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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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	269
4304.2.a.a	$4304$	$2$	4304.a	1.a	$1$	$1$	$1$	$34.368$	\(\Q\)	None	✓				269.2.a.a	$1$	$0$	\(0\)	\(0\)	\(1\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+4q^{7}-3q^{9}+3q^{11}+2q^{13}+\cdots\)
4304.2.a.b	$4304$	$2$	4304.a	1.a	$1$	$1$	$1$	$34.368$	\(\Q\)	None	✓				2152.2.a.a	$1$	$0$	\(0\)	\(2\)	\(-3\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-3q^{5}+2q^{7}+q^{9}+q^{11}+\cdots\)
4304.2.a.c	$4304$	$2$	4304.a	1.a	$1$	$2$	$2$	$34.368$	\(\Q(\sqrt{13}) \)	None	✓				538.2.a.b	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(1-\beta )q^{5}+q^{7}+\beta q^{9}-3q^{11}+\cdots\)
4304.2.a.d	$4304$	$2$	4304.a	1.a	$1$	$2$	$2$	$34.368$	\(\Q(\sqrt{5}) \)	None	✓				538.2.a.a	$1$	$1$	\(0\)	\(1\)	\(-5\)	\(4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(-3+\beta )q^{5}+(3-2\beta )q^{7}+\cdots\)
4304.2.a.e	$4304$	$2$	4304.a	1.a	$1$	$4$	$4$	$34.368$	4.4.4913.1	None	✓				538.2.a.c	$1$	$1$	\(0\)	\(-3\)	\(5\)	\(1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{2})q^{3}+(1-\beta _{3})q^{5}+\beta _{1}q^{7}+\cdots\)
4304.2.a.f	$4304$	$2$	4304.a	1.a	$1$	$5$	$5$	$34.368$	5.5.65657.1	None	✓				269.2.a.b	$1$	$0$	\(0\)	\(5\)	\(-4\)	\(5\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{2}-\beta _{3})q^{3}+(-1-\beta _{3})q^{5}+\cdots\)
4304.2.a.g	$4304$	$2$	4304.a	1.a	$1$	$6$	$6$	$34.368$	6.6.4125937.1	None	✓				1076.2.a.a	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(5\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-1-\beta _{5})q^{5}+(1-\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots\)
4304.2.a.h	$4304$	$2$	4304.a	1.a	$1$	$7$	$7$	$34.368$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓				538.2.a.e	$1$	$0$	\(0\)	\(-1\)	\(7\)	\(-6\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}+(1+\beta _{4})q^{5}+(-1+\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots\)
4304.2.a.i	$4304$	$2$	4304.a	1.a	$1$	$7$	$7$	$34.368$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓				538.2.a.d	$1$	$0$	\(0\)	\(4\)	\(-6\)	\(3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1}-\beta _{6})q^{3}+(\beta _{3}-\beta _{4})q^{5}+(1+\cdots)q^{7}+\cdots\)
4304.2.a.j	$4304$	$2$	4304.a	1.a	$1$	$13$	$13$	$34.368$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓				2152.2.a.b	$1$	$1$	\(0\)	\(3\)	\(-9\)	\(-6\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-1+\beta _{4})q^{5}-\beta _{9}q^{7}+\beta _{2}q^{9}+\cdots\)
4304.2.a.k	$4304$	$2$	4304.a	1.a	$1$	$15$	$15$	$34.368$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓		✓		2152.2.a.c	$1$	$1$	\(0\)	\(-3\)	\(5\)	\(-13\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+\beta _{8}q^{5}+(-1-\beta _{6})q^{7}+(1+\cdots)q^{9}+\cdots\)
4304.2.a.l	$4304$	$2$	4304.a	1.a	$1$	$16$	$16$	$34.368$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓		✓		269.2.a.c	$1$	$1$	\(0\)	\(-5\)	\(-1\)	\(-11\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{7}q^{3}+\beta _{12}q^{5}+(-1-\beta _{15})q^{7}+\cdots\)
4304.2.a.m	$4304$	$2$	4304.a	1.a	$1$	$17$	$17$	$34.368$	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	✓		✓		1076.2.a.b	$1$	$0$	\(0\)	\(1\)	\(5\)	\(-9\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{10}q^{5}+(-1-\beta _{7})q^{7}+\cdots\)
4304.2.a.n	$4304$	$2$	4304.a	1.a	$1$	$18$	$18$	$34.368$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓				2152.2.a.d	$1$	$0$	\(0\)	\(4\)	\(-6\)	\(17\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+\beta _{6}q^{5}+(1+\beta _{3})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
4304.2.a.o	$4304$	$2$	4304.a	1.a	$1$	$20$	$20$	$34.368$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓		✓		2152.2.a.e	$1$	$0$	\(0\)	\(-6\)	\(13\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(1-\beta _{10})q^{5}-\beta _{9}q^{7}+(1+\cdots)q^{9}+\cdots\)

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