# Classical modular forms downloaded from the LMFDB on 17 April 2026.
# Search link: https://www.lmfdb.org/ModularForm/GL2/Q/holomorphic/72/
# Query "{'level': 72}" returned 256 forms, sorted by analytic conductor.

# Each entry in the following data list has the form:
#    [Label, Dim, $A$, Field, CM, RM, Traces, Fricke sign, $q$-expansion]
# For more details, see the definitions at the bottom of the file.



"72.1.p.a"	2	0.03593268090957617	"2.0.3.1"	[-8]	[]	[-1, -1, 0, 0]	NULL	"q+\\zeta_{6}^{2}q^{2}+\\zeta_{6}^{2}q^{3}-\\zeta_{6}q^{4}-\\zeta_{6}q^{6}+\\cdots"
"72.2.a.a"	1	0.5749228945532188	"1.1.1.1"	[]	[]	[0, 0, 2, 0]	-1	"q+2q^{5}-4q^{11}-2q^{13}-2q^{17}-4q^{19}+\\cdots"
"72.2.d.a"	2	0.5749228945532188	"2.0.8.1"	[-24]	[]	[0, 0, 0, 4]	NULL	"q+\\beta q^{2}-2q^{4}+2\\beta q^{5}+2q^{7}-2\\beta q^{8}+\\cdots"
"72.2.d.b"	2	0.5749228945532188	"2.0.4.1"	[]	[]	[2, 0, 0, -4]	NULL	"q+(i+1)q^{2}+2 i q^{4}-2 i q^{5}-2 q^{7}+\\cdots"
"72.2.f.a"	4	0.5749228945532188	"4.0.576.1"	[]	[]	[0, 0, 0, 0]	NULL	"q+\\beta _{1}q^{2}+(1+\\beta _{3})q^{4}+(-2\\beta _{1}+\\beta _{2}+\\cdots)q^{5}+\\cdots"
"72.2.i.a"	2	0.5749228945532188	"2.0.3.1"	[]	[]	[0, 0, 1, 3]	NULL	"q+(-1+2\\zeta_{6})q^{3}+(1-\\zeta_{6})q^{5}+3\\zeta_{6}q^{7}+\\cdots"
"72.2.i.b"	4	0.5749228945532188	"4.0.1089.1"	[]	[]	[0, 1, 1, -3]	NULL	"q+\\beta _{1}q^{3}+(\\beta _{1}-\\beta _{2}-2\\beta _{3})q^{5}+(1-2\\beta _{1}+\\cdots)q^{7}+\\cdots"
"72.2.l.a"	4	0.5749228945532188	"4.0.576.1"	[-8]	[]	[0, 2, 0, 0]	NULL	"q+\\beta _{1}q^{2}+(1-\\beta _{1}-\\beta _{2})q^{3}+2\\beta _{2}q^{4}+\\cdots"
"72.2.l.b"	16	0.5749228945532188	NULL	[]	[]	[-3, -6, 0, 0]	NULL	"q-\\beta _{11}q^{2}+(-\\beta _{3}+\\beta _{6})q^{3}+(-1-\\beta _{1}+\\cdots)q^{4}+\\cdots"
"72.2.n.a"	4	0.5749228945532188	"4.0.144.1"	[]	[]	[-2, 0, 0, -8]	NULL	"q+(-\\zeta_{12}-\\zeta_{12}^{2}+\\zeta_{12}^{3})q^{2}+(-\\zeta_{12}+\\cdots)q^{3}+\\cdots"
"72.2.n.b"	16	0.5749228945532188	NULL	[]	[]	[1, 0, 0, 6]	NULL	"q+\\beta _{6}q^{2}+(-\\beta _{3}-\\beta _{10})q^{3}+(\\beta _{8}-\\beta _{13}+\\cdots)q^{4}+\\cdots"
