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Results (1-50 of 153 matches)

 

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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
243.1.b.a	$243$	$1$	243.b	3.b	$2$	$1$	$1$	$0.121$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None	✓	✓	✓	✓	243.1.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)		$1$		\(q+q^{4}-q^{7}-q^{13}+q^{16}-q^{19}+q^{25}+\cdots\)
243.1.d.a	$243$	$1$	243.d	9.d	$6$	$2$	$1$	$0.121$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None		✓	✓	✓	243.1.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(1\)		$1$		\(q+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{7}-\zeta_{6}^{2}q^{13}-\zeta_{6}q^{16}+\cdots\)
243.2.a.a	$243$	$2$	243.a	1.a	$1$	$1$	$1$	$1.940$	\(\Q\)	$_{}$	\(\Q(\sqrt{-3}) \)	None	✓	✓			243.2.a.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)	$+$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{4}-4q^{7}-7q^{13}+4q^{16}-q^{19}+\cdots\)
243.2.a.b	$243$	$2$	243.a	1.a	$1$	$1$	$1$	$1.940$	\(\Q\)	$_{}$	\(\Q(\sqrt{-3}) \)	None	✓	✓			243.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(5\)	$-$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{4}+5q^{7}+2q^{13}+4q^{16}+8q^{19}+\cdots\)
243.2.a.c	$243$	$2$	243.a	1.a	$1$	$2$	$2$	$1.940$	\(\Q(\sqrt{3}) \)	$_{}$	None	None	✓	✓			243.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{4}+2\beta q^{5}-q^{7}-\beta q^{8}+\cdots\)
243.2.a.d	$243$	$2$	243.a	1.a	$1$	$2$	$2$	$1.940$	\(\Q(\sqrt{6}) \)	$_{}$	None	None	✓	✓			243.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+4q^{4}-\beta q^{5}+2q^{7}+2\beta q^{8}+\cdots\)
243.2.a.e	$243$	$2$	243.a	1.a	$1$	$3$	$3$	$1.940$	\(\Q(\zeta_{18})^+\)	$_{}$	None	None	✓	✓	✓		243.2.a.e	$1$	$1$	\(-3\)	\(0\)	\(-6\)	\(-3\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
243.2.a.f	$243$	$2$	243.a	1.a	$1$	$3$	$3$	$1.940$	\(\Q(\zeta_{18})^+\)	$_{}$	None	None	✓	✓	✓		243.2.a.e	$1$	$0$	\(3\)	\(0\)	\(6\)	\(-3\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+(2+\cdots)q^{5}+\cdots\)
243.2.c.a	$243$	$2$	243.c	9.c	$3$	$2$	$1$	$1.940$	\(\Q(\sqrt{-3}) \)	$_{}$	\(\Q(\sqrt{-3}) \)	None		✓			243.2.a.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-5\)		$1$	$\mathrm{U}(1)[D_{3}]$	\(q+2\zeta_{6}q^{4}+(-5+5\zeta_{6})q^{7}-2\zeta_{6}q^{13}+\cdots\)
243.2.c.b	$243$	$2$	243.c	9.c	$3$	$2$	$1$	$1.940$	\(\Q(\sqrt{-3}) \)	$_{}$	\(\Q(\sqrt{-3}) \)	None		✓			243.2.a.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$1$	$\mathrm{U}(1)[D_{3}]$	\(q+2\zeta_{6}q^{4}+(4-4\zeta_{6})q^{7}+7\zeta_{6}q^{13}+\cdots\)
243.2.c.c	$243$	$2$	243.c	9.c	$3$	$4$	$2$	$1.940$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	$_{}$	None	None		✓			243.2.a.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{2}+(-4+4\beta _{1})q^{4}+(-\beta _{2}+\beta _{3})q^{5}+\cdots\)
