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Results (26 matches)

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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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
332.1.d.a	$332$	$1$	332.d	83.b	$2$	$3$	$3$	$0.166$	\(\Q(\zeta_{18})^+\)	$D_{9}$	\(\Q(\sqrt{-83}) \)	None	✓	✓	✓	✓	332.1.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$		\(q-\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{7}+(1+\beta _{2})q^{9}+\cdots\)
332.2.a.a	$332$	$2$	332.a	1.a	$1$	$2$	$2$	$2.651$	\(\Q(\sqrt{2}) \)	$_{}$	None	None	✓	✓	✓	✓	332.2.a.a	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(-6\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}-\beta q^{5}+(-3-\beta )q^{7}+\cdots\)
332.2.a.b	$332$	$2$	332.a	1.a	$1$	$2$	$2$	$2.651$	\(\Q(\sqrt{7}) \)	$_{}$	None	None	✓	✓			332.2.a.b	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(-1+\beta )q^{5}-\beta q^{7}+4q^{9}+\cdots\)
332.2.a.c	$332$	$2$	332.a	1.a	$1$	$3$	$3$	$2.651$	\(\Q(\zeta_{14})^+\)	$_{}$	None	None	✓	✓	✓		332.2.a.c	$1$	$0$	\(0\)	\(4\)	\(2\)	\(8\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{3}-2\beta _{2}q^{5}+(2+\beta _{1}-\beta _{2})q^{7}+\cdots\)
332.2.b.a	$332$	$2$	332.b	332.b	$2$	$40$	$40$	$2.651$		$_{}$	None	None		✓	✓	✓	332.2.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
332.2.e.a	$332$	$2$	332.e	83.c	$41$	$280$	$7$	$2.651$		$_{}$	None	None		✓	✓	✓	332.2.e.a	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(-2\)			$\mathrm{SU}(2)[C_{41}]$
332.2.h.a	$332$	$2$	332.h	332.h	$82$	$1600$	$40$	$2.651$		$_{}$	None	None		✓	✓	✓	332.2.h.a	$4$	$0$	\(-41\)	\(0\)	\(-82\)	\(0\)			$\mathrm{SU}(2)[C_{82}]$
332.3.c.a	$332$	$3$	332.c	4.b	$2$	$82$	$82$	$9.046$		$_{}$	None	None		✓	✓	✓	332.3.c.a	$2$	$0$	\(-2\)	\(0\)	\(-4\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
332.3.d.a	$332$	$3$	332.d	83.b	$2$	$6$	$6$	$9.046$	6.6.\(\cdots\).2	$_{}$	\(\Q(\sqrt{-83}) \)	None	✓	✓			332.3.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{3}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{3}+(2\beta _{1}+2\beta _{3}+\beta _{5})q^{7}+(9+\cdots)q^{9}+\cdots\)
332.3.d.b	$332$	$3$	332.d	83.b	$2$	$8$	$8$	$9.046$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	$_{}$	None	None		✓	✓		332.3.d.b	$2$	$0$	\(0\)	\(4\)	\(0\)	\(-2\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\beta _{3})q^{3}-\beta _{1}q^{5}+(-1+\beta _{3}-\beta _{6}+\cdots)q^{7}+\cdots\)
332.3.f.a	$332$	$3$	332.f	83.d	$82$	$560$	$14$	$9.046$		$_{}$	None	None		✓	✓	✓	332.3.f.a	$2$	$0$	\(0\)	\(-4\)	\(0\)	\(2\)			$\mathrm{SU}(2)[C_{82}]$
332.3.g.a	$332$	$3$	332.g	332.g	$82$	$3280$	$82$	$9.046$		$_{}$	None	None		✓	✓	✓	332.3.g.a	$4$	$0$	\(-39\)	\(0\)	\(-78\)	\(0\)			$\mathrm{SU}(2)[C_{82}]$
332.4.a.a	$332$	$4$	332.a	1.a	$1$	$9$	$9$	$19.589$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	$_{}$	None	None	✓	✓	✓	✓	332.4.a.a	$1$	$1$	\(0\)	\(-8\)	\(-1\)	\(-57\)	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+\beta _{2}q^{5}+(-6-\beta _{1}+\cdots)q^{7}+\cdots\)