"72.3.b.a"	1	1.9618579033941377	"1.1.1.1"	[-8]	[]	[2, 0, 0, 0]	NULL	"q+2q^{2}+4q^{4}+8q^{8}-14q^{11}+2^{4}q^{16}+\\cdots"
"72.3.b.b"	4	1.9618579033941377	"4.0.4752.1"	[]	[]	[-2, 0, 0, 0]	NULL	"q-\\beta _{1}q^{2}+(-2+\\beta _{1}-\\beta _{3})q^{4}+(1+\\beta _{1}+\\cdots)q^{5}+\\cdots"
"72.3.b.c"	4	1.9618579033941377	"4.0.14400.3"	[]	[]	[0, 0, 0, 0]	NULL	"q+\\beta _{3}q^{2}+(1-\\beta _{2})q^{4}+(\\beta _{1}+2\\beta _{3})q^{5}+\\cdots"
"72.3.e.a"	2	1.9618579033941377	"2.0.8.1"	[]	[]	[0, 0, 0, 24]	NULL	"q+5\\beta q^{5}+12q^{7}-4\\beta q^{11}-8q^{13}+\\cdots"
"72.3.h.a"	8	1.9618579033941377	"8.0.33808912384.2"	[]	[]	[0, 0, 0, 0]	NULL	"q-\\beta _{2}q^{2}+(1+\\beta _{5})q^{4}+(-\\beta _{2}-\\beta _{4}+\\cdots)q^{5}+\\cdots"
"72.3.j.a"	44	1.9618579033941377	NULL	[]	[]	[-3, 0, 0, -2]	NULL	NULL
"72.3.m.a"	4	1.9618579033941377	"4.0.576.1"	[]	[]	[0, -12, 6, -6]	NULL	"q-3q^{3}+(1-\\beta _{1}+\\beta _{2})q^{5}+(-\\beta _{1}-3\\beta _{2}+\\cdots)q^{7}+\\cdots"
"72.3.m.b"	8	1.9618579033941377	"8.0.19269881856.9"	[]	[]	[0, 10, -6, 6]	NULL	"q+(1-\\beta _{2}+\\beta _{3})q^{3}+(-1+\\beta _{1}-\\beta _{2}+\\cdots)q^{5}+\\cdots"
"72.3.p.a"	4	1.9618579033941377	"4.0.576.1"	[-8]	[]	[4, 2, 0, 0]	NULL	"q+2\\beta _{2}q^{2}+(\\beta _{1}+\\beta _{2}-\\beta _{3})q^{3}+(-4+\\cdots)q^{4}+\\cdots"
"72.3.p.b"	40	1.9618579033941377	NULL	[]	[]	[-5, -6, 0, 0]	NULL	NULL
"72.4.a.a"	1	4.248137520413324	"1.1.1.1"	[]	[]	[0, 0, -16, -12]	-1	"q-2^{4}q^{5}-12q^{7}-2^{6}q^{11}+58q^{13}+\\cdots"
"72.4.a.b"	1	4.248137520413324	"1.1.1.1"	[]	[]	[0, 0, -14, -24]	-1	"q-14q^{5}-24q^{7}+28q^{11}-74q^{13}+\\cdots"
"72.4.a.c"	1	4.248137520413324	"1.1.1.1"	[]	[]	[0, 0, 2, 24]	1	"q+2q^{5}+24q^{7}+44q^{11}+22q^{13}+\\cdots"
"72.4.a.d"	1	4.248137520413324	"1.1.1.1"	[]	[]	[0, 0, 16, -12]	1	"q+2^{4}q^{5}-12q^{7}+2^{6}q^{11}+58q^{13}+\\cdots"
"72.4.d.a"	2	4.248137520413324	"2.0.8.1"	[-24]	[]	[0, 0, 0, -68]	NULL	"q+\\beta q^{2}-8q^{4}-7\\beta q^{5}-34q^{7}-8\\beta q^{8}+\\cdots"
"72.4.d.b"	2	4.248137520413324	"2.0.7.1"	[]	[]	[2, 0, 0, -16]	NULL	"q+(1+\\beta )q^{2}+(-6+2\\beta )q^{4}+4\\beta q^{5}+\\cdots"