243.2.c.d	$243$	$2$	243.c	9.c	$3$	$4$	$2$	$1.940$	\(\Q(\zeta_{12})\)	$_{}$	None	None		✓			243.2.a.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{12}^{2}q^{2}+(-1+\zeta_{12})q^{4}+(2\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
243.2.c.e	$243$	$2$	243.c	9.c	$3$	$6$	$3$	$1.940$	\(\Q(\zeta_{18})\)	$_{}$	None	None		✓			243.2.a.e	$2$	$0$	\(-3\)	\(0\)	\(-6\)	\(3\)		$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{18}+\zeta_{18}^{5})q^{2}+(-\zeta_{18}+\cdots)q^{4}+\cdots\)
243.2.c.f	$243$	$2$	243.c	9.c	$3$	$6$	$3$	$1.940$	\(\Q(\zeta_{18})\)	$_{}$	None	None		✓			243.2.a.e	$2$	$0$	\(3\)	\(0\)	\(6\)	\(3\)		$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\zeta_{18}-\zeta_{18}^{3}-\zeta_{18}^{4}+\zeta_{18}^{5})q^{2}+\cdots\)
243.2.e.a	$243$	$2$	243.e	27.e	$9$	$12$	$2$	$1.940$	12.0.\(\cdots\).1	$_{}$	None	None					27.2.e.a	$2$	$0$	\(-3\)	\(0\)	\(-6\)	\(3\)		$3$	$\mathrm{SU}(2)[C_{9}]$	\(q+(-\beta _{2}-\beta _{8}-\beta _{11})q^{2}+(-1-\beta _{1}+\cdots)q^{4}+\cdots\)
243.2.e.b	$243$	$2$	243.e	27.e	$9$	$12$	$2$	$1.940$	12.0.\(\cdots\).1	$_{}$	None	None					27.2.e.a	$2$	$0$	\(-3\)	\(0\)	\(3\)	\(3\)		$3$	$\mathrm{SU}(2)[C_{9}]$	\(q+(-\beta _{4}+\beta _{8}-\beta _{9})q^{2}+(-1-\beta _{1}+\cdots)q^{4}+\cdots\)
243.2.e.c	$243$	$2$	243.e	27.e	$9$	$12$	$2$	$1.940$	12.0.\(\cdots\).1	$_{}$	None	None					27.2.e.a	$2$	$0$	\(3\)	\(0\)	\(-3\)	\(3\)		$3$	$\mathrm{SU}(2)[C_{9}]$	\(q+(1-\beta _{5}-\beta _{8}+\beta _{9}-\beta _{11})q^{2}+(\beta _{1}+\cdots)q^{4}+\cdots\)
243.2.e.d	$243$	$2$	243.e	27.e	$9$	$12$	$2$	$1.940$	12.0.\(\cdots\).1	$_{}$	None	None					27.2.e.a	$2$	$0$	\(3\)	\(0\)	\(6\)	\(3\)		$3$	$\mathrm{SU}(2)[C_{9}]$	\(q+(\beta _{2}+\beta _{8}+\beta _{11})q^{2}+(-1-\beta _{1}+\beta _{4}+\cdots)q^{4}+\cdots\)
243.2.g.a	$243$	$2$	243.g	81.g	$27$	$144$	$8$	$1.940$		$_{}$	None	None			✓	✓	81.2.g.a	$2$	$0$	\(18\)	\(0\)	\(18\)	\(-18\)			$\mathrm{SU}(2)[C_{27}]$
243.2.i.a	$243$	$2$	243.i	243.i	$81$	$1404$	$26$	$1.940$		$_{}$	None	None		✓	✓	✓	243.2.i.a	$2$	$0$	\(-54\)	\(-54\)	\(-54\)	\(-54\)			$\mathrm{SU}(2)[C_{81}]$
243.3.b.a	$243$	$3$	243.b	3.b	$2$	$1$	$1$	$6.621$	\(\Q\)	$_{}$	\(\Q(\sqrt{-3}) \)	None	✓	✓			243.3.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+4q^{4}+2q^{7}+23q^{13}+2^{4}q^{16}+\cdots\)
243.3.b.b	$243$	$3$	243.b	3.b	$2$	$1$	$1$	$6.621$	\(\Q\)	$_{}$	\(\Q(\sqrt{-3}) \)	None	✓	✓			243.3.b.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(11\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+4q^{4}+11q^{7}-22q^{13}+2^{4}q^{16}+\cdots\)
243.3.b.c	$243$	$3$	243.b	3.b	$2$	$2$	$2$	$6.621$	\(\Q(\sqrt{-15}) \)	$_{}$	None	None		✓			243.3.b.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{2}-11q^{4}+\beta q^{5}-4q^{7}+7\beta q^{8}+\cdots\)
243.3.b.d	$243$	$3$	243.b	3.b	$2$	$2$	$2$	$6.621$	\(\Q(\sqrt{-1}) \)	$_{}$	None	None		✓			243.3.b.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(22\)		$3$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-5q^{4}+2iq^{5}+11q^{7}-iq^{8}+\cdots\)