332.4.a.b	$332$	$4$	332.a	1.a	$1$	$12$	$12$	$19.589$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	$_{}$	None	None	✓	✓	✓	✓	332.4.a.b	$1$	$0$	\(0\)	\(10\)	\(-1\)	\(41\)	$+$	$2^{6}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+\beta _{8}q^{5}+(3+\beta _{3})q^{7}+\cdots\)
332.5.d.a	$332$	$5$	332.d	83.b	$2$	$6$	$6$	$34.319$	6.6.\(\cdots\).2	$_{}$	\(\Q(\sqrt{-83}) \)	None	✓	✓			332.5.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q+(-\beta _{3}+\beta _{4}+\beta _{5})q^{3}+(-\beta _{2}+8\beta _{3}+\cdots)q^{7}+\cdots\)
332.5.d.b	$332$	$5$	332.d	83.b	$2$	$22$	$22$	$34.319$		$_{}$	None	None		✓	✓		332.5.d.b	$2$	$0$	\(0\)	\(-8\)	\(0\)	\(50\)			$\mathrm{SU}(2)[C_{2}]$
332.6.a.a	$332$	$6$	332.a	1.a	$1$	$15$	$15$	$53.247$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	$_{}$	None	None	✓	✓	✓	✓	332.6.a.a	$1$	$1$	\(0\)	\(-26\)	\(-40\)	\(-234\)	$+$	$2^{12}$	$\mathrm{SU}(2)$	\(q+(-2+\beta _{1})q^{3}+(-3-\beta _{6})q^{5}+(-2^{4}+\cdots)q^{7}+\cdots\)
332.6.a.b	$332$	$6$	332.a	1.a	$1$	$18$	$18$	$53.247$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	$_{}$	None	None	✓	✓	✓	✓	332.6.a.b	$1$	$0$	\(0\)	\(28\)	\(-40\)	\(452\)	$-$	$2^{20}$	$\mathrm{SU}(2)$	\(q+(2-\beta _{1})q^{3}+(-2-\beta _{1}+\beta _{4})q^{5}+\cdots\)
332.7.d.a	$332$	$7$	332.d	83.b	$2$	$6$	$6$	$76.378$	6.6.\(\cdots\).1	$_{}$	\(\Q(\sqrt{-83}) \)	None	✓	✓			332.7.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{9}\cdot 5^{3}$	$\mathrm{U}(1)[D_{2}]$	\(q+(-2\beta _{2}-\beta _{3}+\beta _{5})q^{3}+(-15\beta _{3}+\cdots)q^{7}+\cdots\)
332.7.d.b	$332$	$7$	332.d	83.b	$2$	$36$	$36$	$76.378$		$_{}$	None	None		✓	✓		332.7.d.b	$2$	$0$	\(0\)	\(-20\)	\(0\)	\(-552\)			$\mathrm{SU}(2)[C_{2}]$
332.8.a.a	$332$	$8$	332.a	1.a	$1$	$23$	$23$	$103.712$		$_{}$	None	None	✓	✓	✓	✓	332.8.a.a	$1$	$1$	\(0\)	\(-68\)	\(-126\)	\(-1924\)	$-$		$\mathrm{SU}(2)$
332.8.a.b	$332$	$8$	332.a	1.a	$1$	$26$	$26$	$103.712$		$_{}$	None	None	✓	✓	✓	✓	332.8.a.b	$1$	$0$	\(0\)	\(94\)	\(-126\)	\(2878\)	$+$		$\mathrm{SU}(2)$
332.9.d.a	$332$	$9$	332.d	83.b	$2$	$6$	$6$	$135.250$	6.6.\(\cdots\).2	$_{}$	\(\Q(\sqrt{-83}) \)	None	✓	✓			332.9.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{5}$	$\mathrm{U}(1)[D_{2}]$	\(q+(3\beta _{2}+10\beta _{3}+11\beta _{4}+6\beta _{5})q^{3}+\cdots\)
332.9.d.b	$332$	$9$	332.d	83.b	$2$	$50$	$50$	$135.250$		$_{}$	None	None		✓	✓		332.9.d.b	$2$	$0$	\(0\)	\(112\)	\(0\)	\(2350\)			$\mathrm{SU}(2)[C_{2}]$
332.10.a.a	$332$	$10$	332.a	1.a	$1$	$29$	$29$	$170.992$		$_{}$	None	None	✓	✓	✓	✓	332.10.a.a	$1$	$1$	\(0\)	\(-398\)	\(1575\)	\(-17263\)	$+$		$\mathrm{SU}(2)$
332.10.a.b	$332$	$10$	332.a	1.a	$1$	$32$	$32$	$170.992$		$_{}$	None	None	✓	✓	✓	✓	332.10.a.b	$1$	$0$	\(0\)	\(88\)	\(1575\)	\(16351\)	$-$		$\mathrm{SU}(2)$

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