23}+\cdots$
3168.1.j.b	$3168$	$1$	3168.j	11.b	$2$	$2$	$2$	$1.581$	$\Q(\sqrt{-2}) $	$D_{4}$	$\Q(\sqrt{-33}) $	None		✓			3168.1.j.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta q^{7}+q^{11}-\beta q^{17}-\beta q^{19}-2q^{23}+\cdots$
3168.1.ba.a	$3168$	$1$	3168.ba	792.s	$6$	$2$	$1$	$1.581$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-2}) $	None					792.1.s.a	$4$	$0$	$0$	$-1$	$0$	$0$		$1$		$q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{9}-q^{11}-q^{17}+(-\zeta_{6}+\cdots)q^{19}+\cdots$
3168.1.ba.b	$3168$	$1$	3168.ba	792.s	$6$	$2$	$1$	$1.581$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-2}) $	None					792.1.s.a	$4$	$0$	$0$	$-1$	$0$	$0$		$1$		$q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{9}-\zeta_{6}q^{11}+q^{17}+\cdots$
3168.1.bf.a	$3168$	$1$	3168.bf	99.h	$6$	$4$	$2$	$1.581$	$\Q(\sqrt{-2}, \sqrt{-3})$	$S_{4}$	None	None		✓			3168.1.bf.a	$4$	$0$	$0$	$-2$	$-2$	$0$		$1$		$q-\beta _{2}q^{3}-\beta _{2}q^{5}+\beta _{1}q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots$
3168.1.bf.b	$3168$	$1$	3168.bf	99.h	$6$	$4$	$2$	$1.581$	$\Q(\sqrt{-2}, \sqrt{-3})$	$S_{4}$	None	None		✓			3168.1.bf.a	$4$	$0$	$0$	$2$	$-2$	$0$		$1$		$q+\beta _{2}q^{3}-\beta _{2}q^{5}+\beta _{1}q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots$
3168.1.cb.a	$3168$	$1$	3168.cb	44.h	$10$	$8$	$2$	$1.581$	$\Q(\zeta_{20})$	$A_{5}$	None	None		✓			3168.1.cb.a	$4$	$0$	$0$	$0$	$-6$	$0$		$1$		$q+(-1+\zeta_{20}^{2})q^{5}-\zeta_{20}^{3}q^{7}-\zeta_{20}q^{11}+\cdots$
3168.1.cb.b	$3168$	$1$	3168.cb	44.h	$10$	$8$	$2$	$1.581$	$\Q(\zeta_{20})$	$A_{5}$	None	None		✓			3168.1.cb.a	$4$	$0$	$0$	$0$	$6$	$0$		$1$		$q+(1-\zeta_{20}^{2})q^{5}-\zeta_{20}^{3}q^{7}+\zeta_{20}q^{11}+\cdots$
3168.1.ci.a	$3168$	$1$	3168.ci	88.p	$10$	$4$	$1$	$1.581$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-6}) $	None					792.1.bs.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{10}^{3}+\zeta_{10}^{4})q^{5}+(-\zeta_{10}^{2}+\zeta_{10}^{4}+\cdots)q^{7}+\cdots$
3168.1.ci.b	$3168$	$1$	3168.ci	88.p	$10$	$4$	$1$	$1.581$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-6}) $	None					792.1.bs.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{10}^{3}-\zeta_{10}^{4})q^{5}+(-\zeta_{10}^{2}+\zeta_{10}^{4}+\cdots)q^{7}+\cdots$
3168.1.ck.a	$3168$	$1$	3168.ck	88.l	$10$	$4$	$1$	$1.581$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-2}) $	None			✓	✓	88.1.l.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{10}^{2}q^{11}+(\zeta_{10}^{3}-\zeta_{10}^{4})q^{17}+\cdots$
