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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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2031.1.d.a	$2031$	$1$	2031.d	2031.d	$2$	$9$	$9$	$1.014$	\(\Q(\zeta_{38})^+\)	$D_{19}$	\(\Q(\sqrt{-2031}) \)	None	✓	✓			2031.1.d.a	$2$	$0$	\(-1\)	\(9\)	\(-1\)	\(0\)		$1$		\(q+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{2}+\cdots\)
2031.1.d.b	$2031$	$1$	2031.d	2031.d	$2$	$9$	$9$	$1.014$	\(\Q(\zeta_{38})^+\)	$D_{19}$	\(\Q(\sqrt{-2031}) \)	None	✓	✓			2031.1.d.a	$2$	$0$	\(1\)	\(-9\)	\(1\)	\(0\)		$1$		\(q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4}-\beta _{5}+\beta _{6}+\cdots)q^{2}+\cdots\)
2031.2.a.a	$2031$	$2$	2031.a	1.a	$1$	$1$	$1$	$16.218$	\(\Q\)	$_{}$	None	None	✓	✓			2031.2.a.a	$1$	$2$	\(-2\)	\(1\)	\(-4\)	\(-4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+q^{3}+2q^{4}-4q^{5}-2q^{6}+\cdots\)
2031.2.a.b	$2031$	$2$	2031.a	1.a	$1$	$1$	$1$	$16.218$	\(\Q\)	$_{}$	None	None	✓	✓			2031.2.a.b	$1$	$1$	\(0\)	\(1\)	\(2\)	\(-2\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}+2q^{5}-2q^{7}+q^{9}-2q^{12}+\cdots\)
2031.2.a.c	$2031$	$2$	2031.a	1.a	$1$	$1$	$1$	$16.218$	\(\Q\)	$_{}$	None	None	✓	✓			2031.2.a.c	$1$	$1$	\(2\)	\(-1\)	\(0\)	\(-2\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-q^{3}+2q^{4}-2q^{6}-2q^{7}+\cdots\)
2031.2.a.d	$2031$	$2$	2031.a	1.a	$1$	$1$	$1$	$16.218$	\(\Q\)	$_{}$	None	None	✓	✓			2031.2.a.d	$1$	$1$	\(2\)	\(-1\)	\(0\)	\(2\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-q^{3}+2q^{4}-2q^{6}+2q^{7}+\cdots\)
2031.2.a.e	$2031$	$2$	2031.a	1.a	$1$	$7$	$7$	$16.218$	7.7.32354821.1	$_{}$	None	None	✓	✓			2031.2.a.e	$1$	$1$	\(-2\)	\(-7\)	\(-10\)	\(8\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{2}-q^{3}+(\beta _{5}-\beta _{6})q^{4}+(-2+\cdots)q^{5}+\cdots\)
2031.2.a.f	$2031$	$2$	2031.a	1.a	$1$	$10$	$10$	$16.218$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	$_{}$	None	None	✓	✓	✓		2031.2.a.f	$1$	$1$	\(-1\)	\(-10\)	\(5\)	\(-15\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1-\beta _{3}-\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots\)
2031.2.a.g	$2031$	$2$	2031.a	1.a	$1$	$18$	$18$	$16.218$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	$_{}$	None	None	✓	✓	✓		2031.2.a.g	$1$	$1$	\(-7\)	\(18\)	\(-13\)	\(-3\)	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
2031.2.a.h	$2031$	$2$	2031.a	1.a	$1$	$36$	$36$	$16.218$		$_{}$	None	None	✓	✓	✓		2031.2.a.h	$1$	$0$	\(10\)	\(36\)	\(19\)	\(5\)	$-$		$\mathrm{SU}(2)$
2031.2.a.i	$2031$	$2$	2031.a	1.a	$1$	$38$	$38$	$16.218$		$_{}$	None	None	✓	✓	✓	✓	2031.2.a.i	$1$	$0$	\(-3\)	\(-38\)	\(3\)	\(7\)	$-$		$\mathrm{SU}(2)$
2031.4.a.a	$2031$	$4$	2031.a	1.a	$1$	$75$	$75$	$119.833$		$_{}$	None	None	✓	✓	✓	✓	2031.4.a.a	$1$	$1$	\(-17\)	\(225\)	\(-76\)	\(-59\)	$-$		$\mathrm{SU}(2)$
2031.4.a.b	$2031$	$4$	2031.a	1.a	$1$	$75$	$75$	$119.833$		$_{}$	None	None	✓	✓	✓	✓	2031.4.a.b	$1$	$1$	\(5\)	\(-225\)	\(-16\)	\(-45\)	$-$		$\mathrm{SU}(2)$
2031.4.a.c	$2031$	$4$	2031.a	1.a	$1$	$94$	$94$	$119.833$		$_{}$	None	None	✓	✓	✓	✓	2031.4.a.c	$1$	$0$	\(-3\)	\(-282\)	\(24\)	\(53\)	$+$		$\mathrm{SU}(2)$
2031.4.a.d	$2031$	$4$	2031.a	1.a	$1$	$94$	$94$	$119.833$		$_{}$	None	None	✓	✓	✓	✓	2031.4.a.d	$1$	$0$	\(19\)	\(282\)	\(84\)	\(39\)	$+$		$\mathrm{SU}(2)$

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