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 80 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
2376.1.e.a	$2376$	$1$	2376.e	88.b	$2$	$2$	$2$	$1.186$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-6}) $	None		✓			2376.1.e.a	$4$	$0$	$-2$	$0$	$0$	$0$		$1$		$q-q^{2}+q^{4}+(\zeta_{6}+\zeta_{6}^{2})q^{5}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{7}+\cdots$
2376.1.e.b	$2376$	$1$	2376.e	88.b	$2$	$2$	$2$	$1.186$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-6}) $	None		✓			2376.1.e.a	$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}+(\zeta_{6}+\zeta_{6}^{2})q^{5}+(-\zeta_{6}+\cdots)q^{7}+\cdots$
2376.1.p.a	$2376$	$1$	2376.p	264.p	$2$	$1$	$1$	$1.186$	$\Q$	$D_{3}$	$\Q(\sqrt{-66}) $	None	✓	✓			2376.1.p.a	$2$	$0$	$-1$	$0$	$-1$	$-2$		$1$		$q-q^{2}+q^{4}-q^{5}-2q^{7}-q^{8}+q^{10}+\cdots$
2376.1.p.b	$2376$	$1$	2376.p	264.p	$2$	$1$	$1$	$1.186$	$\Q$	$D_{3}$	$\Q(\sqrt{-66}) $	None	✓	✓			2376.1.p.a	$2$	$0$	$-1$	$0$	$1$	$2$		$1$		$q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots$
2376.1.p.c	$2376$	$1$	2376.p	264.p	$2$	$1$	$1$	$1.186$	$\Q$	$D_{3}$	$\Q(\sqrt{-66}) $	None	✓	✓			2376.1.p.a	$2$	$0$	$1$	$0$	$-1$	$2$		$1$		$q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{10}+\cdots$
2376.1.p.d	$2376$	$1$	2376.p	264.p	$2$	$1$	$1$	$1.186$	$\Q$	$D_{3}$	$\Q(\sqrt{-66}) $	None	✓	✓			2376.1.p.a	$2$	$0$	$1$	$0$	$1$	$-2$		$1$		$q+q^{2}+q^{4}+q^{5}-2q^{7}+q^{8}+q^{10}+\cdots$
2376.1.p.e	$2376$	$1$	2376.p	264.p	$2$	$2$	$2$	$1.186$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-66}) $	None	✓	✓			2376.1.p.e	$4$	$0$	$-2$	$0$	$0$	$0$		$1$		$q-q^{2}+q^{4}-\beta q^{5}-q^{8}+\beta q^{10}+q^{11}+\cdots$
2376.1.p.f	$2376$	$1$	2376.p	264.p	$2$	$2$	$2$	$1.186$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-66}) $	None	✓	✓			2376.1.p.e	$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}-\beta q^{5}+q^{8}-\beta q^{10}-q^{11}+\cdots$
2376.1.s.a	$2376$	$1$	2376.s	792.s	$6$	$2$	$1$	$1.186$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-2}) $	None					792.1.s.a	$4$	$0$	$-1$	$0$	$0$	$0$		$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+q^{8}-q^{11}+\zeta_{6}^{2}q^{16}+\cdots$
2376.1.s.b	$2376$	$1$	2376.s	792.s	$6$	$2$	$1$	$1.186$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-2}) $	None					792.1.s.a	$4$	$0$	$1$	$0$	$0$	$0$		$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-q^{8}-\zeta_{6}q^{11}+\cdots$
2376.1.bk.a	$2376$	$1$	2376.bk	264.t	$10$	$8$	$2$	$1.186$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-6}) $	None		✓			2376.1.bk.a	$4$	$0$	$-2$	$0$	$2$	$2$		$1$		$q-\zeta_{30}^{3}q^{2}+\zeta_{30}^{6}q^{4}+(-\zeta_{30}+\zeta_{30}^{8}+\cdots)q^{5}+\cdots$
2376.1.bk.b	$2376$	$1$	2376.bk	264.t	$10$	$8$	$2$	$1.186$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-6}) $	None		✓			2376.1.bk.a	$4$	$0$	$2$	$0$	$-2$	$2$		$1$		$q+\zeta_{30}^{3}q^{2}+\zeta_{30}^{6}q^{4}+(\zeta_{30}-\zeta_{30}^{8}+\cdots)q^{5}+\cdots$
