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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	5	37
7400.2.a.a	$7400$	$2$	7400.a	1.a	$1$	$1$	$1$	$59.089$	$\Q$	None	✓				1480.2.a.d	$1$	$1$	$0$	$-2$	$0$	$-3$		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-3q^{7}+q^{9}+3q^{11}-5q^{17}+\cdots$
7400.2.a.b	$7400$	$2$	7400.a	1.a	$1$	$1$	$1$	$59.089$	$\Q$	None	✓				1480.2.d.a	$1$	$1$	$0$	$-2$	$0$	$4$		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+4q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots$
7400.2.a.c	$7400$	$2$	7400.a	1.a	$1$	$1$	$1$	$59.089$	$\Q$	None	✓				1480.2.a.c	$1$	$0$	$0$	$-1$	$0$	$1$		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}-2q^{9}-3q^{11}+8q^{17}+\cdots$
7400.2.a.d	$7400$	$2$	7400.a	1.a	$1$	$1$	$1$	$59.089$	$\Q$	None	✓	✓			7400.2.a.d	$1$	$1$	$0$	$-1$	$0$	$2$		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{7}-2q^{9}-3q^{11}+7q^{17}+\cdots$
7400.2.a.e	$7400$	$2$	7400.a	1.a	$1$	$1$	$1$	$59.089$	$\Q$	None	✓	✓			7400.2.a.d	$1$	$0$	$0$	$1$	$0$	$-2$		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{7}-2q^{9}-3q^{11}-7q^{17}+\cdots$
7400.2.a.f	$7400$	$2$	7400.a	1.a	$1$	$1$	$1$	$59.089$	$\Q$	None	✓				296.2.a.a	$1$	$1$	$0$	$1$	$0$	$-1$		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}-2q^{9}+q^{11}+6q^{13}+\cdots$
7400.2.a.g	$7400$	$2$	7400.a	1.a	$1$	$1$	$1$	$59.089$	$\Q$	None	✓				296.2.a.b	$1$	$1$	$0$	$1$	$0$	$3$		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{7}-2q^{9}-3q^{11}-2q^{17}+\cdots$
7400.2.a.h	$7400$	$2$	7400.a	1.a	$1$	$1$	$1$	$59.089$	$\Q$	None	✓				1480.2.d.a	$1$	$1$	$0$	$2$	$0$	$-4$		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-4q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots$
7400.2.a.i	$7400$	$2$	7400.a	1.a	$1$	$1$	$1$	$59.089$	$\Q$	None	✓				1480.2.a.b	$1$	$0$	$0$	$2$	$0$	$-2$		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{7}+q^{9}+6q^{13}+2q^{17}+\cdots$
7400.2.a.j	$7400$	$2$	7400.a	1.a	$1$	$1$	$1$	$59.089$	$\Q$	None	✓				1480.2.a.a	$1$	$0$	$0$	$3$	$0$	$5$		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+5q^{7}+6q^{9}-3q^{11}+4q^{13}+\cdots$
7400.2.a.k	$7400$	$2$	7400.a	1.a	$1$	$3$	$3$	$59.089$	3.3.229.1	None	✓				296.2.a.c	$1$	$0$	$0$	$-2$	$0$	$-7$		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{3}+(-2-\beta _{1}+\beta _{2})q^{7}+\cdots$
7400.2.a.l	$7400$	$2$	7400.a	1.a	$1$	$3$	$3$	$59.089$	3.3.316.1	None	✓				1480.2.a.e	$1$	$1$	$0$	$-1$	$0$	$1$		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+\beta _{1}q^{7}+\beta _{2}q^{9}+(-1-\beta _{2})q^{11}+\cdots$
7400.2.a.m	$7400$	$2$	7400.a	1.a	$1$	$3$	$3$	$59.089$	3.3.568.1	None	✓				1480.2.a.f	$1$	$1$	$0$	$-1$	$0$	$1$		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+\beta _{1}q^{7}+(1+2\beta _{1}+\beta _{2})q^{9}+\cdots$
7400.2.a.n	$7400$	$2$	7400.a	1.a	$1$	$4$	$4$	$59.089$	4.4.48389.1	None	✓				296.2.a.d	$1$	$0$	$0$	$-2$	$0$	$1$		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(\beta _{2}-\beta _{3})q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots$
7400.2.a.o	$7400$	$2$	7400.a	1.a	$1$	$5$	$5$	$59.089$	5.5.998068.1	None	✓				1480.2.a.j	$1$	$0$	$0$	$-1$	$0$	$2$		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{4}q^{3}+\beta _{2}q^{7}+(2-\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{9}+\cdots$
7400.2.a.p	$7400$	$2$	7400.a	1.a	$1$	$5$	$5$	$59.089$	5.5.6397264.1	None	✓				1480.2.a.i	$1$	$0$	$0$	$0$	$0$	$-3$		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1-\beta _{1}+\beta _{3})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots$
7400.2.a.q	$7400$	$2$	7400.a	1.a	$1$	$5$	$5$	$59.089$	5.5.935504.1	None	✓				1480.2.a.h	$1$	$1$	$0$	$1$	$0$	$1$		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-\beta _{3}q^{7}+(\beta _{1}+\beta _{2}-\beta _{3})q^{9}+\cdots$
