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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces					A-L signs	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		73
5329.2.a.a	$5329$	$2$	5329.a	1.a	$1$	$1$	$1$	$42.552$	\(\Q\)	None	✓				73.2.a.a	$1$	$1$	\(1\)	\(0\)	\(-2\)	\(-2\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-2q^{5}-2q^{7}-3q^{8}-3q^{9}+\cdots\)
5329.2.a.b	$5329$	$2$	5329.a	1.a	$1$	$2$	$2$	$42.552$	\(\Q(\sqrt{5}) \)	None	✓				73.2.a.b	$1$	$1$	\(-3\)	\(-3\)	\(3\)	\(6\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{2}+(-2+\beta )q^{3}+3\beta q^{4}+\cdots\)
5329.2.a.c	$5329$	$2$	5329.a	1.a	$1$	$2$	$2$	$42.552$	\(\Q(\sqrt{13}) \)	None	✓				73.2.a.c	$1$	$1$	\(1\)	\(1\)	\(1\)	\(2\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(1-\beta )q^{3}+(1+\beta )q^{4}+\beta q^{5}+\cdots\)
5329.2.a.d	$5329$	$2$	5329.a	1.a	$1$	$2$	$2$	$42.552$	\(\Q(\sqrt{2}) \)	None	✓				73.2.d.a	$2$	$0$	\(2\)	\(4\)	\(0\)	\(0\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+2q^{3}-q^{4}+\beta q^{5}+2q^{6}+\beta q^{7}+\cdots\)
5329.2.a.e	$5329$	$2$	5329.a	1.a	$1$	$4$	$4$	$42.552$	\(\Q(\sqrt{38 +2 \sqrt{5}})\)	None	✓				73.2.b.a	$2$	$1$	\(-2\)	\(-2\)	\(0\)	\(0\)		$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{2}+\beta _{1}q^{3}+\beta _{1}q^{4}+\beta _{2}q^{5}+\cdots\)
5329.2.a.f	$5329$	$2$	5329.a	1.a	$1$	$4$	$4$	$42.552$	\(\Q(\sqrt{7 +2 \sqrt{2}})\)	None	✓				73.2.d.b	$1$	$2$	\(-2\)	\(-2\)	\(-6\)	\(-8\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+\beta _{2}q^{4}+\cdots\)
5329.2.a.g	$5329$	$2$	5329.a	1.a	$1$	$4$	$4$	$42.552$	\(\Q(\sqrt{7 +2 \sqrt{2}})\)	None	✓				73.2.d.b	$1$	$0$	\(-2\)	\(-2\)	\(6\)	\(8\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+\beta _{2}q^{4}+\cdots\)
5329.2.a.h	$5329$	$2$	5329.a	1.a	$1$	$4$	$4$	$42.552$	4.4.3981.1	None	✓				73.2.c.a	$1$	$1$	\(-1\)	\(-3\)	\(-2\)	\(1\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
5329.2.a.i	$5329$	$2$	5329.a	1.a	$1$	$4$	$4$	$42.552$	4.4.3981.1	None	✓				73.2.c.a	$1$	$1$	\(-1\)	\(-3\)	\(2\)	\(-1\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
5329.2.a.j	$5329$	$2$	5329.a	1.a	$1$	$8$	$8$	$42.552$	\(\Q(\zeta_{60})^+\)	None	✓				73.2.e.a	$2$	$1$	\(2\)	\(2\)	\(0\)	\(0\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{2}-\beta _{2}q^{3}+(\beta _{2}-\beta _{4})q^{4}+(\beta _{5}+\cdots)q^{5}+\cdots\)
5329.2.a.k	$5329$	$2$	5329.a	1.a	$1$	$15$	$15$	$42.552$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓				73.2.g.a	$1$	$1$	\(-6\)	\(0\)	\(-6\)	\(3\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
5329.2.a.l	$5329$	$2$	5329.a	1.a	$1$	$15$	$15$	$42.552$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓				73.2.g.a	$1$	$1$	\(-6\)	\(0\)	\(6\)	\(-3\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)
5329.2.a.m	$5329$	$2$	5329.a	1.a	$1$	$20$	$20$	$42.552$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓				73.2.h.a	$2$	$0$	\(8\)	\(12\)	\(0\)	\(0\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{11}q^{2}+(1-\beta _{15})q^{3}+(1+\beta _{18}+\cdots)q^{4}+\cdots\)
5329.2.a.n	$5329$	$2$	5329.a	1.a	$1$	$30$	$30$	$42.552$		None	✓				73.2.i.a	$2$	$1$	\(0\)	\(-12\)	\(0\)	\(0\)		$+$	$+$		$\mathrm{SU}(2)$
5329.2.a.o	$5329$	$2$	5329.a	1.a	$1$	$72$	$72$	$42.552$		None	✓				73.2.k.a	$2$	$0$	\(12\)	\(12\)	\(0\)	\(0\)		$-$	$-$		$\mathrm{SU}(2)$
5329.2.a.p	$5329$	$2$	5329.a	1.a	$1$	$108$	$108$	$42.552$		None	✓	✓	✓		5329.2.a.p	$1$	$1$	\(-1\)	\(-1\)	\(-35\)	\(-36\)		$+$	$+$		$\mathrm{SU}(2)$
5329.2.a.q	$5329$	$2$	5329.a	1.a	$1$	$108$	$108$	$42.552$		None	✓	✓	✓		5329.2.a.p	$1$	$0$	\(-1\)	\(-1\)	\(35\)	\(36\)		$-$	$-$		$\mathrm{SU}(2)$

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