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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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
372.1.o.a	$372$	$1$	372.o	93.h	$6$	$2$	$1$	$0.186$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None		✓	✓	✓	372.1.o.a	$4$	$0$	\(0\)	\(-1\)	\(0\)	\(-2\)		$1$		\(q-\zeta_{6}q^{3}-\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}-\zeta_{6}^{2}q^{13}+\cdots\)
372.1.be.a	$372$	$1$	372.be	93.o	$30$	$8$	$1$	$0.186$	\(\Q(\zeta_{15})\)	$D_{15}$	\(\Q(\sqrt{-3}) \)	None		✓	✓	✓	372.1.be.a	$4$	$0$	\(0\)	\(1\)	\(0\)	\(2\)		$1$		\(q-\zeta_{30}^{7}q^{3}+(\zeta_{30}^{4}-\zeta_{30}^{13})q^{7}+\zeta_{30}^{14}q^{9}+\cdots\)
372.2.a.a	$372$	$2$	372.a	1.a	$1$	$1$	$1$	$2.970$	\(\Q\)	$_{}$	None	None	✓	✓	✓	✓	372.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-q^{7}+q^{9}-6q^{13}+q^{15}+\cdots\)
372.2.a.b	$372$	$2$	372.a	1.a	$1$	$1$	$1$	$2.970$	\(\Q\)	$_{}$	None	None	✓	✓	✓	✓	372.2.a.b	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(-5\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}-5q^{7}+q^{9}+2q^{11}+\cdots\)
372.2.a.c	$372$	$2$	372.a	1.a	$1$	$1$	$1$	$2.970$	\(\Q\)	$_{}$	None	None	✓	✓			372.2.a.c	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+4q^{7}+q^{9}+2q^{13}+\cdots\)
372.2.a.d	$372$	$2$	372.a	1.a	$1$	$1$	$1$	$2.970$	\(\Q\)	$_{}$	None	None	✓	✓			372.2.a.d	$1$	$0$	\(0\)	\(1\)	\(3\)	\(-1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{5}-q^{7}+q^{9}+2q^{13}+3q^{15}+\cdots\)
372.2.a.e	$372$	$2$	372.a	1.a	$1$	$2$	$2$	$2.970$	\(\Q(\sqrt{17}) \)	$_{}$	None	None	✓	✓	✓	✓	372.2.a.e	$1$	$0$	\(0\)	\(-2\)	\(3\)	\(-1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta )q^{5}+(-1+\beta )q^{7}+q^{9}+\cdots\)
372.2.c.a	$372$	$2$	372.c	12.b	$2$	$4$	$4$	$2.970$	\(\Q(\zeta_{8})\)	$_{}$	None	None		✓			372.2.c.a	$2$	$1$	\(-4\)	\(-4\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\zeta_{8}^{2})q^{2}+(-1-\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{3}+\cdots\)
372.2.c.b	$372$	$2$	372.c	12.b	$2$	$4$	$4$	$2.970$	\(\Q(\zeta_{8})\)	$_{}$	None	None		✓			372.2.c.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_{3} q^{2}+(\beta_{3}+\beta_1)q^{3}+2 q^{4}+\cdots\)
372.2.c.c	$372$	$2$	372.c	12.b	$2$	$4$	$4$	$2.970$	\(\Q(\zeta_{8})\)	$_{}$	None	None		✓			372.2.c.a	$2$	$0$	\(4\)	\(4\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\zeta_{8}^{2})q^{2}+(1+\zeta_{8}-\zeta_{8}^{2})q^{3}+\cdots\)
372.2.c.d	$372$	$2$	372.c	12.b	$2$	$48$	$48$	$2.970$		$_{}$	None	None		✓	✓		372.2.c.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
372.2.e.a	$372$	$2$	372.e	93.c	$2$	$2$	$2$	$2.970$	\(\Q(\sqrt{-3}) \)	$_{}$	\(\Q(\sqrt{-3}) \)	None		✓			372.2.e.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$2$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta q^{3}-4 q^{7}-3 q^{9}-4\beta q^{13}+\cdots\)