7400.2.a.r	$7400$	$2$	7400.a	1.a	$1$	$5$	$5$	$59.089$	5.5.583504.1	None	✓				1480.2.a.g	$1$	$0$	$0$	$5$	$0$	$5$		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(1+\beta _{2}-\beta _{4})q^{7}+(1+\cdots)q^{9}+\cdots$
7400.2.a.s	$7400$	$2$	7400.a	1.a	$1$	$6$	$6$	$59.089$	6.6.693982032.1	None	✓				1480.2.a.k	$1$	$1$	$0$	$-1$	$0$	$-8$		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-1-\beta _{2})q^{7}+(2+\beta _{3}-\beta _{4}+\cdots)q^{9}+\cdots$
7400.2.a.t	$7400$	$2$	7400.a	1.a	$1$	$8$	$8$	$59.089$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	✓	✓		7400.2.a.t	$1$	$1$	$0$	$-4$	$0$	$-6$		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-1+\beta _{7})q^{7}+(1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots$
7400.2.a.u	$7400$	$2$	7400.a	1.a	$1$	$8$	$8$	$59.089$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	✓			7400.2.a.u	$1$	$1$	$0$	$-1$	$0$	$-4$		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-\beta _{7}q^{7}+(-1+\beta _{3}-\beta _{4}+\cdots)q^{9}+\cdots$
7400.2.a.v	$7400$	$2$	7400.a	1.a	$1$	$8$	$8$	$59.089$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	✓	✓		7400.2.a.u	$1$	$0$	$0$	$1$	$0$	$4$		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+\beta _{7}q^{7}+(-1+\beta _{3}-\beta _{4}+\cdots)q^{9}+\cdots$
7400.2.a.w	$7400$	$2$	7400.a	1.a	$1$	$8$	$8$	$59.089$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	✓			7400.2.a.t	$1$	$0$	$0$	$4$	$0$	$6$		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(1-\beta _{7})q^{7}+(1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots$
7400.2.a.x	$7400$	$2$	7400.a	1.a	$1$	$9$	$9$	$59.089$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	✓	✓		7400.2.a.x	$1$	$1$	$0$	$-2$	$0$	$-4$		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-\beta _{7}q^{7}+(1+\beta _{1}+\beta _{3}+\beta _{4}+\cdots)q^{9}+\cdots$
7400.2.a.y	$7400$	$2$	7400.a	1.a	$1$	$9$	$9$	$59.089$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	✓			7400.2.a.x	$1$	$0$	$0$	$2$	$0$	$4$		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+\beta _{7}q^{7}+(1+\beta _{1}+\beta _{3}+\beta _{4}+\cdots)q^{9}+\cdots$
7400.2.a.z	$7400$	$2$	7400.a	1.a	$1$	$10$	$10$	$59.089$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	✓			7400.2.a.z	$1$	$1$	$0$	$-4$	$0$	$-4$		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-\beta _{5}q^{7}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots$
7400.2.a.ba	$7400$	$2$	7400.a	1.a	$1$	$10$	$10$	$59.089$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓		✓		1480.2.d.b	$1$	$1$	$0$	$-4$	$0$	$7$		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(1-\beta _{4})q^{7}+(\beta _{2}+\beta _{3})q^{9}+\cdots$
7400.2.a.bb	$7400$	$2$	7400.a	1.a	$1$	$10$	$10$	$59.089$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓				1480.2.d.b	$1$	$1$	$0$	$4$	$0$	$-7$		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1+\beta _{4})q^{7}+(\beta _{2}+\beta _{3}+\cdots)q^{9}+\cdots$
7400.2.a.bc	$7400$	$2$	7400.a	1.a	$1$	$10$	$10$	$59.089$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	✓	✓		7400.2.a.z	$1$	$0$	$0$	$4$	$0$	$4$		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+\beta _{5}q^{7}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots$
7400.2.a.bd	$7400$	$2$	7400.a	1.a	$1$	$16$	$16$	$59.089$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓		✓		1480.2.d.c	$1$	$0$	$0$	$-2$	$0$	$-9$		$+$	$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-1-\beta _{8})q^{7}+(1+\beta _{2})q^{9}+\cdots$
7400.2.a.be	$7400$	$2$	7400.a	1.a	$1$	$16$	$16$	$59.089$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓		✓		1480.2.d.c	$1$	$0$	$0$	$2$	$0$	$9$		$-$	$-$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(1+\beta _{8})q^{7}+(1+\beta _{2})q^{9}+\cdots$

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