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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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2252.1.d.a	$2252$	$1$	2252.d	563.b	$2$	$9$	$9$	$1.124$	\(\Q(\zeta_{54})^+\)	$D_{27}$	\(\Q(\sqrt{-563}) \)	None	✓	✓	✓	✓	2252.1.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$		\(q-\beta _{1}q^{3}+\beta _{4}q^{7}+(1+\beta _{2})q^{9}+(\beta _{3}+\cdots)q^{11}+\cdots\)
2252.2.a.a	$2252$	$2$	2252.a	1.a	$1$	$19$	$19$	$17.982$	\(\mathbb{Q}[x]/(x^{19} - \cdots)\)	$_{}$	None	None	✓	✓	✓	✓	2252.2.a.a	$1$	$1$	\(0\)	\(-8\)	\(1\)	\(-13\)	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+\beta _{15}q^{5}+(-1+\beta _{7})q^{7}+\cdots\)
2252.2.a.b	$2252$	$2$	2252.a	1.a	$1$	$28$	$28$	$17.982$		$_{}$	None	None	✓	✓	✓	✓	2252.2.a.b	$1$	$0$	\(0\)	\(10\)	\(1\)	\(17\)	$-$		$\mathrm{SU}(2)$
2252.3.d.a	$2252$	$3$	2252.d	563.b	$2$	$18$	$18$	$61.363$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	$_{}$	\(\Q(\sqrt{-563}) \)	None	✓	✓			2252.3.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{12}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{2}q^{3}+\beta _{13}q^{7}+(9+\beta _{6}-\beta _{7})q^{9}+\cdots\)
2252.3.d.b	$2252$	$3$	2252.d	563.b	$2$	$76$	$76$	$61.363$		$_{}$	None	None		✓	✓		2252.3.d.b	$2$	$0$	\(0\)	\(4\)	\(0\)	\(-8\)			$\mathrm{SU}(2)[C_{2}]$
2252.4.a.a	$2252$	$4$	2252.a	1.a	$1$	$66$	$66$	$132.872$		$_{}$	None	None	✓	✓	✓	✓	2252.4.a.a	$1$	$1$	\(0\)	\(-26\)	\(-5\)	\(-111\)	$-$		$\mathrm{SU}(2)$
2252.4.a.b	$2252$	$4$	2252.a	1.a	$1$	$75$	$75$	$132.872$		$_{}$	None	None	✓	✓	✓	✓	2252.4.a.b	$1$	$0$	\(0\)	\(28\)	\(-5\)	\(99\)	$+$		$\mathrm{SU}(2)$

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