Newform search results

Level	Weight	Analytic conductor	\(Nk^2\)	Dim.
Bad \(p\)	Char.	Primitive character	Character order	Coefficient field
Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank
Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Results (1-50 of 258 matches)

 

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2304.1.b.a	$2304$	$1$	2304.b	8.d	$2$	$2$	$2$	$1.150$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{3}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2$		\(q-iq^{13}+q^{25}-iq^{37}+q^{49}+iq^{61}+\cdots\)
2304.1.e.a	$2304$	$1$	2304.e	3.b	$2$	$2$	$2$	$1.150$	\(\Q(\sqrt{-2}) \)	$D_{4}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$		\(q-\beta q^{5}-2q^{13}-\beta q^{17}-q^{25}-\beta q^{29}+\cdots\)
2304.1.e.b	$2304$	$1$	2304.e	3.b	$2$	$2$	$2$	$1.150$	\(\Q(\sqrt{-2}) \)	$D_{4}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$		\(q+\beta q^{5}+2q^{13}-\beta q^{17}-q^{25}+\beta q^{29}+\cdots\)
2304.1.g.a	$2304$	$1$	2304.g	4.b	$2$	$1$	$1$	$1.150$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-6}) \)	\(\Q(\sqrt{6}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$1$		\(q-2q^{5}+3q^{25}+2q^{29}+q^{49}+2q^{53}+\cdots\)
2304.1.g.b	$2304$	$1$	2304.g	4.b	$2$	$1$	$1$	$1.150$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{2}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$		\(q+2q^{17}-q^{25}+2q^{41}+q^{49}+2q^{73}+\cdots\)
2304.1.g.c	$2304$	$1$	2304.g	4.b	$2$	$1$	$1$	$1.150$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-6}) \)	\(\Q(\sqrt{6}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$1$		\(q+2q^{5}+3q^{25}-2q^{29}+q^{49}-2q^{53}+\cdots\)
2304.1.g.d	$2304$	$1$	2304.g	4.b	$2$	$2$	$2$	$1.150$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-6}) \)	\(\Q(\sqrt{2}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2$		\(q-iq^{7}-q^{25}-iq^{31}-3q^{49}+q^{73}+\cdots\)
2304.1.h.a	$2304$	$1$	2304.h	24.h	$2$	$4$	$4$	$1.150$	\(\Q(\zeta_{8})\)	$D_{4}$	\(\Q(\sqrt{-1}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{2}$		\(q+(-\zeta_{8}+\zeta_{8}^{3})q^{5}+(-\zeta_{8}-\zeta_{8}^{3})q^{17}+\cdots\)
2304.1.m.a	$2304$	$1$	2304.m	16.f	$4$	$4$	$2$	$1.150$	\(\Q(\zeta_{8})\)	$D_{4}$	\(\Q(\sqrt{-3}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2$		\(q+(\zeta_{8}-\zeta_{8}^{3})q^{7}+(-1+\zeta_{8}^{2})q^{13}+\cdots\)
2304.1.m.b	$2304$	$1$	2304.m	16.f	$4$	$4$	$2$	$1.150$	\(\Q(\zeta_{8})\)	$D_{4}$	\(\Q(\sqrt{-3}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2$		\(q+(\zeta_{8}-\zeta_{8}^{3})q^{7}+(1-\zeta_{8}^{2})q^{13}-\zeta_{8}q^{19}+\cdots\)
2304.1.o.a	$2304$	$1$	2304.o	36.f	$6$	$2$	$1$	$1.150$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-2}) \)	None		$4$	$0$	\(0\)	\(-1\)	\(0\)	\(0\)		$1$		\(q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{9}+(-1-\zeta_{6})q^{11}+\cdots\)