2376.1.bt.a	$2376$	$1$	2376.bt	88.p	$10$	$8$	$2$	$1.186$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-6}) $	None		✓			2376.1.bt.a	$4$	$0$	$-2$	$0$	$0$	$0$		$1$		$q+\zeta_{30}^{12}q^{2}-\zeta_{30}^{9}q^{4}+(-\zeta_{30}^{2}+\cdots)q^{5}+\cdots$
2376.1.bt.b	$2376$	$1$	2376.bt	88.p	$10$	$8$	$2$	$1.186$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-6}) $	None		✓			2376.1.bt.a	$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q-\zeta_{30}^{12}q^{2}-\zeta_{30}^{9}q^{4}+(-\zeta_{30}^{7}+\cdots)q^{5}+\cdots$
2376.1.cc.a	$2376$	$1$	2376.cc	2376.bc	$18$	$6$	$1$	$1.186$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-2}) $	None		✓			2376.1.cc.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{18}^{5}q^{2}-\zeta_{18}^{2}q^{3}-\zeta_{18}q^{4}+\zeta_{18}^{7}q^{6}+\cdots$
2376.1.cc.b	$2376$	$1$	2376.cc	2376.bc	$18$	$6$	$1$	$1.186$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-2}) $	None		✓			2376.1.cc.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{18}^{5}q^{2}-\zeta_{18}^{2}q^{3}-\zeta_{18}q^{4}-\zeta_{18}^{7}q^{6}+\cdots$
2376.1.cn.a	$2376$	$1$	2376.cn	792.ax	$30$	$8$	$1$	$1.186$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-2}) $	None					792.1.bx.a	$4$	$0$	$-1$	$0$	$0$	$0$		$1$		$q-\zeta_{30}^{14}q^{2}-\zeta_{30}^{13}q^{4}-\zeta_{30}^{12}q^{8}+\cdots$
2376.1.cn.b	$2376$	$1$	2376.cn	792.ax	$30$	$8$	$1$	$1.186$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-2}) $	None					792.1.bx.a	$4$	$0$	$-1$	$0$	$0$	$0$		$1$		$q-\zeta_{30}^{14}q^{2}-\zeta_{30}^{13}q^{4}-\zeta_{30}^{12}q^{8}+\cdots$
2376.1.db.a	$2376$	$1$	2376.db	792.bl	$30$	$8$	$1$	$1.186$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-2}) $	None					792.1.cl.a	$4$	$0$	$-1$	$0$	$0$	$0$		$1$		$q-\zeta_{30}^{2}q^{2}+\zeta_{30}^{4}q^{4}-\zeta_{30}^{6}q^{8}+\cdots$
2376.1.db.b	$2376$	$1$	2376.db	792.bl	$30$	$8$	$1$	$1.186$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-2}) $	None					792.1.cl.a	$4$	$0$	$1$	$0$	$0$	$0$		$1$		$q+\zeta_{30}^{2}q^{2}+\zeta_{30}^{4}q^{4}+\zeta_{30}^{6}q^{8}+\cdots$
2376.1.dn.a	$2376$	$1$	2376.dn	2376.cn	$90$	$24$	$1$	$1.186$	$\Q(\zeta_{45})$	$D_{90}$	$\Q(\sqrt{-2}) $	None		✓			2376.1.dn.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{90}^{19}q^{2}+\zeta_{90}^{13}q^{3}+\zeta_{90}^{38}q^{4}+\cdots$
2376.1.dn.b	$2376$	$1$	2376.dn	2376.cn	$90$	$24$	$1$	$1.186$	$\Q(\zeta_{45})$	$D_{90}$	$\Q(\sqrt{-2}) $	None		✓			2376.1.dn.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{90}^{19}q^{2}+\zeta_{90}^{31}q^{3}+\zeta_{90}^{38}q^{4}+\cdots$
2376.1.dr.a	$2376$	$1$	2376.dr	2376.cr	$90$	$24$	$1$	$1.186$	$\Q(\zeta_{45})$	$D_{45}$	$\Q(\sqrt{-2}) $	None		✓			2376.1.dr.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{90}^{22}q^{2}-\zeta_{90}^{43}q^{3}+\zeta_{90}^{44}q^{4}+\cdots$
2376.1.dr.b	$2376$	$1$	2376.dr	2376.cr	$90$	$24$	$1$	$1.186$	$\Q(\zeta_{45})$	$D_{45}$	$\Q(\sqrt{-2}) $	None		✓			2376.1.dr.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{90}^{22}q^{2}+\zeta_{90}^{34}q^{3}+\zeta_{90}^{44}q^{4}+\cdots$