"72.4.d.c"	4	4.248137520413324	"4.0.193600.1"	[]	[]	[0, 0, 0, 40]	NULL	"q+\\beta _{1}q^{2}+(3+\\beta _{3})q^{4}+(\\beta _{1}+\\beta _{2})q^{5}+\\cdots"
"72.4.d.d"	6	4.248137520413324	"6.0.8248384.1"	[]	[]	[-2, 0, 0, 28]	NULL	"q+\\beta _{1}q^{2}+(3+\\beta _{5})q^{4}+(-\\beta _{1}+\\beta _{2}+\\cdots)q^{5}+\\cdots"
"72.4.f.a"	12	4.248137520413324	NULL	[]	[]	[0, 0, 0, 0]	NULL	"q+\\beta _{3}q^{2}+(-1+\\beta _{6})q^{4}-\\beta _{5}q^{5}+(\\beta _{2}+\\cdots)q^{7}+\\cdots"
"72.4.i.a"	8	4.248137520413324	"8.0.5206055409.1"	[]	[]	[0, -3, -5, 3]	NULL	"q-\\beta _{5}q^{3}+(2\\beta _{1}-\\beta _{2}+\\beta _{4})q^{5}+(1+\\beta _{2}+\\cdots)q^{7}+\\cdots"
"72.4.i.b"	10	4.248137520413324	NULL	[]	[]	[0, 4, -5, -3]	NULL	"q-\\beta _{4}q^{3}+(-1+\\beta _{1}+\\beta _{8})q^{5}+(\\beta _{4}+\\cdots)q^{7}+\\cdots"
"72.4.l.a"	4	4.248137520413324	"4.0.576.1"	[-8]	[]	[0, -10, 0, 0]	NULL	"q+2\\beta _{1}q^{2}+(-5+\\beta _{1}+5\\beta _{2})q^{3}+8\\beta _{2}q^{4}+\\cdots"
"72.4.l.b"	64	4.248137520413324	NULL	[]	[]	[-3, 6, 0, 0]	NULL	NULL
"72.4.n.a"	68	4.248137520413324	NULL	[]	[]	[-1, 0, 0, -2]	NULL	NULL
"72.5.b.a"	1	7.442637342036791	"1.1.1.1"	[-8]	[]	[-4, 0, 0, 0]	NULL	"q-4q^{2}+2^{4}q^{4}-2^{6}q^{8}+46q^{11}+\\cdots"
"72.5.b.b"	2	7.442637342036791	"2.0.15.1"	[]	[]	[2, 0, 0, 0]	NULL	"q+(1+\\beta )q^{2}+(-14+2\\beta )q^{4}-8\\beta q^{5}+\\cdots"
"72.5.b.c"	8	7.442637342036791	"8.0.5922408960000.5"	[]	[]	[0, 0, 0, 0]	NULL	"q+\\beta _{1}q^{2}+(3-\\beta _{4})q^{4}+(-\\beta _{1}+\\beta _{2}+\\cdots)q^{5}+\\cdots"
"72.5.b.d"	8	7.442637342036791	NULL	[]	[]	[6, 0, 0, 0]	NULL	"q+(1+\\beta _{1})q^{2}+(1+\\beta _{1}+\\beta _{5})q^{4}+(3\\beta _{1}+\\cdots)q^{5}+\\cdots"
"72.5.e.a"	2	7.442637342036791	"2.0.8.1"	[]	[]	[0, 0, 0, -120]	NULL	"q+11\\beta q^{5}-60q^{7}+44\\beta q^{11}-176q^{13}+\\cdots"
"72.5.e.b"	2	7.442637342036791	"2.0.8.1"	[]	[]	[0, 0, 0, 72]	NULL	"q+5\\beta q^{5}+6^{2}q^{7}+116\\beta q^{11}+304q^{13}+\\cdots"
"72.5.h.a"	16	7.442637342036791	NULL	[]	[]	[0, 0, 0, 0]	NULL	"q+\\beta _{1}q^{2}+(-2-\\beta _{2})q^{4}+\\beta _{5}q^{5}+(\\beta _{2}+\\cdots)q^{7}+\\cdots"