2304.1.o.b	$2304$	$1$	2304.o	36.f	$6$	$2$	$1$	$1.150$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-2}) \)	None		$4$	$0$	\(0\)	\(1\)	\(0\)	\(0\)		$1$		\(q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{9}+(1+\zeta_{6})q^{11}+q^{17}+\cdots\)
2304.1.o.c	$2304$	$1$	2304.o	36.f	$6$	$4$	$2$	$1.150$	\(\Q(\zeta_{12})\)	$D_{3}$	\(\Q(\sqrt{-2}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$		\(q+\zeta_{12}^{5}q^{3}-\zeta_{12}^{4}q^{9}+\zeta_{12}^{5}q^{11}+\cdots\)
2304.1.q.a	$2304$	$1$	2304.q	9.d	$6$	$2$	$1$	$1.150$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-2}) \)	None		$4$	$0$	\(0\)	\(-1\)	\(0\)	\(0\)		$1$		\(q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{9}+(1+\zeta_{6})q^{11}+(-\zeta_{6}+\cdots)q^{17}+\cdots\)
2304.1.q.b	$2304$	$1$	2304.q	9.d	$6$	$2$	$1$	$1.150$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-2}) \)	None		$4$	$0$	\(0\)	\(1\)	\(0\)	\(0\)		$1$		\(q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{9}+(-1-\zeta_{6})q^{11}+\cdots\)
2304.1.q.c	$2304$	$1$	2304.q	9.d	$6$	$4$	$2$	$1.150$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-2}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$		\(q+\zeta_{12}^{5}q^{3}-\zeta_{12}^{4}q^{9}-\zeta_{12}^{5}q^{11}+\cdots\)
2304.1.t.a	$2304$	$1$	2304.t	72.p	$6$	$4$	$2$	$1.150$	\(\Q(\zeta_{12})\)	$A_{4}$	None	None		$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)		$1$		\(q-q^{3}+\zeta_{12}^{5}q^{5}-\zeta_{12}q^{7}+q^{9}-\zeta_{12}^{4}q^{11}+\cdots\)
2304.1.t.b	$2304$	$1$	2304.t	72.p	$6$	$4$	$2$	$1.150$	\(\Q(\zeta_{12})\)	$A_{4}$	None	None		$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)		$1$		\(q+q^{3}+\zeta_{12}^{5}q^{5}+\zeta_{12}q^{7}+q^{9}+\zeta_{12}^{4}q^{11}+\cdots\)
2304.1.z.a	$2304$	$1$	2304.z	144.v	$12$	$8$	$2$	$1.150$	\(\Q(\zeta_{24})\)	$S_{4}$	None	None		$8$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)		$1$		\(q+\zeta_{24}^{5}q^{3}+(-\zeta_{24}^{4}+\zeta_{24}^{10})q^{5}+\cdots\)
2304.1.z.b	$2304$	$1$	2304.z	144.v	$12$	$8$	$2$	$1.150$	\(\Q(\zeta_{24})\)	$S_{4}$	None	None		$8$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$1$		\(q+\zeta_{24}^{5}q^{3}+(\zeta_{24}^{4}-\zeta_{24}^{10})q^{5}+(\zeta_{24}^{5}+\cdots)q^{7}+\cdots\)
2304.2.a.a	$2304$	$2$	2304.a	1.a	$1$	$1$	$1$	$18.398$	\(\Q\)	$_{}$	\(\Q(\sqrt{-1}) \)	None	✓	$2$	$1$	\(0\)	\(0\)	\(-4\)	\(0\)	$+$	$1$	$N(\mathrm{U}(1))$	\(q-4q^{5}+4q^{13}+2q^{17}+11q^{25}+\cdots\)
2304.2.a.b	$2304$	$2$	2304.a	1.a	$1$	$1$	$1$	$18.398$	\(\Q\)	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-2\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-2q^{7}+4q^{13}+2q^{17}+4q^{19}+\cdots\)
2304.2.a.c	$2304$	$2$	2304.a	1.a	$1$	$1$	$1$	$18.398$	\(\Q\)	$_{}$	\(\Q(\sqrt{-1}) \)	None	✓	$2$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)	$+$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{5}-4q^{13}+8q^{17}-q^{25}+10q^{29}+\cdots\)