372.2.e.b	$372$	$2$	372.e	93.c	$2$	$8$	$8$	$2.970$	8.0.\(\cdots\).1	$_{}$	None	None		✓	✓		372.2.e.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{3}q^{5}-\beta _{6}q^{7}+\beta _{2}q^{9}+\cdots\)
372.2.g.a	$372$	$2$	372.g	124.d	$2$	$16$	$16$	$2.970$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	$_{}$	None	None		✓			372.2.g.a	$2$	$0$	\(0\)	\(-16\)	\(0\)	\(0\)		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{7}q^{2}-q^{3}+\beta _{5}q^{4}+\beta _{6}q^{5}-\beta _{7}q^{6}+\cdots\)
372.2.g.b	$372$	$2$	372.g	124.d	$2$	$16$	$16$	$2.970$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	$_{}$	None	None		✓			372.2.g.a	$2$	$0$	\(0\)	\(16\)	\(0\)	\(0\)		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{7}q^{2}+q^{3}+\beta _{5}q^{4}+\beta _{6}q^{5}+\beta _{7}q^{6}+\cdots\)
372.2.i.a	$372$	$2$	372.i	31.c	$3$	$4$	$2$	$2.970$	\(\Q(\sqrt{-3}, \sqrt{7})\)	$_{}$	None	None		✓			372.2.i.a	$2$	$0$	\(0\)	\(-2\)	\(2\)	\(4\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{2}q^{3}+(1-\beta _{1}+\beta _{2})q^{5}-2\beta _{2}q^{7}+\cdots\)
372.2.i.b	$372$	$2$	372.i	31.c	$3$	$6$	$3$	$2.970$	6.0.65370672.1	$_{}$	None	None		✓	✓		372.2.i.b	$2$	$0$	\(0\)	\(3\)	\(-2\)	\(-4\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{4}q^{3}+(-1-\beta _{1}+\beta _{2}-\beta _{4})q^{5}+\cdots\)
372.2.j.a	$372$	$2$	372.j	31.d	$5$	$4$	$1$	$2.970$	\(\Q(\zeta_{10})\)	$_{}$	None	None		✓			372.2.j.a	$2$	$0$	\(0\)	\(1\)	\(-4\)	\(6\)		$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{3}+(-2+\cdots)q^{5}+\cdots\)
372.2.j.b	$372$	$2$	372.j	31.d	$5$	$8$	$2$	$2.970$	8.0.1903140625.1	$_{}$	None	None		✓			372.2.j.b	$2$	$0$	\(0\)	\(2\)	\(2\)	\(-9\)		$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-\beta _{6}q^{3}+(\beta _{2}-\beta _{4}-\beta _{6})q^{5}+(-2+\cdots)q^{7}+\cdots\)
372.2.j.c	$372$	$2$	372.j	31.d	$5$	$12$	$3$	$2.970$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	$_{}$	None	None		✓	✓		372.2.j.c	$2$	$0$	\(0\)	\(-3\)	\(2\)	\(-3\)		$5$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\beta _{6}+\beta _{7}+\beta _{8})q^{3}-\beta _{3}q^{5}+\cdots\)
372.2.l.a	$372$	$2$	372.l	124.g	$6$	$32$	$16$	$2.970$		$_{}$	None	None		✓			372.2.l.a	$2$	$0$	\(0\)	\(-16\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{6}]$
372.2.l.b	$372$	$2$	372.l	124.g	$6$	$32$	$16$	$2.970$		$_{}$	None	None		✓			372.2.l.a	$2$	$0$	\(0\)	\(16\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{6}]$
372.2.n.a	$372$	$2$	372.n	93.g	$6$	$2$	$1$	$2.970$	\(\Q(\sqrt{-3}) \)	$_{}$	\(\Q(\sqrt{-3}) \)	None		✓			372.2.n.a	$4$	$0$	\(0\)	\(3\)	\(0\)	\(4\)		$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(1+\zeta_{6})q^{3}+(4-4\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots\)
372.2.n.b	$372$	$2$	372.n	93.g	$6$	$20$	$10$	$2.970$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	$_{}$	None	None		✓	✓		372.2.n.b	$4$	$0$	\(0\)	\(-3\)	\(0\)	\(-10\)		$2^{4}\cdot 3$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{9}q^{3}+\beta _{17}q^{5}+(-1+\beta _{10}+\beta _{12}+\cdots)q^{7}+\cdots\)
