LMFDB - Newform Search Results

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Level	Weight	Analytic conductor	$Nk^2$	Dim.

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Self-twists	CM/RM discriminant	Inner twist count*	Is self-dual?	Analytic rank

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Results (displaying matches 1-50 of 140) Next

Label	Dim.	$A$	Field	CM	Traces				Fricke sign	$q$-expansion
Label	Dim.	$A$	Field	CM	$a_2$	$a_3$	$a_5$	$a_7$	Fricke sign	$q$-expansion
38.2.a.a	$1$	$0.303$	$\Q$	None	$-1$	$1$	$0$	$-1$	$-$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots$
38.2.a.b	$1$	$0.303$	$\Q$	None	$1$	$-1$	$-4$	$3$	$-$	$q+q^{2}-q^{3}+q^{4}-4q^{5}-q^{6}+3q^{7}+\cdots$
38.2.c.a	$2$	$0.303$	$\Q(\sqrt{-3}) $	None	$1$	$-1$	$0$	$-8$		$q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
38.2.c.b	$4$	$0.303$	$\Q(\sqrt{-3}, \sqrt{7})$	None	$-2$	$0$	$-2$	$4$		$q+\beta _{2}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots$
38.2.e.a	$6$	$0.303$	$\Q(\zeta_{18})$	None	$0$	$-3$	$0$	$-6$		$q-\zeta_{18}q^{2}+(-\zeta_{18}^{3}-\zeta_{18}^{5})q^{3}+\zeta_{18}^{2}q^{4}+\cdots$
38.3.b.a	$2$	$1.035$	$\Q(\sqrt{-2}) $	None	$0$	$0$	$-2$	$10$		$q+\beta q^{2}+2\beta q^{3}-2q^{4}-q^{5}-4q^{6}+\cdots$
38.3.d.a	$4$	$1.035$	$\Q(\sqrt{-2}, \sqrt{-3})$	None	$0$	$6$	$2$	$8$		$q+\beta _{1}q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots$
38.3.f.a	$24$	$1.035$		None	$0$	$-6$	$0$	$-18$
38.4.a.a	$1$	$2.242$	$\Q$	None	$-2$	$-2$	$-9$	$-31$	$-$	$q-2q^{2}-2q^{3}+4q^{4}-9q^{5}+4q^{6}+\cdots$
38.4.a.b	$2$	$2.242$	$\Q(\sqrt{177}) $	None	$-4$	$1$	$10$	$57$	$+$	$q-2q^{2}+(1-\beta )q^{3}+4q^{4}+(4+2\beta )q^{5}+\cdots$
38.4.a.c	$2$	$2.242$	$\Q(\sqrt{73}) $	None	$4$	$9$	$-9$	$-18$	$+$	$q+2q^{2}+(5-\beta )q^{3}+4q^{4}+(-6+3\beta )q^{5}+\cdots$
38.4.c.a	$2$	$2.242$	$\Q(\sqrt{-3}) $	None	$-2$	$-5$	$-3$	$-64$		$q+(-2+2\zeta_{6})q^{2}+(-5+5\zeta_{6})q^{3}+\cdots$
38.4.c.b	$2$	$2.242$	$\Q(\sqrt{-3}) $	None	$-2$	$5$	$12$	$16$		$q+(-2+2\zeta_{6})q^{2}+(5-5\zeta_{6})q^{3}-4\zeta_{6}q^{4}+\cdots$
38.4.c.c	$6$	$2.242$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	$6$	$-5$	$-1$	$52$		$q+(2-2\beta _{4})q^{2}+(-2-\beta _{1}-\beta _{2}+2\beta _{4}+\cdots)q^{3}+\cdots$
38.4.e.a	$12$	$2.242$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	$0$	$-9$	$0$	$21$		$q-2\beta _{3}q^{2}+(-1+2\beta _{2}-\beta _{4}+2\beta _{6}+\cdots)q^{3}+\cdots$
