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Results (1-50 of 86 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
407.1.d.a	$407$	$1$	407.d	407.d	$2$	$1$	$1$	$0.203$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-407}) \)	\(\Q(\sqrt{37}) \)	✓	$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$1$		\(q-2q^{3}-q^{4}+3q^{9}+q^{11}+2q^{12}+\cdots\)
407.1.d.b	$407$	$1$	407.d	407.d	$2$	$2$	$2$	$0.203$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-407}) \)	None	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$		\(q-\beta q^{2}+q^{4}-q^{9}+q^{11}+\beta q^{13}+\cdots\)
407.1.d.c	$407$	$1$	407.d	407.d	$2$	$4$	$4$	$0.203$	\(\Q(\zeta_{16})^+\)	$D_{8}$	\(\Q(\sqrt{-407}) \)	None	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$		\(q-\beta _{1}q^{2}-\beta _{2}q^{3}+(1+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots\)
407.1.i.a	$407$	$1$	407.i	407.i	$6$	$2$	$1$	$0.203$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-11}) \)	None		$4$	$0$	\(0\)	\(-1\)	\(0\)	\(0\)		$1$		\(q-\zeta_{6}q^{3}+\zeta_{6}q^{4}+q^{11}-\zeta_{6}^{2}q^{12}+\cdots\)
407.1.j.a	$407$	$1$	407.j	407.j	$6$	$2$	$1$	$0.203$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-11}) \)	None		$4$	$0$	\(0\)	\(1\)	\(-2\)	\(0\)		$1$		\(q-\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}+q^{11}+\cdots\)
407.1.t.a	$407$	$1$	407.t	407.t	$18$	$6$	$1$	$0.203$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-11}) \)	None		$4$	$0$	\(0\)	\(-3\)	\(0\)	\(0\)		$1$		\(q+(\zeta_{18}^{2}+\zeta_{18}^{6})q^{3}-\zeta_{18}q^{4}+\zeta_{18}^{7}q^{5}+\cdots\)
407.1.u.a	$407$	$1$	407.u	407.u	$18$	$6$	$1$	$0.203$	\(\Q(\zeta_{18})\)	$D_{18}$	\(\Q(\sqrt{-11}) \)	None		$4$	$0$	\(0\)	\(3\)	\(0\)	\(0\)		$1$		\(q+(-\zeta_{18}^{6}-\zeta_{18}^{8})q^{3}-\zeta_{18}^{4}q^{4}+\cdots\)
407.2.a.a	$407$	$2$	407.a	1.a	$1$	$4$	$4$	$3.250$	4.4.1957.1	$_{}$	None	None	✓	$1$	$1$	\(-1\)	\(0\)	\(1\)	\(-7\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(-\beta _{1}-2\beta _{2}-\beta _{3})q^{4}+\cdots\)
407.2.a.b	$407$	$2$	407.a	1.a	$1$	$4$	$4$	$3.250$	4.4.1957.1	$_{}$	None	None	✓	$1$	$1$	\(1\)	\(-4\)	\(-5\)	\(-1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}-\beta _{2})q^{2}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
407.2.a.c	$407$	$2$	407.a	1.a	$1$	$11$	$11$	$3.250$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	$_{}$	None	None	✓	$1$	$0$	\(2\)	\(0\)	\(1\)	\(9\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}+\beta _{9}q^{5}+\cdots\)
407.2.a.d	$407$	$2$	407.a	1.a	$1$	$12$	$12$	$3.250$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	$_{}$	None	None	✓	$1$	$0$	\(1\)	\(8\)	\(5\)	\(7\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{10})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
407.2.b.a	$407$	$2$	407.b	37.b	$2$	$14$	$14$	$3.250$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	$_{}$	None	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(-10\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{8}q^{3}+(-1+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots\)
407.2.b.b	$407$	$2$	407.b	37.b	$2$	$18$	$18$	$3.250$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	$_{}$	None	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(-2\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{7}q^{3}+(-1+\beta _{2})q^{4}-\beta _{8}q^{5}+\cdots\)
