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 208 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1764.1.d.a	$1764$	$1$	1764.d	7.b	$2$	$2$	$2$	$0.880$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2$		\(q+(\zeta_{6}+\zeta_{6}^{2})q^{13}+(\zeta_{6}+\zeta_{6}^{2})q^{19}+\cdots\)
1764.1.g.a	$1764$	$1$	1764.g	4.b	$2$	$1$	$1$	$0.880$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \)	\(\Q(\sqrt{7}) \)	✓	$4$	$0$	\(1\)	\(0\)	\(0\)	\(0\)		$1$		\(q+q^{2}+q^{4}+q^{8}+q^{16}-q^{25}+2q^{29}+\cdots\)
1764.1.g.b	$1764$	$1$	1764.g	4.b	$2$	$2$	$2$	$0.880$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-1}) \)	None	✓	$4$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$1$		\(q-q^{2}+q^{4}-\beta q^{5}-q^{8}+\beta q^{10}-\beta q^{13}+\cdots\)
1764.1.g.c	$1764$	$1$	1764.g	4.b	$2$	$2$	$2$	$0.880$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-21}) \)	\(\Q(\sqrt{3}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$		\(q-iq^{2}-q^{4}+iq^{8}+iq^{11}+q^{16}+\cdots\)
1764.1.g.d	$1764$	$1$	1764.g	4.b	$2$	$2$	$2$	$0.880$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-1}) \)	None	✓	$4$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$1$		\(q+q^{2}+q^{4}-\beta q^{5}+q^{8}-\beta q^{10}+\beta q^{13}+\cdots\)
1764.1.h.a	$1764$	$1$	1764.h	84.h	$2$	$8$	$8$	$0.880$	\(\Q(\zeta_{16})\)	$D_{8}$	\(\Q(\sqrt{-1}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{3}$		\(q-\zeta_{16}^{4}q^{2}-q^{4}+(\zeta_{16}^{3}-\zeta_{16}^{5})q^{5}+\cdots\)
1764.1.q.a	$1764$	$1$	1764.q	84.j	$6$	$8$	$4$	$0.880$	\(\Q(\zeta_{24})\)	$D_{4}$	\(\Q(\sqrt{-7}) \)	None		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$		\(q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+\zeta_{24}^{9}q^{8}+\cdots\)
1764.1.q.b	$1764$	$1$	1764.q	84.j	$6$	$16$	$8$	$0.880$	\(\Q(\zeta_{48})\)	$D_{8}$	\(\Q(\sqrt{-1}) \)	None		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{6}$		\(q-\zeta_{48}^{20}q^{2}-\zeta_{48}^{16}q^{4}+(-\zeta_{48}^{5}+\cdots)q^{5}+\cdots\)
1764.1.y.a	$1764$	$1$	1764.y	28.g	$6$	$2$	$1$	$0.880$	\(\Q(\sqrt{-3}) \)	$D_{2}$	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \)	\(\Q(\sqrt{7}) \)		$8$	$0$	\(-1\)	\(0\)	\(0\)	\(0\)		$1$		\(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+q^{8}-\zeta_{6}q^{16}+\cdots\)
1764.1.y.b	$1764$	$1$	1764.y	28.g	$6$	$4$	$2$	$0.880$	\(\Q(\sqrt{2}, \sqrt{-3})\)	$D_{4}$	\(\Q(\sqrt{-1}) \)	None		$8$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$1$		\(q+\beta _{2}q^{2}+(-1-\beta _{2})q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots\)
1764.1.y.c	$1764$	$1$	1764.y	28.g	$6$	$4$	$2$	$0.880$	\(\Q(\zeta_{12})\)	$D_{2}$	\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-21}) \)	\(\Q(\sqrt{3}) \)		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$		\(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{8}+\zeta_{12}^{5}q^{11}+\cdots\)
1764.1.y.d	$1764$	$1$	1764.y	28.g	$6$	$4$	$2$	$0.880$	\(\Q(\sqrt{2}, \sqrt{-3})\)	$D_{4}$	\(\Q(\sqrt{-1}) \)	None		$8$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$1$		\(q-\beta _{2}q^{2}+(-1-\beta _{2})q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots\)
1764.1.z.a	$1764$	$1$	1764.z	7.d	$6$	$2$	$1$	$0.880$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$		\(q+(-\zeta_{6}-\zeta_{6}^{2})q^{13}+(1+\zeta_{6})q^{19}+\cdots\)
1764.1.co.a	$1764$	$1$	1764.co	49.h	$42$	$12$	$1$	$0.880$	\(\Q(\zeta_{21})\)	$D_{42}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)		$1$		\(q-\zeta_{42}^{16}q^{7}+(-\zeta_{42}^{8}+\zeta_{42}^{10})q^{13}+\cdots\)