38.4.e.b	$18$	$2.242$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	None	$0$	$6$	$0$	$-33$		$q-2\beta _{8}q^{2}+(\beta _{3}+\beta _{4}+\beta _{6}+\beta _{9})q^{3}+\cdots$
38.5.b.a	$8$	$3.928$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None	$0$	$0$	$18$	$-162$		$q+\beta _{2}q^{2}+(\beta _{1}+\beta _{2})q^{3}-8q^{4}+(2-\beta _{6}+\cdots)q^{5}+\cdots$
38.5.d.a	$16$	$3.928$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	$0$	$-12$	$-18$	$72$		$q+(-\beta _{5}+\beta _{9})q^{2}+(-1+\beta _{3})q^{3}+8\beta _{7}q^{4}+\cdots$
38.5.f.a	$36$	$3.928$		None	$0$	$12$	$0$	$90$
38.6.a.a	$1$	$6.095$	$\Q$	None	$-4$	$-6$	$31$	$-27$	$+$	$q-4q^{2}-6q^{3}+2^{4}q^{4}+31q^{5}+24q^{6}+\cdots$
38.6.a.b	$1$	$6.095$	$\Q$	None	$4$	$-14$	$-45$	$-121$	$+$	$q+4q^{2}-14q^{3}+2^{4}q^{4}-45q^{5}-56q^{6}+\cdots$
38.6.a.c	$2$	$6.095$	$\Q(\sqrt{1441}) $	None	$-8$	$3$	$-45$	$114$	$-$	$q-4q^{2}+(2-\beta )q^{3}+2^{4}q^{4}+(-21+\cdots)q^{5}+\cdots$
38.6.a.d	$3$	$6.095$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	$12$	$13$	$81$	$228$	$-$	$q+4q^{2}+(4+\beta _{1})q^{3}+2^{4}q^{4}+(3^{3}-\beta _{1}+\cdots)q^{5}+\cdots$
38.6.c.a	$6$	$6.095$	$\mathbb{Q}[x]/(x^{6} + \cdots)$	None	$12$	$-15$	$14$	$-624$		$q+(4-4\beta _{3})q^{2}+(-5+\beta _{1}+\beta _{2}+5\beta _{3}+\cdots)q^{3}+\cdots$
38.6.c.b	$8$	$6.095$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	$-16$	$-14$	$-36$	$76$		$q+(-4+4\beta _{2})q^{2}+(-3+3\beta _{2}-\beta _{3}+\cdots)q^{3}+\cdots$
38.6.e.a	$24$	$6.095$		None	$0$	$18$	$0$	$438$
38.6.e.b	$30$	$6.095$		None	$0$	$15$	$0$	$-84$
38.7.b.a	$10$	$8.742$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None	$0$	$0$	$-112$	$-224$		$q-\beta _{6}q^{2}+(\beta _{5}+\beta _{6})q^{3}-2^{5}q^{4}+(-11+\cdots)q^{5}+\cdots$
38.7.d.a	$20$	$8.742$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None	$0$	$-30$	$112$	$-208$		$q-\beta _{8}q^{2}+(-2+\beta _{2}+\beta _{6})q^{3}+(2^{5}+\cdots)q^{4}+\cdots$
38.7.f.a	$60$	$8.742$		None	$0$	$30$	$0$	$432$
38.8.a.a	$1$	$11.871$	$\Q$	None	$-8$	$77$	$440$	$951$	$+$	$q-8q^{2}+77q^{3}+2^{6}q^{4}+440q^{5}+\cdots$
38.8.a.b	$2$	$11.871$	$\Q(\sqrt{2737}) $	None	$-16$	$-61$	$175$	$-2592$	$+$	$q-8q^{2}+(-30-\beta )q^{3}+2^{6}q^{4}+(95+\cdots)q^{5}+\cdots$
38.8.a.c	$2$	$11.871$	$\Q(\sqrt{17953}) $	None	$-16$	$-11$	$-69$	$-348$	$-$	$q-8q^{2}+(-5-\beta )q^{3}+2^{6}q^{4}+(-6^{2}+\cdots)q^{5}+\cdots$
38.8.a.d	$2$	$11.871$	$\Q(\sqrt{633}) $	None	$16$	$-69$	$155$	$-2238$	$-$	$q+8q^{2}+(-33-3\beta )q^{3}+2^{6}q^{4}+(62+\cdots)q^{5}+\cdots$