3168.1.dl.a	$3168$	$1$	3168.dl	792.ax	$30$	$8$	$1$	$1.581$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-2}) $	None					792.1.bx.a	$4$	$0$	$0$	$-1$	$0$	$0$		$1$		$q-\zeta_{30}^{4}q^{3}+\zeta_{30}^{8}q^{9}-\zeta_{30}^{8}q^{11}+\cdots$
3168.1.dl.b	$3168$	$1$	3168.dl	792.ax	$30$	$8$	$1$	$1.581$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-2}) $	None					792.1.bx.a	$4$	$0$	$0$	$-1$	$0$	$0$		$1$		$q+\zeta_{30}^{7}q^{3}+\zeta_{30}^{14}q^{9}+\zeta_{30}^{3}q^{11}+\cdots$
3168.1.dw.a	$3168$	$1$	3168.dw	396.ae	$30$	$16$	$2$	$1.581$	$\Q(\zeta_{60})$	$A_{5}$	None	None		✓	✓	✓	3168.1.dw.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{60}^{29}q^{3}-\zeta_{60}q^{7}-\zeta_{60}^{28}q^{9}+\cdots$
3168.1.dz.a	$3168$	$1$	3168.dz	792.bl	$30$	$8$	$1$	$1.581$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-2}) $	None					792.1.cl.a	$4$	$0$	$0$	$1$	$0$	$0$		$1$		$q-\zeta_{30}^{11}q^{3}-\zeta_{30}^{7}q^{9}-\zeta_{30}^{7}q^{11}+\cdots$
3168.1.dz.b	$3168$	$1$	3168.dz	792.bl	$30$	$8$	$1$	$1.581$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-2}) $	None					792.1.cl.a	$4$	$0$	$0$	$1$	$0$	$0$		$1$		$q+\zeta_{30}^{8}q^{3}-\zeta_{30}q^{9}-\zeta_{30}^{12}q^{11}+\cdots$
3168.2.a.a	$3168$	$2$	3168.a	1.a	$1$	$1$	$1$	$25.297$	$\Q$	$_{}$	None	None	✓				1056.2.a.e	$1$	$0$	$0$	$0$	$-2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-4q^{7}-q^{11}-2q^{13}-2q^{17}+\cdots$
3168.2.a.b	$3168$	$2$	3168.a	1.a	$1$	$1$	$1$	$25.297$	$\Q$	$_{}$	None	None	✓	✓			3168.2.a.b	$1$	$1$	$0$	$0$	$-2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-4q^{7}-q^{11}+4q^{13}+6q^{17}+\cdots$
3168.2.a.c	$3168$	$2$	3168.a	1.a	$1$	$1$	$1$	$25.297$	$\Q$	$_{}$	None	None	✓	✓			3168.2.a.c	$1$	$0$	$0$	$0$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-q^{11}+2q^{17}+6q^{19}-6q^{23}+\cdots$
3168.2.a.d	$3168$	$2$	3168.a	1.a	$1$	$1$	$1$	$25.297$	$\Q$	$_{}$	None	None	✓	✓			3168.2.a.c	$1$	$1$	$0$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+q^{11}+2q^{17}-6q^{19}+6q^{23}+\cdots$
3168.2.a.e	$3168$	$2$	3168.a	1.a	$1$	$1$	$1$	$25.297$	$\Q$	$_{}$	None	None	✓				1056.2.a.e	$1$	$0$	$0$	$0$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+4q^{7}+q^{11}-2q^{13}-2q^{17}+\cdots$
3168.2.a.f	$3168$	$2$	3168.a	1.a	$1$	$1$	$1$	$25.297$	$\Q$	$_{}$	None	None	✓	✓			3168.2.a.b	$1$	$0$	$0$	$0$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+4q^{7}+q^{11}+4q^{13}+6q^{17}+\cdots$
3168.2.a.g	$3168$	$2$	3168.a	1.a	$1$	$1$	$1$	$25.297$	$\Q$	$_{}$	None	None	✓				352.2.a.c	$1$	$0$	$0$	$0$	$-1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-4q^{7}+q^{11}-2q^{13}+2q^{19}+\cdots$
