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 213 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
392.1.g.a	$392$	$1$	392.g	8.d	$2$	$1$	$1$	$0.196$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{14}) \)	✓	$4$	$0$	\(1\)	\(0\)	\(0\)	\(0\)		$1$		\(q+q^{2}+q^{4}+q^{8}-q^{9}-2q^{11}+q^{16}+\cdots\)
392.1.g.b	$392$	$1$	392.g	8.d	$2$	$2$	$2$	$0.196$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-2}) \)	None	✓	$4$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$1$		\(q-q^{2}-\beta q^{3}+q^{4}+\beta q^{6}-q^{8}+q^{9}+\cdots\)
392.1.j.a	$392$	$1$	392.j	56.j	$6$	$2$	$1$	$0.196$	\(\Q(\sqrt{-3}) \)	$D_{2}$	\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-14}) \)	\(\Q(\sqrt{2}) \)		$8$	$0$	\(1\)	\(0\)	\(0\)	\(0\)		$1$		\(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-q^{8}+\zeta_{6}q^{9}-\zeta_{6}q^{16}+\cdots\)
392.1.k.a	$392$	$1$	392.k	56.k	$6$	$2$	$1$	$0.196$	\(\Q(\sqrt{-3}) \)	$D_{2}$	\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{14}) \)		$8$	$0$	\(-1\)	\(0\)	\(0\)	\(0\)		$1$		\(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+q^{8}+\zeta_{6}q^{9}-\zeta_{6}^{2}q^{11}+\cdots\)
392.1.k.b	$392$	$1$	392.k	56.k	$6$	$4$	$2$	$0.196$	\(\Q(\sqrt{2}, \sqrt{-3})\)	$D_{4}$	\(\Q(\sqrt{-2}) \)	None		$8$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$1$		\(q-\beta _{2}q^{2}-\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+\beta _{3}q^{6}+\cdots\)
392.2.a.a	$392$	$2$	392.a	1.a	$1$	$1$	$1$	$3.130$	\(\Q\)	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(-3\)	\(1\)	\(0\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+q^{5}+6q^{9}-q^{11}-2q^{13}+\cdots\)
392.2.a.b	$392$	$2$	392.a	1.a	$1$	$1$	$1$	$3.130$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(-2\)	\(4\)	\(0\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+4q^{5}+q^{9}-8q^{15}+2q^{17}+\cdots\)
392.2.a.c	$392$	$2$	392.a	1.a	$1$	$1$	$1$	$3.130$	\(\Q\)	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(0\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-2q^{9}+3q^{11}-6q^{13}+\cdots\)
392.2.a.d	$392$	$2$	392.a	1.a	$1$	$1$	$1$	$3.130$	\(\Q\)	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-3q^{9}-4q^{11}-2q^{13}+6q^{17}+\cdots\)
392.2.a.e	$392$	$2$	392.a	1.a	$1$	$1$	$1$	$3.130$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(0\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-2q^{9}+3q^{11}+6q^{13}+\cdots\)
392.2.a.f	$392$	$2$	392.a	1.a	$1$	$1$	$1$	$3.130$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(3\)	\(-1\)	\(0\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-q^{5}+6q^{9}-q^{11}+2q^{13}+\cdots\)
392.2.a.g	$392$	$2$	392.a	1.a	$1$	$2$	$2$	$3.130$	\(\Q(\sqrt{2}) \)	$_{}$	None	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+2\beta q^{5}-q^{9}+6q^{11}-4\beta q^{13}+\cdots\)
392.2.a.h	$392$	$2$	392.a	1.a	$1$	$2$	$2$	$3.130$	\(\Q(\sqrt{2}) \)	$_{}$	None	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+\beta q^{5}+5q^{9}-4q^{11}-\beta q^{13}+\cdots\)
392.2.b.a	$392$	$2$	392.b	8.b	$2$	$2$	$2$	$3.130$	\(\Q(\sqrt{-7}) \)	$_{}$	\(\Q(\sqrt{-7}) \)	None		$4$	$0$	\(-1\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta q^{2}+(-2+\beta )q^{4}+(2+\beta )q^{8}+3q^{9}+\cdots\)
392.2.b.b	$392$	$2$	392.b	8.b	$2$	$2$	$2$	$3.130$	\(\Q(\sqrt{-2}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-\beta q^{3}-2q^{4}+\beta q^{5}+2q^{6}+\cdots\)
392.2.b.c	$392$	$2$	392.b	8.b	$2$	$4$	$4$	$3.130$	4.0.2312.1	$_{}$	None	None		$2$	$0$	\(-1\)	\(0\)	\(0\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+\beta _{2}q^{4}+\cdots\)