38.8.a.e	$4$	$11.871$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	$32$	$12$	$-279$	$2485$	$+$	$q+8q^{2}+(3-\beta _{1})q^{3}+2^{6}q^{4}+(-70+\cdots)q^{5}+\cdots$
38.8.c.a	$12$	$11.871$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None	$-48$	$12$	$124$	$-1036$		$q+8\beta _{2}q^{2}+(\beta _{1}-2\beta _{2})q^{3}+(-2^{6}-2^{6}\beta _{2}+\cdots)q^{4}+\cdots$
38.8.c.b	$14$	$11.871$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	$56$	$55$	$-126$	$1928$		$q+8\beta _{3}q^{2}+(\beta _{1}+\beta _{2}+8\beta _{3})q^{3}+(-2^{6}+\cdots)q^{4}+\cdots$
38.8.e.a	$30$	$11.871$		None	$0$	$45$	$0$	$1806$
38.8.e.b	$36$	$11.871$		None	$0$	$-84$	$0$	$-2988$
38.9.b.a	$12$	$15.480$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None	$0$	$0$	$558$	$-5422$		$q+\beta _{7}q^{2}+(\beta _{6}-\beta _{7})q^{3}-2^{7}q^{4}+(47+\cdots)q^{5}+\cdots$
38.9.d.a	$24$	$15.480$		None	$0$	$168$	$-558$	$11992$
38.9.f.a	$84$	$15.480$		None	$0$	$-168$	$0$	$-6570$
38.10.a.a	$1$	$19.571$	$\Q$	None	$16$	$-119$	$-684$	$9149$	$+$	$q+2^{4}q^{2}-119q^{3}+2^{8}q^{4}-684q^{5}+\cdots$
38.10.a.b	$1$	$19.571$	$\Q$	None	$16$	$102$	$-1581$	$-4865$	$+$	$q+2^{4}q^{2}+102q^{3}+2^{8}q^{4}-1581q^{5}+\cdots$
38.10.a.c	$3$	$19.571$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	$-48$	$3$	$486$	$-13317$	$+$	$q-2^{4}q^{2}+(1+\beta _{1})q^{3}+2^{8}q^{4}+(162+\cdots)q^{5}+\cdots$
38.10.a.d	$4$	$19.571$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	$-64$	$84$	$-1395$	$12307$	$-$	$q-2^{4}q^{2}+(21+\beta _{1})q^{3}+2^{8}q^{4}+(-350+\cdots)q^{5}+\cdots$
38.10.a.e	$4$	$19.571$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	$64$	$226$	$866$	$2670$	$-$	$q+2^{4}q^{2}+(57+\beta _{2})q^{3}+2^{8}q^{4}+(218+\cdots)q^{5}+\cdots$
38.10.c.a	$14$	$19.571$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	$112$	$165$	$909$	$3692$		$q+(2^{4}-2^{4}\beta _{2})q^{2}+(24-\beta _{1}-24\beta _{2}+\cdots)q^{3}+\cdots$
38.10.c.b	$16$	$19.571$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	$-128$	$70$	$-341$	$3704$		$q+(-2^{4}+2^{4}\beta _{2})q^{2}+(9-\beta _{1}-9\beta _{2}+\cdots)q^{3}+\cdots$
38.10.e.a	$42$	$19.571$		None	$0$	$-252$	$0$	$14373$

Introduction	Features
Universe	News

Label	Dim.	\(A\)	Field	CM	Traces				Fricke sign	$q$-expansion
Label	Dim.	\(A\)	Field	CM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	Fricke sign	$q$-expansion
38.2.a.a	\(1\)	\(0.303\)	\(\Q\)	None	\(-1\)	\(1\)	\(0\)	\(-1\)	\(-\)	\(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