2304.2.a.d	$2304$	$2$	2304.a	1.a	$1$	$1$	$1$	$18.398$	\(\Q\)	$_{}$	\(\Q(\sqrt{-1}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$-$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{5}+4q^{13}-8q^{17}-q^{25}+10q^{29}+\cdots\)
2304.2.a.e	$2304$	$2$	2304.a	1.a	$1$	$1$	$1$	$18.398$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+2q^{7}+4q^{13}+2q^{17}-4q^{19}+\cdots\)
2304.2.a.f	$2304$	$2$	2304.a	1.a	$1$	$1$	$1$	$18.398$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{7}-4q^{11}+4q^{13}+2q^{17}-4q^{19}+\cdots\)
2304.2.a.g	$2304$	$2$	2304.a	1.a	$1$	$1$	$1$	$18.398$	\(\Q\)	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{7}+4q^{11}-4q^{13}+2q^{17}+4q^{19}+\cdots\)
2304.2.a.h	$2304$	$2$	2304.a	1.a	$1$	$1$	$1$	$18.398$	\(\Q\)	$_{}$	\(\Q(\sqrt{-2}) \)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$+$	$1$	$N(\mathrm{U}(1))$	\(q-6q^{11}+6q^{17}+2q^{19}-5q^{25}+\cdots\)
2304.2.a.i	$2304$	$2$	2304.a	1.a	$1$	$1$	$1$	$18.398$	\(\Q\)	$_{}$	\(\Q(\sqrt{-2}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$-$	$1$	$N(\mathrm{U}(1))$	\(q+6q^{11}+6q^{17}-2q^{19}-5q^{25}+\cdots\)
2304.2.a.j	$2304$	$2$	2304.a	1.a	$1$	$1$	$1$	$18.398$	\(\Q\)	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(4\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{7}-4q^{11}-4q^{13}+2q^{17}-4q^{19}+\cdots\)
2304.2.a.k	$2304$	$2$	2304.a	1.a	$1$	$1$	$1$	$18.398$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{7}+4q^{11}+4q^{13}+2q^{17}+4q^{19}+\cdots\)
2304.2.a.l	$2304$	$2$	2304.a	1.a	$1$	$1$	$1$	$18.398$	\(\Q\)	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-2\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-2q^{7}-4q^{13}+2q^{17}-4q^{19}+\cdots\)
2304.2.a.m	$2304$	$2$	2304.a	1.a	$1$	$1$	$1$	$18.398$	\(\Q\)	$_{}$	\(\Q(\sqrt{-1}) \)	None	✓	$2$	$1$	\(0\)	\(0\)	\(2\)	\(0\)	$+$	$1$	$N(\mathrm{U}(1))$	\(q+2q^{5}-4q^{13}-8q^{17}-q^{25}-10q^{29}+\cdots\)
2304.2.a.n	$2304$	$2$	2304.a	1.a	$1$	$1$	$1$	$18.398$	\(\Q\)	$_{}$	\(\Q(\sqrt{-1}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$-$	$1$	$N(\mathrm{U}(1))$	\(q+2q^{5}+4q^{13}+8q^{17}-q^{25}-10q^{29}+\cdots\)
2304.2.a.o	$2304$	$2$	2304.a	1.a	$1$	$1$	$1$	$18.398$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+2q^{7}-4q^{13}+2q^{17}+4q^{19}+\cdots\)
2304.2.a.p	$2304$	$2$	2304.a	1.a	$1$	$1$	$1$	$18.398$	\(\Q\)	$_{}$	\(\Q(\sqrt{-1}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$-$	$1$	$N(\mathrm{U}(1))$	\(q+4q^{5}-4q^{13}+2q^{17}+11q^{25}+\cdots\)
2304.2.a.q	$2304$	$2$	2304.a	1.a	$1$	$2$	$2$	$18.398$	\(\Q(\sqrt{2}) \)	$_{}$	\(\Q(\sqrt{-6}) \)	None	✓	$4$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)	$+$	$2$	$N(\mathrm{U}(1))$	\(q+\beta q^{5}-2q^{7}-2\beta q^{11}+3q^{25}-\beta q^{29}+\cdots\)