372.2.p.a	$372$	$2$	372.p	372.p	$6$	$120$	$60$	$2.970$		$_{}$	None	None		✓	✓	✓	372.2.p.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{6}]$
372.2.r.a	$372$	$2$	372.r	93.k	$10$	$8$	$2$	$2.970$	8.0.123765625.1	$_{}$	None	None		✓			372.2.r.a	$4$	$0$	\(0\)	\(-5\)	\(0\)	\(10\)		$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(-1-\beta _{1}-\beta _{3}+\beta _{4}-\beta _{7})q^{3}+(1+\cdots)q^{7}+\cdots\)
372.2.r.b	$372$	$2$	372.r	93.k	$10$	$8$	$2$	$2.970$	\(\Q(\zeta_{15})\)	$_{}$	\(\Q(\sqrt{-3}) \)	None		✓			372.2.r.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)		$2^{4}$	$\mathrm{U}(1)[D_{10}]$	\(q+\beta_{6} q^{3}+(-2\beta_{7}+\beta_{6}-\beta_{5}+\cdots+2)q^{7}+\cdots\)
372.2.r.c	$372$	$2$	372.r	93.k	$10$	$24$	$6$	$2.970$		$_{}$	None	None		✓	✓		372.2.r.c	$4$	$0$	\(0\)	\(5\)	\(0\)	\(-20\)			$\mathrm{SU}(2)[C_{10}]$
372.2.t.a	$372$	$2$	372.t	372.t	$10$	$240$	$60$	$2.970$		$_{}$	None	None		✓	✓	✓	372.2.t.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{10}]$
372.2.w.a	$372$	$2$	372.w	124.j	$10$	$64$	$16$	$2.970$		$_{}$	None	None		✓			372.2.w.a	$2$	$0$	\(0\)	\(-16\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{10}]$
372.2.w.b	$372$	$2$	372.w	124.j	$10$	$64$	$16$	$2.970$		$_{}$	None	None		✓			372.2.w.a	$2$	$0$	\(0\)	\(16\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{10}]$
372.2.y.a	$372$	$2$	372.y	31.g	$15$	$16$	$2$	$2.970$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	$_{}$	None	None		✓			372.2.y.a	$2$	$0$	\(0\)	\(2\)	\(-2\)	\(1\)		$1$	$\mathrm{SU}(2)[C_{15}]$	\(q-\beta _{2}q^{3}+(\beta _{4}+\beta _{5}+\beta _{7}-\beta _{11}-\beta _{12}+\cdots)q^{5}+\cdots\)
372.2.y.b	$372$	$2$	372.y	31.g	$15$	$24$	$3$	$2.970$		$_{}$	None	None		✓	✓		372.2.y.b	$2$	$0$	\(0\)	\(-3\)	\(2\)	\(9\)			$\mathrm{SU}(2)[C_{15}]$
372.2.ba.a	$372$	$2$	372.ba	124.p	$30$	$128$	$16$	$2.970$		$_{}$	None	None		✓			372.2.ba.a	$2$	$0$	\(0\)	\(-16\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{30}]$
372.2.ba.b	$372$	$2$	372.ba	124.p	$30$	$128$	$16$	$2.970$		$_{}$	None	None		✓			372.2.ba.a	$2$	$0$	\(0\)	\(16\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{30}]$
372.2.bd.a	$372$	$2$	372.bd	372.ad	$30$	$480$	$60$	$2.970$		$_{}$	None	None		✓	✓	✓	372.2.bd.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{30}]$
372.2.bf.a	$372$	$2$	372.bf	93.p	$30$	$8$	$1$	$2.970$	\(\Q(\zeta_{15})\)	$_{}$	\(\Q(\sqrt{-3}) \)	None		✓			372.2.bf.a	$4$	$0$	\(0\)	\(-3\)	\(0\)	\(-4\)		$1$	$\mathrm{U}(1)[D_{30}]$	\(q+(1-\zeta_{15}+2\zeta_{15}^{3}-\zeta_{15}^{4}+\zeta_{15}^{5}+\cdots)q^{3}+\cdots\)
372.2.bf.b	$372$	$2$	372.bf	93.p	$30$	$80$	$10$	$2.970$		$_{}$	None	None		✓	✓		372.2.bf.b	$4$	$0$	\(0\)	\(3\)	\(0\)	\(20\)			$\mathrm{SU}(2)[C_{30}]$
372.3.b.a	$372$	$3$	372.b	372.b	$2$	$1$	$1$	$10.136$	\(\Q\)	$_{}$	\(\Q(\sqrt{-93}) \)	None	✓	✓			372.3.b.a	$2$	$0$	\(-2\)	\(-3\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2q^{2}-3q^{3}+4q^{4}+6q^{6}-8q^{8}+\cdots\)