38.2.a.b	\(1\)	\(0.303\)	\(\Q\)	None	\(1\)	\(-1\)	\(-4\)	\(3\)	\(-\)	\(q+q^{2}-q^{3}+q^{4}-4q^{5}-q^{6}+3q^{7}+\cdots\)
38.2.c.a	\(2\)	\(0.303\)	\(\Q(\sqrt{-3}) \)	None	\(1\)	\(-1\)	\(0\)	\(-8\)		\(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
38.2.c.b	\(4\)	\(0.303\)	\(\Q(\sqrt{-3}, \sqrt{7})\)	None	\(-2\)	\(0\)	\(-2\)	\(4\)		\(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots\)
38.2.e.a	\(6\)	\(0.303\)	\(\Q(\zeta_{18})\)	None	\(0\)	\(-3\)	\(0\)	\(-6\)		\(q-\zeta_{18}q^{2}+(-\zeta_{18}^{3}-\zeta_{18}^{5})q^{3}+\zeta_{18}^{2}q^{4}+\cdots\)
38.3.b.a	\(2\)	\(1.035\)	\(\Q(\sqrt{-2}) \)	None	\(0\)	\(0\)	\(-2\)	\(10\)		\(q+\beta q^{2}+2\beta q^{3}-2q^{4}-q^{5}-4q^{6}+\cdots\)
38.3.d.a	\(4\)	\(1.035\)	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None	\(0\)	\(6\)	\(2\)	\(8\)		\(q+\beta _{1}q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots\)
38.3.f.a	\(24\)	\(1.035\)		None	\(0\)	\(-6\)	\(0\)	\(-18\)
38.4.a.a	\(1\)	\(2.242\)	\(\Q\)	None	\(-2\)	\(-2\)	\(-9\)	\(-31\)	\(-\)	\(q-2q^{2}-2q^{3}+4q^{4}-9q^{5}+4q^{6}+\cdots\)
38.4.a.b	\(2\)	\(2.242\)	\(\Q(\sqrt{177}) \)	None	\(-4\)	\(1\)	\(10\)	\(57\)	\(+\)	\(q-2q^{2}+(1-\beta )q^{3}+4q^{4}+(4+2\beta )q^{5}+\cdots\)
38.4.a.c	\(2\)	\(2.242\)	\(\Q(\sqrt{73}) \)	None	\(4\)	\(9\)	\(-9\)	\(-18\)	\(+\)	\(q+2q^{2}+(5-\beta )q^{3}+4q^{4}+(-6+3\beta )q^{5}+\cdots\)
38.4.c.a	\(2\)	\(2.242\)	\(\Q(\sqrt{-3}) \)	None	\(-2\)	\(-5\)	\(-3\)	\(-64\)		\(q+(-2+2\zeta_{6})q^{2}+(-5+5\zeta_{6})q^{3}+\cdots\)
38.4.c.b	\(2\)	\(2.242\)	\(\Q(\sqrt{-3}) \)	None	\(-2\)	\(5\)	\(12\)	\(16\)		\(q+(-2+2\zeta_{6})q^{2}+(5-5\zeta_{6})q^{3}-4\zeta_{6}q^{4}+\cdots\)
38.4.c.c	\(6\)	\(2.242\)	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	\(6\)	\(-5\)	\(-1\)	\(52\)		\(q+(2-2\beta _{4})q^{2}+(-2-\beta _{1}-\beta _{2}+2\beta _{4}+\cdots)q^{3}+\cdots\)
38.4.e.a	\(12\)	\(2.242\)	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	\(0\)	\(-9\)	\(0\)	\(21\)		\(q-2\beta _{3}q^{2}+(-1+2\beta _{2}-\beta _{4}+2\beta _{6}+\cdots)q^{3}+\cdots\)
38.4.e.b	\(18\)	\(2.242\)	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None	\(0\)	\(6\)	\(0\)	\(-33\)		\(q-2\beta _{8}q^{2}+(\beta _{3}+\beta _{4}+\beta _{6}+\beta _{9})q^{3}+\cdots\)
38.5.b.a	\(8\)	\(3.928\)	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None	\(0\)	\(0\)	\(18\)	\(-162\)		\(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{2})q^{3}-8q^{4}+(2-\beta _{6}+\cdots)q^{5}+\cdots\)