1764.2.a.a	$1764$	$2$	1764.a	1.a	$1$	$1$	$1$	$14.086$	\(\Q\)	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(0\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}+3q^{11}+2q^{13}-3q^{17}-q^{19}+\cdots\)
1764.2.a.b	$1764$	$2$	1764.a	1.a	$1$	$1$	$1$	$14.086$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-2q^{11}-4q^{13}-6q^{17}+8q^{19}+\cdots\)
1764.2.a.c	$1764$	$2$	1764.a	1.a	$1$	$1$	$1$	$14.086$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-2q^{11}+3q^{13}+8q^{17}+q^{19}+\cdots\)
1764.2.a.d	$1764$	$2$	1764.a	1.a	$1$	$1$	$1$	$14.086$	\(\Q\)	$_{}$	\(\Q(\sqrt{-3}) \)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$+$	$1$	$N(\mathrm{U}(1))$	\(q-5q^{13}+q^{19}-5q^{25}-11q^{31}+\cdots\)
1764.2.a.e	$1764$	$2$	1764.a	1.a	$1$	$1$	$1$	$14.086$	\(\Q\)	$_{}$	\(\Q(\sqrt{-3}) \)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$+$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{13}-8q^{19}-5q^{25}+4q^{31}+\cdots\)
1764.2.a.f	$1764$	$2$	1764.a	1.a	$1$	$1$	$1$	$14.086$	\(\Q\)	$_{}$	\(\Q(\sqrt{-3}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$-$	$1$	$N(\mathrm{U}(1))$	\(q+5q^{13}-q^{19}-5q^{25}+11q^{31}+\cdots\)
1764.2.a.g	$1764$	$2$	1764.a	1.a	$1$	$1$	$1$	$14.086$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+6q^{11}-2q^{13}+4q^{19}+6q^{23}+\cdots\)
1764.2.a.h	$1764$	$2$	1764.a	1.a	$1$	$1$	$1$	$14.086$	\(\Q\)	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(0\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-2q^{11}-3q^{13}-8q^{17}-q^{19}+\cdots\)
1764.2.a.i	$1764$	$2$	1764.a	1.a	$1$	$1$	$1$	$14.086$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-2q^{11}+4q^{13}+6q^{17}-8q^{19}+\cdots\)
1764.2.a.j	$1764$	$2$	1764.a	1.a	$1$	$1$	$1$	$14.086$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(0\)	\(3\)	\(0\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}+3q^{11}-2q^{13}+3q^{17}+q^{19}+\cdots\)
1764.2.a.k	$1764$	$2$	1764.a	1.a	$1$	$1$	$1$	$14.086$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}-2q^{11}+6q^{13}-4q^{17}+4q^{19}+\cdots\)
1764.2.a.l	$1764$	$2$	1764.a	1.a	$1$	$2$	$2$	$14.086$	\(\Q(\sqrt{2}) \)	$_{}$	None	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}-4q^{11}-3\beta q^{13}+\beta q^{17}+\cdots\)
1764.2.a.m	$1764$	$2$	1764.a	1.a	$1$	$4$	$4$	$14.086$	\(\Q(\sqrt{2}, \sqrt{7})\)	$_{}$	None	None	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{5}-\beta _{3}q^{11}-3\beta _{1}q^{13}+\beta _{2}q^{17}+\cdots\)
1764.2.b.a	$1764$	$2$	1764.b	28.d	$2$	$4$	$4$	$14.086$	\(\Q(\zeta_{12})\)	$_{}$	None	None		$4$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\zeta_{12})q^{2}-2\zeta_{12}q^{4}-\zeta_{12}^{2}q^{5}+\cdots\)
1764.2.b.b	$1764$	$2$	1764.b	28.d	$2$	$4$	$4$	$14.086$	\(\Q(\sqrt{-3}, \sqrt{-7})\)	$_{}$	None	None		$4$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+(-2-\beta _{2})q^{4}+\beta _{3}q^{5}+(2+\cdots)q^{8}+\cdots\)
1764.2.b.c	$1764$	$2$	1764.b	28.d	$2$	$4$	$4$	$14.086$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}+(1-\beta _{2})q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots\)
1764.2.b.d	$1764$	$2$	1764.b	28.d	$2$	$4$	$4$	$14.086$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}+(1-\beta _{2})q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots\)
1764.2.b.e	$1764$	$2$	1764.b	28.d	$2$	$4$	$4$	$14.086$	4.0.2048.2	$_{}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{2}q^{2}+2q^{4}+(\beta _{1}+2\beta _{3})q^{5}+2\beta _{2}q^{8}+\cdots\)
1764.2.b.f	$1764$	$2$	1764.b	28.d	$2$	$4$	$4$	$14.086$	4.0.2048.2	$_{}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$7$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{2}q^{2}+2q^{4}+\beta _{1}q^{5}+2\beta _{2}q^{8}+\cdots\)