372.3.b.b	$372$	$3$	372.b	372.b	$2$	$1$	$1$	$10.136$	\(\Q\)	$_{}$	\(\Q(\sqrt{-93}) \)	None	✓	✓			372.3.b.a	$2$	$0$	\(-2\)	\(3\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2q^{2}+3q^{3}+4q^{4}-6q^{6}-8q^{8}+\cdots\)
372.3.b.c	$372$	$3$	372.b	372.b	$2$	$1$	$1$	$10.136$	\(\Q\)	$_{}$	\(\Q(\sqrt{-93}) \)	None	✓	✓			372.3.b.a	$2$	$0$	\(2\)	\(-3\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2q^{2}-3q^{3}+4q^{4}-6q^{6}+8q^{8}+\cdots\)
372.3.b.d	$372$	$3$	372.b	372.b	$2$	$1$	$1$	$10.136$	\(\Q\)	$_{}$	\(\Q(\sqrt{-93}) \)	None	✓	✓			372.3.b.a	$2$	$0$	\(2\)	\(3\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2q^{2}+3q^{3}+4q^{4}+6q^{6}+8q^{8}+\cdots\)
372.3.b.e	$372$	$3$	372.b	372.b	$2$	$120$	$120$	$10.136$		$_{}$	None	None		✓	✓		372.3.b.e	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
372.3.d.a	$372$	$3$	372.d	3.b	$2$	$20$	$20$	$10.136$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	$_{}$	None	None		✓	✓	✓	372.3.d.a	$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)		$2^{4}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{3}-\beta _{6}q^{5}+\beta _{5}q^{7}-\beta _{8}q^{9}+\cdots\)
372.3.f.a	$372$	$3$	372.f	4.b	$2$	$60$	$60$	$10.136$		$_{}$	None	None		✓	✓	✓	372.3.f.a	$2$	$0$	\(4\)	\(0\)	\(8\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
372.3.h.a	$372$	$3$	372.h	31.b	$2$	$2$	$2$	$10.136$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		✓			372.3.h.a	$2$	$0$	\(0\)	\(0\)	\(6\)	\(-2\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{3}+3 q^{5}-q^{7}-3 q^{9}-4\beta q^{11}+\cdots\)
372.3.h.b	$372$	$3$	372.h	31.b	$2$	$8$	$8$	$10.136$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	$_{}$	None	None		✓	✓		372.3.h.b	$2$	$0$	\(0\)	\(0\)	\(-6\)	\(18\)		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(-1-\beta _{4})q^{5}+(2+\beta _{5})q^{7}+\cdots\)
372.3.k.a	$372$	$3$	372.k	31.e	$6$	$10$	$5$	$10.136$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	$_{}$	None	None		✓			372.3.k.a	$2$	$0$	\(0\)	\(15\)	\(0\)	\(-5\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(2+\beta _{3})q^{3}-\beta _{1}q^{5}+(\beta _{3}+\beta _{4}+\beta _{8}+\cdots)q^{7}+\cdots\)
372.3.k.b	$372$	$3$	372.k	31.e	$6$	$12$	$6$	$10.136$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	$_{}$	None	None		✓	✓		372.3.k.b	$2$	$0$	\(0\)	\(-18\)	\(0\)	\(5\)		$3$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\beta _{3})q^{3}-\beta _{2}q^{5}+(1+\beta _{3}-\beta _{8}+\cdots)q^{7}+\cdots\)
372.3.m.a	$372$	$3$	372.m	124.i	$6$	$2$	$1$	$10.136$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		✓			372.3.m.a	$2$	$0$	\(-2\)	\(-3\)	\(2\)	\(15\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2+2\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}-4\zeta_{6}q^{4}+\cdots\)

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