3168.2.a.h	$3168$	$2$	3168.a	1.a	$1$	$1$	$1$	$25.297$	$\Q$	$_{}$	None	None	✓				352.2.a.a	$1$	$0$	$0$	$0$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-q^{11}-6q^{13}+4q^{17}-6q^{19}+\cdots$
3168.2.a.i	$3168$	$2$	3168.a	1.a	$1$	$1$	$1$	$25.297$	$\Q$	$_{}$	None	None	✓				352.2.a.a	$1$	$1$	$0$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+q^{11}-6q^{13}+4q^{17}+6q^{19}+\cdots$
3168.2.a.j	$3168$	$2$	3168.a	1.a	$1$	$1$	$1$	$25.297$	$\Q$	$_{}$	None	None	✓				352.2.a.c	$1$	$1$	$0$	$0$	$-1$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+4q^{7}-q^{11}-2q^{13}-2q^{19}+\cdots$
3168.2.a.k	$3168$	$2$	3168.a	1.a	$1$	$1$	$1$	$25.297$	$\Q$	$_{}$	None	None	✓	✓			3168.2.a.k	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}-q^{11}-2q^{13}-2q^{17}+6q^{19}+\cdots$
3168.2.a.l	$3168$	$2$	3168.a	1.a	$1$	$1$	$1$	$25.297$	$\Q$	$_{}$	None	None	✓	✓			3168.2.a.k	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}+q^{11}-2q^{13}+2q^{17}+6q^{19}+\cdots$
3168.2.a.m	$3168$	$2$	3168.a	1.a	$1$	$1$	$1$	$25.297$	$\Q$	$_{}$	None	None	✓				1056.2.a.d	$1$	$0$	$0$	$0$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}+q^{11}+4q^{13}+2q^{17}+2q^{23}+\cdots$
3168.2.a.n	$3168$	$2$	3168.a	1.a	$1$	$1$	$1$	$25.297$	$\Q$	$_{}$	None	None	✓	✓			3168.2.a.k	$1$	$1$	$0$	$0$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}-q^{11}-2q^{13}+2q^{17}-6q^{19}+\cdots$
3168.2.a.o	$3168$	$2$	3168.a	1.a	$1$	$1$	$1$	$25.297$	$\Q$	$_{}$	None	None	✓				1056.2.a.d	$1$	$0$	$0$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}-q^{11}+4q^{13}+2q^{17}-2q^{23}+\cdots$
3168.2.a.p	$3168$	$2$	3168.a	1.a	$1$	$1$	$1$	$25.297$	$\Q$	$_{}$	None	None	✓	✓			3168.2.a.k	$1$	$1$	$0$	$0$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}+q^{11}-2q^{13}-2q^{17}-6q^{19}+\cdots$
3168.2.a.q	$3168$	$2$	3168.a	1.a	$1$	$1$	$1$	$25.297$	$\Q$	$_{}$	None	None	✓	✓			3168.2.a.b	$1$	$1$	$0$	$0$	$2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-4q^{7}+q^{11}+4q^{13}-6q^{17}+\cdots$
3168.2.a.r	$3168$	$2$	3168.a	1.a	$1$	$1$	$1$	$25.297$	$\Q$	$_{}$	None	None	✓				1056.2.a.c	$1$	$1$	$0$	$0$	$2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-2q^{7}-q^{11}-2q^{13}-2q^{19}+\cdots$
3168.2.a.s	$3168$	$2$	3168.a	1.a	$1$	$1$	$1$	$25.297$	$\Q$	$_{}$	None	None	✓				1056.2.a.b	$1$	$1$	$0$	$0$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-q^{11}-6q^{13}-2q^{17}+4q^{19}+\cdots$
3168.2.a.t	$3168$	$2$	3168.a	1.a	$1$	$1$	$1$	$25.297$	$\Q$	$_{}$	None	None	✓	✓			3168.2.a.c	$1$	$1$	$0$	$0$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-q^{11}-2q^{17}-6q^{19}-6q^{23}+\cdots$
3168.2.a.u	$3168$	$2$	3168.a	1.a	$1$	$1$	$1$	$25.297$	$\Q$	$_{}$	None	None	✓				1056.2.a.b	$1$	$1$	$0$	$0$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+q^{11}-6q^{13}-2q^{17}-4q^{19}+\cdots$