392.2.b.d	$392$	$2$	392.b	8.b	$2$	$4$	$4$	$3.130$	4.0.7168.1	$_{}$	\(\Q(\sqrt{-14}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{3}q^{2}+\beta _{1}q^{3}+2q^{4}-\beta _{2}q^{5}+(-\beta _{1}+\cdots)q^{6}+\cdots\)
392.2.b.e	$392$	$2$	392.b	8.b	$2$	$6$	$6$	$3.130$	6.0.1142512.1	$_{}$	None	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}+\beta _{3}q^{3}-\beta _{2}q^{4}+(-\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)
392.2.b.f	$392$	$2$	392.b	8.b	$2$	$6$	$6$	$3.130$	6.0.1142512.1	$_{}$	None	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}-\beta _{3}q^{3}-\beta _{2}q^{4}+(\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
392.2.b.g	$392$	$2$	392.b	8.b	$2$	$12$	$12$	$3.130$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	$_{}$	None	None		$4$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}-\beta _{9}q^{3}-\beta _{1}q^{4}+(\beta _{7}-\beta _{8}+\cdots)q^{5}+\cdots\)
392.2.e.a	$392$	$2$	392.e	56.e	$2$	$4$	$4$	$3.130$	4.0.2048.2	$_{}$	\(\Q(\sqrt{-2}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$7$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{2}q^{2}-\beta _{3}q^{3}+2q^{4}-\beta _{1}q^{6}-2\beta _{2}q^{8}+\cdots\)
392.2.e.b	$392$	$2$	392.e	56.e	$2$	$4$	$4$	$3.130$	4.0.2048.2	$_{}$	\(\Q(\sqrt{-2}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{2}q^{2}+\beta _{1}q^{3}+2q^{4}+(-\beta _{1}+\beta _{3})q^{6}+\cdots\)
392.2.e.c	$392$	$2$	392.e	56.e	$2$	$8$	$8$	$3.130$	8.0.339738624.1	$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}+(\beta _{4}+\beta _{7})q^{3}+(-1+\beta _{6}+\cdots)q^{4}+\cdots\)
392.2.e.d	$392$	$2$	392.e	56.e	$2$	$8$	$8$	$3.130$	8.0.\(\cdots\).10	$_{}$	None	None		$4$	$0$	\(4\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\beta _{5})q^{2}-\beta _{2}q^{3}+(\beta _{3}-\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots\)
392.2.e.e	$392$	$2$	392.e	56.e	$2$	$12$	$12$	$3.130$	12.0.\(\cdots\).2	$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}-\beta _{10}q^{3}+\beta _{1}q^{4}-\beta _{9}q^{5}+\cdots\)
392.2.i.a	$392$	$2$	392.i	7.c	$3$	$2$	$1$	$3.130$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(-2\)	\(4\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{3}+4\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
392.2.i.b	$392$	$2$	392.i	7.c	$3$	$2$	$1$	$3.130$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(-1\)	\(-1\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+2\zeta_{6}q^{9}+\cdots\)
392.2.i.c	$392$	$2$	392.i	7.c	$3$	$2$	$1$	$3.130$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\zeta_{6}q^{5}+3\zeta_{6}q^{9}+(4-4\zeta_{6})q^{11}+\cdots\)
392.2.i.d	$392$	$2$	392.i	7.c	$3$	$2$	$1$	$3.130$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{5}+3\zeta_{6}q^{9}+(4-4\zeta_{6})q^{11}+\cdots\)
392.2.i.e	$392$	$2$	392.i	7.c	$3$	$2$	$1$	$3.130$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(2\)	\(-4\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\zeta_{6})q^{3}-4\zeta_{6}q^{5}-\zeta_{6}q^{9}-8q^{15}+\cdots\)
392.2.i.f	$392$	$2$	392.i	7.c	$3$	$2$	$1$	$3.130$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(3\)	\(-1\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(3-3\zeta_{6})q^{3}-\zeta_{6}q^{5}-6\zeta_{6}q^{9}+(1+\cdots)q^{11}+\cdots\)
392.2.i.g	$392$	$2$	392.i	7.c	$3$	$4$	$2$	$3.130$	\(\Q(\sqrt{2}, \sqrt{-3})\)	$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{5}+5\beta _{2}q^{9}+\cdots\)
392.2.i.h	$392$	$2$	392.i	7.c	$3$	$4$	$2$	$3.130$	\(\Q(\sqrt{2}, \sqrt{-3})\)	$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{3}+(-2\beta _{1}-2\beta _{3})q^{5}-\beta _{2}q^{9}+\cdots\)