2376.2.a.a	$2376$	$2$	2376.a	1.a	$1$	$1$	$1$	$18.972$	$\Q$	$_{}$	None	None	✓	✓			2376.2.a.a	$1$	$0$	$0$	$0$	$-3$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}+4q^{7}+q^{11}+3q^{13}+3q^{17}+\cdots$
2376.2.a.b	$2376$	$2$	2376.a	1.a	$1$	$1$	$1$	$18.972$	$\Q$	$_{}$	None	None	✓	✓			2376.2.a.b	$1$	$1$	$0$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{7}-q^{11}-3q^{13}-5q^{19}+4q^{23}+\cdots$
2376.2.a.c	$2376$	$2$	2376.a	1.a	$1$	$1$	$1$	$18.972$	$\Q$	$_{}$	None	None	✓	✓			2376.2.a.b	$1$	$1$	$0$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{7}+q^{11}-3q^{13}-5q^{19}-4q^{23}+\cdots$
2376.2.a.d	$2376$	$2$	2376.a	1.a	$1$	$1$	$1$	$18.972$	$\Q$	$_{}$	None	None	✓	✓			2376.2.a.a	$1$	$0$	$0$	$0$	$3$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}+4q^{7}-q^{11}+3q^{13}-3q^{17}+\cdots$
2376.2.a.e	$2376$	$2$	2376.a	1.a	$1$	$2$	$2$	$18.972$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			2376.2.a.e	$1$	$0$	$0$	$0$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2\beta q^{5}+(-1+\beta )q^{7}-q^{11}+(-4+\cdots)q^{13}+\cdots$
2376.2.a.f	$2376$	$2$	2376.a	1.a	$1$	$2$	$2$	$18.972$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			2376.2.a.f	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}+(-1-\beta )q^{7}-q^{11}+(-1+\cdots)q^{13}+\cdots$
2376.2.a.g	$2376$	$2$	2376.a	1.a	$1$	$2$	$2$	$18.972$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			2376.2.a.e	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2\beta q^{5}+(-1-\beta )q^{7}+q^{11}+(-4+\cdots)q^{13}+\cdots$
2376.2.a.h	$2376$	$2$	2376.a	1.a	$1$	$2$	$2$	$18.972$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			2376.2.a.f	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}+(-1+\beta )q^{7}+q^{11}+(-1+\cdots)q^{13}+\cdots$
2376.2.a.i	$2376$	$2$	2376.a	1.a	$1$	$2$	$2$	$18.972$	$\Q(\sqrt{7}) $	$_{}$	None	None	✓	✓	✓		2376.2.a.i	$1$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{7}-q^{11}+(-2+\beta )q^{17}+2\beta q^{19}+\cdots$
2376.2.a.j	$2376$	$2$	2376.a	1.a	$1$	$2$	$2$	$18.972$	$\Q(\sqrt{7}) $	$_{}$	None	None	✓	✓			2376.2.a.i	$1$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{7}+q^{11}+(2+\beta )q^{17}-2\beta q^{19}+\cdots$
2376.2.a.k	$2376$	$2$	2376.a	1.a	$1$	$3$	$3$	$18.972$	3.3.564.1	$_{}$	None	None	✓	✓	✓		2376.2.a.k	$1$	$1$	$0$	$0$	$-2$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{5}+(-1+\beta _{1}+\beta _{2})q^{7}+\cdots$
2376.2.a.l	$2376$	$2$	2376.a	1.a	$1$	$3$	$3$	$18.972$	3.3.788.1	$_{}$	None	None	✓	✓	✓		2376.2.a.l	$1$	$1$	$0$	$0$	$-2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{2})q^{5}+\beta _{1}q^{7}-q^{11}+(1+\cdots)q^{13}+\cdots$
2376.2.a.m	$2376$	$2$	2376.a	1.a	$1$	$3$	$3$	$18.972$	3.3.1016.1	$_{}$	None	None	✓	✓	✓		2376.2.a.m	$1$	$0$	$0$	$0$	$-2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{5}+(\beta _{1}+\beta _{2})q^{7}-q^{11}+\cdots$
2376.2.a.n	$2376$	$2$	2376.a	1.a	$1$	$3$	$3$	$18.972$	3.3.7032.1	$_{}$	None	None	✓	✓			2376.2.a.n	$1$	$0$	$0$	$0$	$-1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{5}+(-1+\beta _{1})q^{7}-q^{11}+(-1+\cdots)q^{13}+\cdots$