38.5.d.a	\(16\)	\(3.928\)	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	\(0\)	\(-12\)	\(-18\)	\(72\)		\(q+(-\beta _{5}+\beta _{9})q^{2}+(-1+\beta _{3})q^{3}+8\beta _{7}q^{4}+\cdots\)
38.5.f.a	\(36\)	\(3.928\)		None	\(0\)	\(12\)	\(0\)	\(90\)
38.6.a.a	\(1\)	\(6.095\)	\(\Q\)	None	\(-4\)	\(-6\)	\(31\)	\(-27\)	\(+\)	\(q-4q^{2}-6q^{3}+2^{4}q^{4}+31q^{5}+24q^{6}+\cdots\)
38.6.a.b	\(1\)	\(6.095\)	\(\Q\)	None	\(4\)	\(-14\)	\(-45\)	\(-121\)	\(+\)	\(q+4q^{2}-14q^{3}+2^{4}q^{4}-45q^{5}-56q^{6}+\cdots\)
38.6.a.c	\(2\)	\(6.095\)	\(\Q(\sqrt{1441}) \)	None	\(-8\)	\(3\)	\(-45\)	\(114\)	\(-\)	\(q-4q^{2}+(2-\beta )q^{3}+2^{4}q^{4}+(-21+\cdots)q^{5}+\cdots\)
38.6.a.d	\(3\)	\(6.095\)	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	\(12\)	\(13\)	\(81\)	\(228\)	\(-\)	\(q+4q^{2}+(4+\beta _{1})q^{3}+2^{4}q^{4}+(3^{3}-\beta _{1}+\cdots)q^{5}+\cdots\)
38.6.c.a	\(6\)	\(6.095\)	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None	\(12\)	\(-15\)	\(14\)	\(-624\)		\(q+(4-4\beta _{3})q^{2}+(-5+\beta _{1}+\beta _{2}+5\beta _{3}+\cdots)q^{3}+\cdots\)
38.6.c.b	\(8\)	\(6.095\)	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	\(-16\)	\(-14\)	\(-36\)	\(76\)		\(q+(-4+4\beta _{2})q^{2}+(-3+3\beta _{2}-\beta _{3}+\cdots)q^{3}+\cdots\)
38.6.e.a	\(24\)	\(6.095\)		None	\(0\)	\(18\)	\(0\)	\(438\)
38.6.e.b	\(30\)	\(6.095\)		None	\(0\)	\(15\)	\(0\)	\(-84\)
38.7.b.a	\(10\)	\(8.742\)	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None	\(0\)	\(0\)	\(-112\)	\(-224\)		\(q-\beta _{6}q^{2}+(\beta _{5}+\beta _{6})q^{3}-2^{5}q^{4}+(-11+\cdots)q^{5}+\cdots\)
38.7.d.a	\(20\)	\(8.742\)	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None	\(0\)	\(-30\)	\(112\)	\(-208\)		\(q-\beta _{8}q^{2}+(-2+\beta _{2}+\beta _{6})q^{3}+(2^{5}+\cdots)q^{4}+\cdots\)
38.7.f.a	\(60\)	\(8.742\)		None	\(0\)	\(30\)	\(0\)	\(432\)
38.8.a.a	\(1\)	\(11.871\)	\(\Q\)	None	\(-8\)	\(77\)	\(440\)	\(951\)	\(+\)	\(q-8q^{2}+77q^{3}+2^{6}q^{4}+440q^{5}+\cdots\)
38.8.a.b	\(2\)	\(11.871\)	\(\Q(\sqrt{2737}) \)	None	\(-16\)	\(-61\)	\(175\)	\(-2592\)	\(+\)	\(q-8q^{2}+(-30-\beta )q^{3}+2^{6}q^{4}+(95+\cdots)q^{5}+\cdots\)
38.8.a.c	\(2\)	\(11.871\)	\(\Q(\sqrt{17953}) \)	None	\(-16\)	\(-11\)	\(-69\)	\(-348\)	\(-\)	\(q-8q^{2}+(-5-\beta )q^{3}+2^{6}q^{4}+(-6^{2}+\cdots)q^{5}+\cdots\)
38.8.a.d	\(2\)	\(11.871\)	\(\Q(\sqrt{633}) \)	None	\(16\)	\(-69\)	\(155\)	\(-2238\)	\(-\)	\(q+8q^{2}+(-33-3\beta )q^{3}+2^{6}q^{4}+(62+\cdots)q^{5}+\cdots\)