392.2.m.a	$392$	$2$	392.m	56.m	$6$	$4$	$2$	$3.130$	\(\Q(\sqrt{-3}, \sqrt{-7})\)	$_{}$	\(\Q(\sqrt{-7}) \)	None		$8$	$0$	\(-1\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{6}]$	\(q-\beta _{3}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(-3+\beta _{1}+\cdots)q^{8}+\cdots\)
392.2.m.b	$392$	$2$	392.m	56.m	$6$	$8$	$4$	$3.130$	8.0.339738624.1	$_{}$	\(\Q(\sqrt{-2}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{6}]$	\(q-\beta _{6}q^{2}+\beta _{3}q^{3}+(-2-2\beta _{4})q^{4}+\cdots\)
392.2.m.c	$392$	$2$	392.m	56.m	$6$	$8$	$4$	$3.130$	8.0.339738624.1	$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{6}q^{2}+(-\beta _{3}+\beta _{5}-\beta _{7})q^{3}+(-2+\cdots)q^{4}+\cdots\)
392.2.m.d	$392$	$2$	392.m	56.m	$6$	$8$	$4$	$3.130$	8.0.339738624.1	$_{}$	\(\Q(\sqrt{-2}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$7^{2}$	$\mathrm{U}(1)[D_{6}]$	\(q+\beta _{5}q^{2}-\beta _{1}q^{3}+(-2-2\beta _{4})q^{4}+\cdots\)
392.2.m.e	$392$	$2$	392.m	56.m	$6$	$8$	$4$	$3.130$	8.0.339738624.1	$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{2}q^{2}+(-\beta _{1}+\beta _{3})q^{3}+2q^{4}+(2\beta _{1}+\cdots)q^{5}+\cdots\)
392.2.m.f	$392$	$2$	392.m	56.m	$6$	$8$	$4$	$3.130$	\(\Q(\zeta_{24})\)	$_{}$	None	None		$8$	$0$	\(4\)	\(0\)	\(0\)	\(0\)		$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1+\zeta_{24}-\zeta_{24}^{2})q^{2}+(-\zeta_{24}^{4}+\zeta_{24}^{7})q^{3}+\cdots\)
392.2.m.g	$392$	$2$	392.m	56.m	$6$	$12$	$6$	$3.130$	12.0.\(\cdots\).2	$_{}$	None	None		$4$	$0$	\(0\)	\(6\)	\(0\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{1}-\beta _{8})q^{2}+(1+\beta _{10})q^{3}+(\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots\)
392.2.m.h	$392$	$2$	392.m	56.m	$6$	$16$	$8$	$3.130$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	$_{}$	None	None		$8$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{5}+\beta _{14})q^{2}-\beta _{15}q^{3}+(1+\beta _{5}+\cdots)q^{4}+\cdots\)
392.2.p.a	$392$	$2$	392.p	56.p	$6$	$4$	$2$	$3.130$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{3})q^{3}+2\beta _{2}q^{4}+\cdots\)
392.2.p.b	$392$	$2$	392.p	56.p	$6$	$4$	$2$	$3.130$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{3})q^{3}+2\beta _{2}q^{4}+\beta _{1}q^{5}+\cdots\)
392.2.p.c	$392$	$2$	392.p	56.p	$6$	$4$	$2$	$3.130$	\(\Q(\sqrt{-3}, \sqrt{-7})\)	$_{}$	\(\Q(\sqrt{-7}) \)	None		$8$	$0$	\(1\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{6}]$	\(q+\beta _{3}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(3-\beta _{1}+\cdots)q^{8}+\cdots\)
392.2.p.d	$392$	$2$	392.p	56.p	$6$	$8$	$4$	$3.130$	8.0.\(\cdots\).10	$_{}$	\(\Q(\sqrt{-14}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{2}$	$\mathrm{U}(1)[D_{6}]$	\(q-\beta _{5}q^{2}-\beta _{6}q^{3}+(-2+2\beta _{2})q^{4}+\cdots\)
392.2.p.e	$392$	$2$	392.p	56.p	$6$	$8$	$4$	$3.130$	8.0.432972864.2	$_{}$	None	None		$4$	$0$	\(1\)	\(0\)	\(0\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{1}-\beta _{6})q^{2}+(\beta _{5}+\beta _{6})q^{3}+\beta _{5}q^{4}+\cdots\)
392.2.p.f	$392$	$2$	392.p	56.p	$6$	$8$	$4$	$3.130$	8.0.432972864.2	$_{}$	None	None		$4$	$0$	\(1\)	\(0\)	\(0\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{1}-\beta _{6})q^{2}+(-\beta _{5}-\beta _{6})q^{3}+\cdots\)
392.2.p.g	$392$	$2$	392.p	56.p	$6$	$12$	$6$	$3.130$	12.0.\(\cdots\).1	$_{}$	None	None		$4$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{1}+\beta _{5})q^{2}-\beta _{6}q^{3}-\beta _{3}q^{4}+\cdots\)
392.2.p.h	$392$	$2$	392.p	56.p	$6$	$24$	$12$	$3.130$		$_{}$	None	None		$8$	$0$	\(2\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{6}]$
392.2.q.a	$392$	$2$	392.q	49.e	$7$	$42$	$7$	$3.130$		$_{}$	None	None		$2$	$0$	\(0\)	\(-7\)	\(-2\)	\(1\)			$\mathrm{SU}(2)[C_{7}]$