407.2.e.a	$407$	$2$	407.e	37.c	$3$	$2$	$1$	$3.250$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(-1\)	\(3\)	\(-2\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{3}+2\zeta_{6}q^{4}+3\zeta_{6}q^{5}-2\zeta_{6}q^{7}+\cdots\)
407.2.e.b	$407$	$2$	407.e	37.c	$3$	$2$	$1$	$3.250$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(1\)	\(2\)	\(3\)	\(-2\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+2\zeta_{6}q^{3}+\zeta_{6}q^{4}+3\zeta_{6}q^{5}+\cdots\)
407.2.e.c	$407$	$2$	407.e	37.c	$3$	$4$	$2$	$3.250$	\(\Q(\sqrt{-3}, \sqrt{5})\)	$_{}$	None	None		$2$	$0$	\(-3\)	\(2\)	\(0\)	\(4\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{1}-\beta _{3})q^{2}-\beta _{3}q^{3}+(3\beta _{1}+\cdots)q^{4}+\cdots\)
407.2.e.d	$407$	$2$	407.e	37.c	$3$	$28$	$14$	$3.250$		$_{}$	None	None		$2$	$0$	\(-2\)	\(-2\)	\(1\)	\(9\)			$\mathrm{SU}(2)[C_{3}]$
407.2.e.e	$407$	$2$	407.e	37.c	$3$	$32$	$16$	$3.250$		$_{}$	None	None		$2$	$0$	\(2\)	\(-4\)	\(-5\)	\(-3\)			$\mathrm{SU}(2)[C_{3}]$
407.2.f.a	$407$	$2$	407.f	407.f	$4$	$4$	$2$	$3.250$	\(\Q(i, \sqrt{11})\)	$_{}$	\(\Q(\sqrt{-11}) \)	None		$4$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)		$1$	$\mathrm{U}(1)[D_{4}]$	\(q+\beta _{2}q^{3}+2\beta _{2}q^{4}+(-2+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
407.2.f.b	$407$	$2$	407.f	407.f	$4$	$4$	$2$	$3.250$	\(\Q(i, \sqrt{19})\)	$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(8\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{2}q^{3}+2\beta _{2}q^{4}+(2-2\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots\)
407.2.f.c	$407$	$2$	407.f	407.f	$4$	$64$	$32$	$3.250$		$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)			$\mathrm{SU}(2)[C_{4}]$
407.2.h.a	$407$	$2$	407.h	11.c	$5$	$72$	$18$	$3.250$		$_{}$	None	None		$2$	$0$	\(-6\)	\(-2\)	\(-2\)	\(-9\)			$\mathrm{SU}(2)[C_{5}]$
407.2.h.b	$407$	$2$	407.h	11.c	$5$	$72$	$18$	$3.250$		$_{}$	None	None		$2$	$0$	\(4\)	\(-2\)	\(-2\)	\(7\)			$\mathrm{SU}(2)[C_{5}]$
407.2.k.a	$407$	$2$	407.k	37.e	$6$	$2$	$1$	$3.250$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(3\)	\(-1\)	\(0\)	\(-4\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1+\zeta_{6})q^{2}-\zeta_{6}q^{3}+\zeta_{6}q^{4}+(1-2\zeta_{6})q^{6}+\cdots\)
407.2.k.b	$407$	$2$	407.k	37.e	$6$	$4$	$2$	$3.250$	\(\Q(\zeta_{12})\)	$_{}$	None	None		$2$	$1$	\(-6\)	\(-4\)	\(-6\)	\(-6\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\zeta_{12}-\zeta_{12}^{2})q^{2}-2\zeta_{12}^{2}q^{3}+\cdots\)
407.2.k.c	$407$	$2$	407.k	37.e	$6$	$4$	$2$	$3.250$	\(\Q(\sqrt{-3}, \sqrt{-7})\)	$_{}$	None	None		$2$	$0$	\(-3\)	\(2\)	\(0\)	\(-6\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\beta _{3})q^{2}+(1-\beta _{2})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
407.2.k.d	$407$	$2$	407.k	37.e	$6$	$6$	$3$	$3.250$	6.0.1156923.1	$_{}$	None	None		$2$	$0$	\(3\)	\(0\)	\(9\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\beta _{1}+\beta _{3}+\beta _{4})q^{2}+(-\beta _{1}+\beta _{3}+\cdots)q^{3}+\cdots\)
407.2.k.e	$407$	$2$	407.k	37.e	$6$	$16$	$8$	$3.250$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	$_{}$	None	None		$2$	$0$	\(-3\)	\(-5\)	\(-6\)	\(11\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{3}q^{2}+(-1+\beta _{1}+\beta _{8})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
407.2.k.f	$407$	$2$	407.k	37.e	$6$	$32$	$16$	$3.250$		$_{}$	None	None		$2$	$0$	\(6\)	\(3\)	\(9\)	\(-1\)			$\mathrm{SU}(2)[C_{6}]$
407.2.l.a	$407$	$2$	407.l	37.f	$9$	$84$	$14$	$3.250$		$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(-6\)	\(3\)			$\mathrm{SU}(2)[C_{9}]$
