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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				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
454.2.a.a	$454$	$2$	454.a	1.a	$1$	$2$	$2$	$3.625$	\(\Q(\sqrt{5}) \)	None	✓	✓	✓	✓	454.2.a.a	$1$	$1$	\(2\)	\(-3\)	\(-2\)	\(-5\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1-\beta )q^{3}+q^{4}+(-2+2\beta )q^{5}+\cdots\)
454.2.a.b	$454$	$2$	454.a	1.a	$1$	$4$	$4$	$3.625$	4.4.2624.1	None	✓	✓	✓	✓	454.2.a.b	$1$	$1$	\(-4\)	\(-2\)	\(-4\)	\(2\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(-1+\beta _{1}-\beta _{3})q^{3}+q^{4}+(-2+\cdots)q^{5}+\cdots\)
454.2.a.c	$454$	$2$	454.a	1.a	$1$	$5$	$5$	$3.625$	5.5.307829.1	None	✓	✓	✓	✓	454.2.a.c	$1$	$0$	\(-5\)	\(-1\)	\(3\)	\(-6\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(-\beta _{3}+\beta _{4})q^{3}+q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
454.2.a.d	$454$	$2$	454.a	1.a	$1$	$7$	$7$	$3.625$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓	✓	✓	454.2.a.d	$1$	$0$	\(7\)	\(4\)	\(-1\)	\(5\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(1-\beta _{3})q^{3}+q^{4}+\beta _{6}q^{5}+(1+\cdots)q^{6}+\cdots\)
454.2.c.a	$454$	$2$	454.c	227.c	$113$	$1008$	$9$	$3.625$		None		✓			454.2.c.a	$2$	$0$	\(9\)	\(3\)	\(1\)	\(4\)			$\mathrm{SU}(2)[C_{113}]$
454.2.c.b	$454$	$2$	454.c	227.c	$113$	$1120$	$10$	$3.625$		None		✓	✓		454.2.c.b	$2$	$0$	\(-10\)	\(-5\)	\(-3\)	\(-8\)			$\mathrm{SU}(2)[C_{113}]$
454.3.b.a	$454$	$3$	454.b	227.b	$2$	$38$	$38$	$12.371$		None		✓	✓	✓	454.3.b.a	$2$	$0$	\(0\)	\(4\)	\(0\)	\(8\)			$\mathrm{SU}(2)[C_{2}]$
454.4.a.a	$454$	$4$	454.a	1.a	$1$	$11$	$11$	$26.787$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	✓	✓	✓	454.4.a.a	$1$	$1$	\(22\)	\(-16\)	\(-17\)	\(-67\)	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+2q^{2}+(-1-\beta _{1})q^{3}+4q^{4}+(-2+\cdots)q^{5}+\cdots\)
454.4.a.b	$454$	$4$	454.a	1.a	$1$	$14$	$14$	$26.787$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	✓	✓	✓	454.4.a.b	$1$	$1$	\(-28\)	\(-1\)	\(-23\)	\(26\)	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-2q^{2}-\beta _{1}q^{3}+4q^{4}+(-2-\beta _{10}+\cdots)q^{5}+\cdots\)
454.4.a.c	$454$	$4$	454.a	1.a	$1$	$15$	$15$	$26.787$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	✓	✓	✓	454.4.a.c	$1$	$0$	\(-30\)	\(2\)	\(12\)	\(-30\)	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q-2q^{2}+\beta _{1}q^{3}+4q^{4}+(1+\beta _{9})q^{5}+\cdots\)
454.4.a.d	$454$	$4$	454.a	1.a	$1$	$17$	$17$	$26.787$	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	✓	✓	✓	✓	454.4.a.d	$1$	$0$	\(34\)	\(17\)	\(18\)	\(59\)	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+2q^{2}+(1-\beta _{1})q^{3}+4q^{4}+(1-\beta _{9}+\cdots)q^{5}+\cdots\)
454.5.b.a	$454$	$5$	454.b	227.b	$2$	$76$	$76$	$46.930$		None		✓	✓	✓	454.5.b.a	$2$	$0$	\(0\)	\(-8\)	\(0\)	\(-80\)			$\mathrm{SU}(2)[C_{2}]$
454.6.a.a	$454$	$6$	454.a	1.a	$1$	$21$	$21$	$72.814$		None	✓	✓	✓	✓	454.6.a.a	$1$	$1$	\(84\)	\(-55\)	\(-106\)	\(-405\)	$+$		$\mathrm{SU}(2)$
454.6.a.b	$454$	$6$	454.a	1.a	$1$	$23$	$23$	$72.814$		None	✓	✓	✓	✓	454.6.a.b	$1$	$1$	\(-92\)	\(-10\)	\(-44\)	\(122\)	$+$		$\mathrm{SU}(2)$
454.6.a.c	$454$	$6$	454.a	1.a	$1$	$24$	$24$	$72.814$		None	✓	✓	✓	✓	454.6.a.c	$1$	$0$	\(-96\)	\(-1\)	\(131\)	\(-270\)	$-$		$\mathrm{SU}(2)$
454.6.a.d	$454$	$6$	454.a	1.a	$1$	$27$	$27$	$72.814$		None	✓	✓	✓	✓	454.6.a.d	$1$	$0$	\(108\)	\(44\)	\(69\)	\(477\)	$-$		$\mathrm{SU}(2)$
454.8.a.a	$454$	$8$	454.a	1.a	$1$	$30$	$30$	$141.823$		None	✓	✓	✓	✓	454.8.a.a	$1$	$1$	\(240\)	\(-148\)	\(-513\)	\(-3539\)	$-$		$\mathrm{SU}(2)$
454.8.a.b	$454$	$8$	454.a	1.a	$1$	$32$	$32$	$141.823$		None	✓	✓	✓	✓	454.8.a.b	$1$	$1$	\(-256\)	\(-13\)	\(-277\)	\(1482\)	$-$		$\mathrm{SU}(2)$
454.8.a.c	$454$	$8$	454.a	1.a	$1$	$33$	$33$	$141.823$		None	✓	✓	✓	✓	454.8.a.c	$1$	$0$	\(-264\)	\(14\)	\(598\)	\(-1262\)	$+$		$\mathrm{SU}(2)$
454.8.a.d	$454$	$8$	454.a	1.a	$1$	$36$	$36$	$141.823$		None	✓	✓	✓	✓	454.8.a.d	$1$	$0$	\(288\)	\(149\)	\(362\)	\(2635\)	$+$		$\mathrm{SU}(2)$

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