1764.2.b.g	$1764$	$2$	1764.b	28.d	$2$	$4$	$4$	$14.086$	4.0.2048.2	$_{}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{2}q^{2}+2q^{4}+(\beta _{1}+2\beta _{3})q^{5}-2\beta _{2}q^{8}+\cdots\)
1764.2.b.h	$1764$	$2$	1764.b	28.d	$2$	$4$	$4$	$14.086$	\(\Q(\sqrt{-3}, \sqrt{-7})\)	$_{}$	None	None		$4$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+(-2-\beta _{2})q^{4}+\beta _{3}q^{5}+(-2+\cdots)q^{8}+\cdots\)
1764.2.b.i	$1764$	$2$	1764.b	28.d	$2$	$8$	$8$	$14.086$	8.0.562828176.1	$_{}$	None	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{2}-\beta _{5})q^{5}+(\beta _{3}+\cdots)q^{8}+\cdots\)
1764.2.b.j	$1764$	$2$	1764.b	28.d	$2$	$8$	$8$	$14.086$	8.0.562828176.1	$_{}$	None	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}+\beta _{6}q^{4}+(\beta _{2}-\beta _{6})q^{5}+(-1+\cdots)q^{8}+\cdots\)
1764.2.b.k	$1764$	$2$	1764.b	28.d	$2$	$8$	$8$	$14.086$	8.0.\(\cdots\).10	$_{}$	None	None		$4$	$0$	\(4\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta _{3})q^{2}+(1+\beta _{3}+\beta _{5}-\beta _{6})q^{4}+\cdots\)
1764.2.b.l	$1764$	$2$	1764.b	28.d	$2$	$12$	$12$	$14.086$	12.0.\(\cdots\).1	$_{}$	None	None		$2$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+(\beta _{5}+\beta _{6})q^{4}+(1-\beta _{1}+\beta _{6}+\cdots)q^{5}+\cdots\)
1764.2.b.m	$1764$	$2$	1764.b	28.d	$2$	$12$	$12$	$14.086$	12.0.\(\cdots\).1	$_{}$	None	None		$2$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{2}+(-\beta _{2}-\beta _{11})q^{4}+(-1+\beta _{3}+\cdots)q^{5}+\cdots\)
1764.2.b.n	$1764$	$2$	1764.b	28.d	$2$	$16$	$16$	$14.086$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	$_{}$	None	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{5}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{7}q^{2}+(-1+\beta _{1}-\beta _{10})q^{4}+\beta _{12}q^{5}+\cdots\)
1764.2.e.a	$1764$	$2$	1764.e	12.b	$2$	$2$	$2$	$14.086$	\(\Q(\sqrt{-2}) \)	$_{}$	\(\Q(\sqrt{-1}) \)	None		$4$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{2}-2q^{4}+3\beta q^{5}-2\beta q^{8}-6q^{10}+\cdots\)
1764.2.e.b	$1764$	$2$	1764.e	12.b	$2$	$2$	$2$	$14.086$	\(\Q(\sqrt{-2}) \)	$_{}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{2}-2q^{4}+\beta q^{5}-2\beta q^{8}-2q^{10}+\cdots\)
1764.2.e.c	$1764$	$2$	1764.e	12.b	$2$	$2$	$2$	$14.086$	\(\Q(\sqrt{-2}) \)	$_{}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta q^{2}-2q^{4}+3\beta q^{5}+2\beta q^{8}+6q^{10}+\cdots\)
1764.2.e.d	$1764$	$2$	1764.e	12.b	$2$	$4$	$4$	$14.086$	\(\Q(\zeta_{8})\)	$_{}$	\(\Q(\sqrt{-1}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q-\zeta_{8}^{2}q^{2}-2q^{4}+2\zeta_{8}q^{5}+2\zeta_{8}^{2}q^{8}+\cdots\)
1764.2.e.e	$1764$	$2$	1764.e	12.b	$2$	$4$	$4$	$14.086$	\(\Q(\zeta_{8})\)	$_{}$	\(\Q(\sqrt{-1}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+\zeta_{8}^{2}q^{2}-2q^{4}-\zeta_{8}q^{5}-2\zeta_{8}^{2}q^{8}+\cdots\)
1764.2.e.f	$1764$	$2$	1764.e	12.b	$2$	$8$	$8$	$14.086$	8.0.157351936.1	$_{}$	\(\Q(\sqrt{-7}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{2}\cdot 3^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{6}q^{2}-\beta _{1}q^{4}-\beta _{5}q^{8}+(\beta _{5}+\beta _{6}+\cdots)q^{11}+\cdots\)
1764.2.e.g	$1764$	$2$	1764.e	12.b	$2$	$12$	$12$	$14.086$	12.0.\(\cdots\).1	$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{2}+(1+\beta _{10})q^{4}-\beta _{4}q^{5}+(\beta _{6}+\cdots)q^{8}+\cdots\)
1764.2.e.h	$1764$	$2$	1764.e	12.b	$2$	$16$	$16$	$14.086$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{5}q^{5}+(\beta _{3}-\beta _{5}+\cdots)q^{8}+\cdots\)
1764.2.e.i	$1764$	$2$	1764.e	12.b	$2$	$16$	$16$	$14.086$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{5}q^{5}+(-\beta _{3}+\beta _{5}+\cdots)q^{8}+\cdots\)