243.3.b.e	$243$	$3$	243.b	3.b	$2$	$2$	$2$	$6.621$	\(\Q(\sqrt{-6}) \)	$_{}$	None	None		✓			243.3.b.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-2q^{4}-\beta q^{5}-4q^{7}+2\beta q^{8}+\cdots\)
243.3.b.f	$243$	$3$	243.b	3.b	$2$	$2$	$2$	$6.621$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		✓			243.3.b.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-20\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{6}q^{2}+q^{4}-5\zeta_{6}q^{5}-10q^{7}-5\zeta_{6}q^{8}+\cdots\)
243.3.b.g	$243$	$3$	243.b	3.b	$2$	$2$	$2$	$6.621$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		✓			243.3.b.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{6}q^{2}+q^{4}+4\zeta_{6}q^{5}-q^{7}-5\zeta_{6}q^{8}+\cdots\)
243.3.b.h	$243$	$3$	243.b	3.b	$2$	$12$	$12$	$6.621$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	$_{}$	None	None		✓	✓		243.3.b.h	$2$	$0$	\(0\)	\(0\)	\(0\)	\(6\)		$3^{18}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{2}+(-2+\beta _{3})q^{4}-\beta _{7}q^{5}+(1+\cdots)q^{7}+\cdots\)
243.3.d.a	$243$	$3$	243.d	9.d	$6$	$2$	$1$	$6.621$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		✓			243.3.b.g	$2$	$0$	\(-3\)	\(0\)	\(-12\)	\(1\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-8+4\zeta_{6})q^{5}+\cdots\)
243.3.d.b	$243$	$3$	243.d	9.d	$6$	$2$	$1$	$6.621$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		✓			243.3.b.f	$2$	$0$	\(-3\)	\(0\)	\(15\)	\(10\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(10-5\zeta_{6})q^{5}+\cdots\)
243.3.d.c	$243$	$3$	243.d	9.d	$6$	$2$	$1$	$6.621$	\(\Q(\sqrt{-3}) \)	$_{}$	\(\Q(\sqrt{-3}) \)	None		✓			243.3.b.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-11\)		$1$	$\mathrm{U}(1)[D_{6}]$	\(q-4\zeta_{6}q^{4}+(-11+11\zeta_{6})q^{7}+22\zeta_{6}q^{13}+\cdots\)
243.3.d.d	$243$	$3$	243.d	9.d	$6$	$2$	$1$	$6.621$	\(\Q(\sqrt{-3}) \)	$_{}$	\(\Q(\sqrt{-3}) \)	None		✓			243.3.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)		$1$	$\mathrm{U}(1)[D_{6}]$	\(q-4\zeta_{6}q^{4}+(-2+2\zeta_{6})q^{7}-23\zeta_{6}q^{13}+\cdots\)
243.3.d.e	$243$	$3$	243.d	9.d	$6$	$2$	$1$	$6.621$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		✓			243.3.b.f	$2$	$0$	\(3\)	\(0\)	\(-15\)	\(10\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-10+5\zeta_{6})q^{5}+\cdots\)
243.3.d.f	$243$	$3$	243.d	9.d	$6$	$2$	$1$	$6.621$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		✓			243.3.b.g	$2$	$0$	\(3\)	\(0\)	\(12\)	\(1\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(8-4\zeta_{6})q^{5}+\cdots\)
243.3.d.g	$243$	$3$	243.d	9.d	$6$	$4$	$2$	$6.621$	\(\Q(\sqrt{2}, \sqrt{-3})\)	$_{}$	None	None		✓			243.3.b.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)		$3$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{3}q^{2}+(2+2\beta _{1})q^{4}+(-\beta _{2}+\beta _{3})q^{5}+\cdots\)