2376.2.a.o	$2376$	$2$	2376.a	1.a	$1$	$3$	$3$	$18.972$	3.3.7032.1	$_{}$	None	None	✓	✓	✓		2376.2.a.n	$1$	$0$	$0$	$0$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{5}+(-1+\beta _{1})q^{7}+q^{11}+(-1+\cdots)q^{13}+\cdots$
2376.2.a.p	$2376$	$2$	2376.a	1.a	$1$	$3$	$3$	$18.972$	3.3.564.1	$_{}$	None	None	✓	✓			2376.2.a.k	$1$	$0$	$0$	$0$	$2$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{5}+(-1+\beta _{1}+\beta _{2})q^{7}+\cdots$
2376.2.a.q	$2376$	$2$	2376.a	1.a	$1$	$3$	$3$	$18.972$	3.3.788.1	$_{}$	None	None	✓	✓			2376.2.a.l	$1$	$0$	$0$	$0$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{2})q^{5}+\beta _{1}q^{7}+q^{11}+(1-2\beta _{1}+\cdots)q^{13}+\cdots$
2376.2.a.r	$2376$	$2$	2376.a	1.a	$1$	$3$	$3$	$18.972$	3.3.1016.1	$_{}$	None	None	✓	✓			2376.2.a.m	$1$	$0$	$0$	$0$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{5}+(\beta _{1}+\beta _{2})q^{7}+q^{11}+\cdots$
2376.2.b.a	$2376$	$2$	2376.b	33.d	$2$	$12$	$12$	$18.972$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓			2376.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}+\beta _{4}q^{7}+\beta _{6}q^{11}-\beta _{11}q^{13}+\cdots$
2376.2.b.b	$2376$	$2$	2376.b	33.d	$2$	$12$	$12$	$18.972$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓			2376.2.b.b	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}+\beta _{5}q^{7}-\beta _{8}q^{11}+\beta _{9}q^{13}+\cdots$
2376.2.b.c	$2376$	$2$	2376.b	33.d	$2$	$12$	$12$	$18.972$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓			2376.2.b.b	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}-\beta _{5}q^{7}+\beta _{7}q^{11}-\beta _{9}q^{13}+\cdots$
2376.2.b.d	$2376$	$2$	2376.b	33.d	$2$	$12$	$12$	$18.972$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓			2376.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}-\beta _{4}q^{7}-\beta _{7}q^{11}+\beta _{11}q^{13}+\cdots$
2376.2.q.a	$2376$	$2$	2376.q	9.c	$3$	$2$	$1$	$18.972$	$\Q(\sqrt{-3}) $	$_{}$	None	None					792.2.q.c	$2$	$0$	$0$	$0$	$-3$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-3\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+(-1+\zeta_{6})q^{11}+\cdots$
2376.2.q.b	$2376$	$2$	2376.q	9.c	$3$	$2$	$1$	$18.972$	$\Q(\sqrt{-3}) $	$_{}$	None	None					792.2.q.b	$2$	$0$	$0$	$0$	$-1$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+(1-\zeta_{6})q^{11}+\cdots$
2376.2.q.c	$2376$	$2$	2376.q	9.c	$3$	$2$	$1$	$18.972$	$\Q(\sqrt{-3}) $	$_{}$	None	None					792.2.q.a	$2$	$0$	$0$	$0$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{5}+(-1+\zeta_{6})q^{11}-2\zeta_{6}q^{13}+\cdots$
2376.2.q.d	$2376$	$2$	2376.q	9.c	$3$	$4$	$2$	$18.972$	$\Q(\zeta_{12})$	$_{}$	None	None					792.2.q.d	$2$	$0$	$0$	$0$	$0$	$-2$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta_{2} q^{5}+(-\beta_{3}+\beta_{2}+\beta_1-1)q^{7}+\cdots$

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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.