3168.2.a.v	$3168$	$2$	3168.a	1.a	$1$	$1$	$1$	$25.297$	$\Q$	$_{}$	None	None	✓	✓			3168.2.a.c	$1$	$0$	$0$	$0$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+q^{11}-2q^{17}+6q^{19}+6q^{23}+\cdots$
3168.2.a.w	$3168$	$2$	3168.a	1.a	$1$	$1$	$1$	$25.297$	$\Q$	$_{}$	None	None	✓				1056.2.a.c	$1$	$0$	$0$	$0$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+2q^{7}+q^{11}-2q^{13}+2q^{19}+\cdots$
3168.2.a.x	$3168$	$2$	3168.a	1.a	$1$	$1$	$1$	$25.297$	$\Q$	$_{}$	None	None	✓	✓			3168.2.a.b	$1$	$0$	$0$	$0$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+4q^{7}-q^{11}+4q^{13}-6q^{17}+\cdots$
3168.2.a.y	$3168$	$2$	3168.a	1.a	$1$	$1$	$1$	$25.297$	$\Q$	$_{}$	None	None	✓				352.2.a.b	$1$	$0$	$0$	$0$	$3$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}-4q^{7}-q^{11}-2q^{13}+8q^{17}+\cdots$
3168.2.a.z	$3168$	$2$	3168.a	1.a	$1$	$1$	$1$	$25.297$	$\Q$	$_{}$	None	None	✓				352.2.a.b	$1$	$0$	$0$	$0$	$3$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}+4q^{7}+q^{11}-2q^{13}+8q^{17}+\cdots$
3168.2.a.ba	$3168$	$2$	3168.a	1.a	$1$	$1$	$1$	$25.297$	$\Q$	$_{}$	None	None	✓				1056.2.a.a	$1$	$0$	$0$	$0$	$4$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}-2q^{7}+q^{11}+4q^{13}-2q^{17}+\cdots$
3168.2.a.bb	$3168$	$2$	3168.a	1.a	$1$	$1$	$1$	$25.297$	$\Q$	$_{}$	None	None	✓				1056.2.a.a	$1$	$0$	$0$	$0$	$4$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}+2q^{7}-q^{11}+4q^{13}-2q^{17}+\cdots$
3168.2.a.bc	$3168$	$2$	3168.a	1.a	$1$	$2$	$2$	$25.297$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓				352.2.a.g	$1$	$1$	$0$	$0$	$-3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{5}-q^{11}+2q^{13}+(-4+\cdots)q^{17}+\cdots$
3168.2.a.bd	$3168$	$2$	3168.a	1.a	$1$	$2$	$2$	$25.297$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓				352.2.a.g	$1$	$1$	$0$	$0$	$-3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{5}+q^{11}+2q^{13}+(-4+\cdots)q^{17}+\cdots$
3168.2.a.be	$3168$	$2$	3168.a	1.a	$1$	$2$	$2$	$25.297$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				1056.2.a.k	$1$	$1$	$0$	$0$	$-2$	$-2$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{5}+(-1+\beta )q^{7}-q^{11}+\cdots$
3168.2.a.bf	$3168$	$2$	3168.a	1.a	$1$	$2$	$2$	$25.297$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓		✓		1056.2.a.k	$1$	$0$	$0$	$0$	$-2$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{5}+(1-\beta )q^{7}+q^{11}+(3+\cdots)q^{13}+\cdots$

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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.