243.3.d.h	$243$	$3$	243.d	9.d	$6$	$4$	$2$	$6.621$	\(\Q(\zeta_{12})\)	$_{}$	None	None		✓			243.3.b.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-22\)		$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+5\zeta_{12}^{2}q^{4}+(-2\zeta_{12}+2\zeta_{12}^{3})q^{5}+\cdots\)
243.3.d.i	$243$	$3$	243.d	9.d	$6$	$4$	$2$	$6.621$	\(\Q(\sqrt{-3}, \sqrt{5})\)	$_{}$	None	None		✓			243.3.b.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)		$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{2}q^{2}+(11+11\beta _{1})q^{4}+(-\beta _{2}+\beta _{3})q^{5}+\cdots\)
243.3.d.j	$243$	$3$	243.d	9.d	$6$	$24$	$12$	$6.621$		$_{}$	None	None		✓	✓		243.3.b.h	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)			$\mathrm{SU}(2)[C_{6}]$
243.3.f.a	$243$	$3$	243.f	27.f	$18$	$30$	$5$	$6.621$		$_{}$	None	None					27.3.f.a	$2$	$0$	\(-3\)	\(0\)	\(-21\)	\(3\)			$\mathrm{SU}(2)[C_{18}]$
243.3.f.b	$243$	$3$	243.f	27.f	$18$	$30$	$5$	$6.621$		$_{}$	None	None					27.3.f.a	$2$	$0$	\(-3\)	\(0\)	\(6\)	\(3\)			$\mathrm{SU}(2)[C_{18}]$
243.3.f.c	$243$	$3$	243.f	27.f	$18$	$30$	$5$	$6.621$		$_{}$	None	None					27.3.f.a	$2$	$0$	\(3\)	\(0\)	\(-6\)	\(3\)			$\mathrm{SU}(2)[C_{18}]$
243.3.f.d	$243$	$3$	243.f	27.f	$18$	$30$	$5$	$6.621$		$_{}$	None	None					27.3.f.a	$2$	$0$	\(3\)	\(0\)	\(21\)	\(3\)			$\mathrm{SU}(2)[C_{18}]$
243.3.h.a	$243$	$3$	243.h	81.h	$54$	$306$	$17$	$6.621$		$_{}$	None	None			✓	✓	81.3.h.a	$2$	$0$	\(18\)	\(0\)	\(18\)	\(-18\)			$\mathrm{SU}(2)[C_{54}]$
243.3.j.a	$243$	$3$	243.j	243.j	$162$	$2862$	$53$	$6.621$		$_{}$	None	None		✓	✓	✓	243.3.j.a	$2$	$0$	\(-54\)	\(-54\)	\(-54\)	\(-54\)			$\mathrm{SU}(2)[C_{162}]$
243.4.a.a	$243$	$4$	243.a	1.a	$1$	$1$	$1$	$14.337$	\(\Q\)	$_{}$	None	None	✓	✓			243.4.a.a	$1$	$1$	\(-3\)	\(0\)	\(3\)	\(-10\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{2}+q^{4}+3q^{5}-10q^{7}+21q^{8}+\cdots\)
243.4.a.b	$243$	$4$	243.a	1.a	$1$	$1$	$1$	$14.337$	\(\Q\)	$_{}$	\(\Q(\sqrt{-3}) \)	None	✓	✓			243.4.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-37\)	$+$	$1$	$N(\mathrm{U}(1))$	\(q-8q^{4}-37q^{7}+89q^{13}+2^{6}q^{16}+\cdots\)
243.4.a.c	$243$	$4$	243.a	1.a	$1$	$1$	$1$	$14.337$	\(\Q\)	$_{}$	\(\Q(\sqrt{-3}) \)	None	✓	✓			243.4.a.c	$2$	$1$	\(0\)	\(0\)	\(0\)	\(17\)	$-$	$1$	$N(\mathrm{U}(1))$	\(q-8q^{4}+17q^{7}-19q^{13}+2^{6}q^{16}+\cdots\)
243.4.a.d	$243$	$4$	243.a	1.a	$1$	$1$	$1$	$14.337$	\(\Q\)	$_{}$	None	None	✓	✓			243.4.a.a	$1$	$1$	\(3\)	\(0\)	\(-3\)	\(-10\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{2}+q^{4}-3q^{5}-10q^{7}-21q^{8}+\cdots\)
243.4.a.e	$243$	$4$	243.a	1.a	$1$	$2$	$2$	$14.337$	\(\Q(\sqrt{6}) \)	$_{}$	None	None	✓	✓			243.4.a.e	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-8\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-2q^{4}+2\beta q^{5}-4q^{7}-10\beta q^{8}+\cdots\)
243.4.a.f	$243$	$4$	243.a	1.a	$1$	$2$	$2$	$14.337$	\(\Q(\sqrt{15}) \)	$_{}$	None	None	✓	✓			243.4.a.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(46\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+7q^{4}+2\beta q^{5}+23q^{7}-\beta q^{8}+\cdots\)