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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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		5	7
175.10.a.a	$175$	$10$	175.a	1.a	$1$	$1$	$1$	$90.131$	\(\Q\)	None	✓				35.10.a.a	$1$	$1$	\(-28\)	\(116\)	\(0\)	\(-2401\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-28q^{2}+116q^{3}+272q^{4}-3248q^{6}+\cdots\)
175.10.a.c	$175$	$10$	175.a	1.a	$1$	$2$	$2$	$90.131$	\(\Q(\sqrt{2}) \)	None	✓				35.10.a.b	$1$	$1$	\(24\)	\(174\)	\(0\)	\(-4802\)		$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(12+\beta )q^{2}+(87+54\beta )q^{3}+(-360+\cdots)q^{4}+\cdots\)
175.10.a.d	$175$	$10$	175.a	1.a	$1$	$3$	$3$	$90.131$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓				7.10.a.b	$1$	$1$	\(-21\)	\(-84\)	\(0\)	\(-7203\)		$+$	$+$	$+$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+(-7+\beta _{2})q^{2}+(-28+\beta _{1}+\beta _{2})q^{3}+\cdots\)
175.10.a.f	$175$	$10$	175.a	1.a	$1$	$5$	$5$	$90.131$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓				35.10.a.d	$1$	$1$	\(-2\)	\(-140\)	\(0\)	\(-12005\)		$+$	$+$	$+$	$2^{3}\cdot 5$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-28-\beta _{2})q^{3}+(168-4\beta _{1}+\cdots)q^{4}+\cdots\)
175.10.a.i	$175$	$10$	175.a	1.a	$1$	$8$	$8$	$90.131$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	✓	✓		175.10.a.h	$1$	$1$	\(27\)	\(-69\)	\(0\)	\(-19208\)		$+$	$+$	$+$	$2^{7}\cdot 5^{3}$	$\mathrm{SU}(2)$	\(q+(3+\beta _{1})q^{2}+(-8-\beta _{1}+\beta _{2})q^{3}+\cdots\)

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