407.2.l.b	$407$	$2$	407.l	37.f	$9$	$108$	$18$	$3.250$		$_{}$	None	None		$2$	$0$	\(0\)	\(-3\)	\(-6\)	\(3\)			$\mathrm{SU}(2)[C_{9}]$
407.2.o.a	$407$	$2$	407.o	407.o	$10$	$144$	$36$	$3.250$		$_{}$	None	None		$4$	$0$	\(0\)	\(-8\)	\(0\)	\(-10\)			$\mathrm{SU}(2)[C_{10}]$
407.2.q.a	$407$	$2$	407.q	407.q	$12$	$8$	$2$	$3.250$	8.0.22581504.2	$_{}$	None	None		$2$	$0$	\(0\)	\(-6\)	\(-2\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-1+\beta _{2}+\beta _{3}+\beta _{4}+\beta _{6}+\beta _{7})q^{2}+\cdots\)
407.2.q.b	$407$	$2$	407.q	407.q	$12$	$8$	$2$	$3.250$	8.0.22581504.2	$_{}$	None	None		$2$	$0$	\(0\)	\(-6\)	\(-2\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(1-\beta _{2}-\beta _{3}-\beta _{4}-\beta _{6}-\beta _{7})q^{2}+\cdots\)
407.2.q.c	$407$	$2$	407.q	407.q	$12$	$8$	$2$	$3.250$	8.0.303595776.1	$_{}$	\(\Q(\sqrt{-11}) \)	None		$4$	$0$	\(0\)	\(0\)	\(6\)	\(0\)		$1$	$\mathrm{U}(1)[D_{12}]$	\(q+(2\beta _{1}-\beta _{5}-\beta _{7})q^{3}-2\beta _{3}q^{4}+(1+\cdots)q^{5}+\cdots\)
407.2.q.d	$407$	$2$	407.q	407.q	$12$	$120$	$30$	$3.250$		$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)			$\mathrm{SU}(2)[C_{12}]$
407.2.r.a	$407$	$2$	407.r	407.r	$15$	$288$	$36$	$3.250$		$_{}$	None	None		$4$	$0$	\(-1\)	\(-2\)	\(-5\)	\(-7\)			$\mathrm{SU}(2)[C_{15}]$
407.2.s.a	$407$	$2$	407.s	37.h	$18$	$78$	$13$	$3.250$		$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(-3\)	\(-3\)			$\mathrm{SU}(2)[C_{18}]$
407.2.s.b	$407$	$2$	407.s	37.h	$18$	$102$	$17$	$3.250$		$_{}$	None	None		$2$	$0$	\(0\)	\(3\)	\(-3\)	\(-3\)			$\mathrm{SU}(2)[C_{18}]$
407.2.w.a	$407$	$2$	407.w	407.w	$20$	$288$	$36$	$3.250$		$_{}$	None	None		$4$	$0$	\(-10\)	\(0\)	\(-4\)	\(-20\)			$\mathrm{SU}(2)[C_{20}]$
407.2.x.a	$407$	$2$	407.x	407.x	$30$	$288$	$36$	$3.250$		$_{}$	None	None		$4$	$0$	\(-15\)	\(-4\)	\(-9\)	\(1\)			$\mathrm{SU}(2)[C_{30}]$
407.2.bb.a	$407$	$2$	407.bb	407.ab	$36$	$24$	$2$	$3.250$		$_{}$	\(\Q(\sqrt{-11}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{U}(1)[D_{36}]$
407.2.bb.b	$407$	$2$	407.bb	407.ab	$36$	$408$	$34$	$3.250$		$_{}$	None	None		$4$	$0$	\(0\)	\(-24\)	\(-24\)	\(0\)			$\mathrm{SU}(2)[C_{36}]$
407.2.bc.a	$407$	$2$	407.bc	407.ac	$45$	$864$	$36$	$3.250$		$_{}$	None	None		$4$	$0$	\(-24\)	\(-21\)	\(-18\)	\(-18\)			$\mathrm{SU}(2)[C_{45}]$
407.2.bd.a	$407$	$2$	407.bd	407.ad	$60$	$576$	$36$	$3.250$		$_{}$	None	None		$4$	$0$	\(-20\)	\(-18\)	\(-14\)	\(-10\)			$\mathrm{SU}(2)[C_{60}]$
407.2.bg.a	$407$	$2$	407.bg	407.ag	$90$	$864$	$36$	$3.250$		$_{}$	None	None		$4$	$0$	\(-12\)	\(-15\)	\(-18\)	\(-18\)			$\mathrm{SU}(2)[C_{90}]$
407.2.bj.a	$407$	$2$	407.bj	407.aj	$180$	$1728$	$36$	$3.250$		$_{}$	None	None		$4$	$0$	\(-60\)	\(-36\)	\(-36\)	\(-60\)			$\mathrm{SU}(2)[C_{180}]$
407.3.c.a	$407$	$3$	407.c	11.b	$2$	$72$	$72$	$11.090$		$_{}$	None	None		$2$	$0$	\(0\)	\(8\)	\(4\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
407.3.d.a	$407$	$3$	407.d	407.d	$2$	$2$	$2$	$11.090$	\(\Q(\sqrt{-11}) \)	$_{}$	\(\Q(\sqrt{-11}) \)	None		$4$	$0$	\(0\)	\(10\)	\(0\)	\(0\)		$3$	$\mathrm{U}(1)[D_{2}]$	\(q+5q^{3}-4q^{4}+(1-2\beta )q^{5}+2^{4}q^{9}+\cdots\)
407.3.d.b	$407$	$3$	407.d	407.d	$2$	$8$	$8$	$11.090$	8.8.\(\cdots\).2	$_{}$	\(\Q(\sqrt{-407}) \)	None	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{4}\cdot 3$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{2}q^{2}+\beta _{3}q^{3}+(4+\beta _{3}-\beta _{6})q^{4}+\cdots\)