38.8.a.e	\(4\)	\(11.871\)	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	\(32\)	\(12\)	\(-279\)	\(2485\)	\(+\)	\(q+8q^{2}+(3-\beta _{1})q^{3}+2^{6}q^{4}+(-70+\cdots)q^{5}+\cdots\)
38.8.c.a	\(12\)	\(11.871\)	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None	\(-48\)	\(12\)	\(124\)	\(-1036\)		\(q+8\beta _{2}q^{2}+(\beta _{1}-2\beta _{2})q^{3}+(-2^{6}-2^{6}\beta _{2}+\cdots)q^{4}+\cdots\)
38.8.c.b	\(14\)	\(11.871\)	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	\(56\)	\(55\)	\(-126\)	\(1928\)		\(q+8\beta _{3}q^{2}+(\beta _{1}+\beta _{2}+8\beta _{3})q^{3}+(-2^{6}+\cdots)q^{4}+\cdots\)
38.8.e.a	\(30\)	\(11.871\)		None	\(0\)	\(45\)	\(0\)	\(1806\)
38.8.e.b	\(36\)	\(11.871\)		None	\(0\)	\(-84\)	\(0\)	\(-2988\)
38.9.b.a	\(12\)	\(15.480\)	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None	\(0\)	\(0\)	\(558\)	\(-5422\)		\(q+\beta _{7}q^{2}+(\beta _{6}-\beta _{7})q^{3}-2^{7}q^{4}+(47+\cdots)q^{5}+\cdots\)
38.9.d.a	\(24\)	\(15.480\)		None	\(0\)	\(168\)	\(-558\)	\(11992\)
38.9.f.a	\(84\)	\(15.480\)		None	\(0\)	\(-168\)	\(0\)	\(-6570\)
38.10.a.a	\(1\)	\(19.571\)	\(\Q\)	None	\(16\)	\(-119\)	\(-684\)	\(9149\)	\(+\)	\(q+2^{4}q^{2}-119q^{3}+2^{8}q^{4}-684q^{5}+\cdots\)
38.10.a.b	\(1\)	\(19.571\)	\(\Q\)	None	\(16\)	\(102\)	\(-1581\)	\(-4865\)	\(+\)	\(q+2^{4}q^{2}+102q^{3}+2^{8}q^{4}-1581q^{5}+\cdots\)
38.10.a.c	\(3\)	\(19.571\)	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	\(-48\)	\(3\)	\(486\)	\(-13317\)	\(+\)	\(q-2^{4}q^{2}+(1+\beta _{1})q^{3}+2^{8}q^{4}+(162+\cdots)q^{5}+\cdots\)
38.10.a.d	\(4\)	\(19.571\)	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	\(-64\)	\(84\)	\(-1395\)	\(12307\)	\(-\)	\(q-2^{4}q^{2}+(21+\beta _{1})q^{3}+2^{8}q^{4}+(-350+\cdots)q^{5}+\cdots\)
38.10.a.e	\(4\)	\(19.571\)	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	\(64\)	\(226\)	\(866\)	\(2670\)	\(-\)	\(q+2^{4}q^{2}+(57+\beta _{2})q^{3}+2^{8}q^{4}+(218+\cdots)q^{5}+\cdots\)
38.10.c.a	\(14\)	\(19.571\)	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	\(112\)	\(165\)	\(909\)	\(3692\)		\(q+(2^{4}-2^{4}\beta _{2})q^{2}+(24-\beta _{1}-24\beta _{2}+\cdots)q^{3}+\cdots\)
38.10.c.b	\(16\)	\(19.571\)	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	\(-128\)	\(70\)	\(-341\)	\(3704\)		\(q+(-2^{4}+2^{4}\beta _{2})q^{2}+(9-\beta _{1}-9\beta _{2}+\cdots)q^{3}+\cdots\)
38.10.e.a	\(42\)	\(19.571\)		None	\(0\)	\(-252\)	\(0\)	\(14373\)

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.