2304.2.a.r	$2304$	$2$	2304.a	1.a	$1$	$2$	$2$	$18.398$	\(\Q(\sqrt{2}) \)	$_{}$	None	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{5}-\beta q^{7}-4q^{11}+2\beta q^{13}+2q^{17}+\cdots\)
2304.2.a.s	$2304$	$2$	2304.a	1.a	$1$	$2$	$2$	$18.398$	\(\Q(\sqrt{3}) \)	$_{}$	None	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{5}-\beta q^{7}-6q^{17}-4q^{19}-2\beta q^{23}+\cdots\)
2304.2.a.t	$2304$	$2$	2304.a	1.a	$1$	$2$	$2$	$18.398$	\(\Q(\sqrt{2}) \)	$_{}$	\(\Q(\sqrt{-2}) \)	None	✓	$4$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$+$	$2$	$N(\mathrm{U}(1))$	\(q+\beta q^{11}-6q^{17}-3\beta q^{19}-5q^{25}+\cdots\)
2304.2.a.u	$2304$	$2$	2304.a	1.a	$1$	$2$	$2$	$18.398$	\(\Q(\sqrt{3}) \)	$_{}$	None	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+\beta q^{7}-6q^{17}+4q^{19}+2\beta q^{23}+\cdots\)
2304.2.a.v	$2304$	$2$	2304.a	1.a	$1$	$2$	$2$	$18.398$	\(\Q(\sqrt{3}) \)	$_{}$	\(\Q(\sqrt{-3}) \)	None	✓	$4$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$+$	$2$	$N(\mathrm{U}(1))$	\(q+\beta q^{7}-2\beta q^{13}-8q^{19}-5q^{25}+\cdots\)
2304.2.a.w	$2304$	$2$	2304.a	1.a	$1$	$2$	$2$	$18.398$	\(\Q(\sqrt{3}) \)	$_{}$	\(\Q(\sqrt{-3}) \)	None	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$-$	$2$	$N(\mathrm{U}(1))$	\(q-\beta q^{7}-2\beta q^{13}+8q^{19}-5q^{25}+\cdots\)
2304.2.a.x	$2304$	$2$	2304.a	1.a	$1$	$2$	$2$	$18.398$	\(\Q(\sqrt{2}) \)	$_{}$	None	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+\beta q^{7}+4q^{11}+2\beta q^{13}+2q^{17}+\cdots\)
2304.2.a.y	$2304$	$2$	2304.a	1.a	$1$	$2$	$2$	$18.398$	\(\Q(\sqrt{2}) \)	$_{}$	\(\Q(\sqrt{-6}) \)	None	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$-$	$2$	$N(\mathrm{U}(1))$	\(q+\beta q^{5}+2q^{7}+2\beta q^{11}+3q^{25}-\beta q^{29}+\cdots\)
2304.2.a.z	$2304$	$2$	2304.a	1.a	$1$	$4$	$4$	$18.398$	\(\Q(\zeta_{24})^+\)	$_{}$	\(\Q(\sqrt{-6}) \)	None	✓	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$-$	$2^{5}$	$N(\mathrm{U}(1))$	\(q+\beta _{2}q^{5}+\beta _{1}q^{7}+\beta _{3}q^{11}+7q^{25}+\cdots\)
2304.2.c.a	$2304$	$2$	2304.c	12.b	$2$	$2$	$2$	$18.398$	\(\Q(\sqrt{-2}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}-2\beta q^{7}-4q^{11}-2q^{13}+\beta q^{17}+\cdots\)
2304.2.c.b	$2304$	$2$	2304.c	12.b	$2$	$2$	$2$	$18.398$	\(\Q(\sqrt{-2}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}-2\beta q^{7}-4q^{11}+2q^{13}-\beta q^{17}+\cdots\)
2304.2.c.c	$2304$	$2$	2304.c	12.b	$2$	$2$	$2$	$18.398$	\(\Q(\sqrt{-2}) \)	$_{}$	\(\Q(\sqrt{-1}) \)	None		$4$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+3\beta q^{5}-6q^{13}-5\beta q^{17}-13q^{25}+\cdots\)
2304.2.c.d	$2304$	$2$	2304.c	12.b	$2$	$2$	$2$	$18.398$	\(\Q(\sqrt{-2}) \)	$_{}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{5}-6q^{13}-3\beta q^{17}+3q^{25}+\cdots\)