"72.5.j.a"	92	7.442637342036791	NULL	[]	[]	[-3, 0, 0, -2]	NULL	NULL
"72.5.m.a"	24	7.442637342036791	NULL	[]	[]	[0, 4, 0, 0]	NULL	NULL
"72.5.p.a"	4	7.442637342036791	"4.0.576.1"	[-8]	[]	[-8, 14, 0, 0]	NULL	"q-4\\beta _{2}q^{2}+(\\beta _{1}+7\\beta _{2}-\\beta _{3})q^{3}+(-2^{4}+\\cdots)q^{4}+\\cdots"
"72.5.p.b"	88	7.442637342036791	NULL	[]	[]	[7, -18, 0, 0]	NULL	NULL
"72.6.a.a"	1	11.547635026534605	"1.1.1.1"	[]	[]	[0, 0, -94, 144]	-1	"q-94q^{5}+12^{2}q^{7}+380q^{11}+814q^{13}+\\cdots"
"72.6.a.b"	1	11.547635026534605	"1.1.1.1"	[]	[]	[0, 0, -38, 120]	1	"q-38q^{5}+120q^{7}-524q^{11}-962q^{13}+\\cdots"
"72.6.a.c"	1	11.547635026534605	"1.1.1.1"	[]	[]	[0, 0, -16, 12]	1	"q-2^{4}q^{5}+12q^{7}-448q^{11}-206q^{13}+\\cdots"
"72.6.a.d"	1	11.547635026534605	"1.1.1.1"	[]	[]	[0, 0, 16, 12]	-1	"q+2^{4}q^{5}+12q^{7}+448q^{11}-206q^{13}+\\cdots"
"72.6.a.e"	1	11.547635026534605	"1.1.1.1"	[]	[]	[0, 0, 34, -240]	1	"q+34q^{5}-240q^{7}+124q^{11}+46q^{13}+\\cdots"
"72.6.a.f"	1	11.547635026534605	"1.1.1.1"	[]	[]	[0, 0, 74, -24]	-1	"q+74q^{5}-24q^{7}-124q^{11}+478q^{13}+\\cdots"
"72.6.d.a"	2	11.547635026534605	"2.0.8.1"	[-24]	[]	[0, 0, 0, 484]	NULL	"q+2\\beta q^{2}-2^{5}q^{4}-11\\beta q^{5}+242q^{7}+\\cdots"
"72.6.d.b"	4	11.547635026534605	"4.0.218489.1"	[]	[]	[2, 0, 0, 96]	NULL	"q+\\beta _{1}q^{2}+(5+\\beta _{1}+\\beta _{2}+\\beta _{3})q^{4}+(2+\\cdots)q^{5}+\\cdots"
"72.6.d.c"	8	11.547635026534605	NULL	[]	[]	[0, 0, 0, -288]	NULL	"q+\\beta _{1}q^{2}+(10+\\beta _{2})q^{4}+(\\beta _{1}-\\beta _{4})q^{5}+\\cdots"
"72.6.d.d"	10	11.547635026534605	NULL	[]	[]	[-2, 0, 0, -196]	NULL	"q-\\beta _{2}q^{2}+(-3-\\beta _{4})q^{4}+(-2\\beta _{2}+\\beta _{4}+\\cdots)q^{5}+\\cdots"
"72.6.f.a"	20	11.547635026534605	NULL	[]	[]	[0, 0, 0, 0]	NULL	"q-\\beta _{1}q^{2}+(1-\\beta _{2})q^{4}+(\\beta _{1}-\\beta _{4})q^{5}+\\cdots"
"72.6.i.a"	14	11.547635026534605	NULL	[]	[]	[0, 0, 25, 93]	NULL	"q+(1-\\beta _{2}-\\beta _{4})q^{3}+(3-3\\beta _{2}-\\beta _{3}+\\cdots)q^{5}+\\cdots"
"72.6.i.b"	16	11.547635026534605	NULL	[]	[]	[0, -11, 25, -93]	NULL	"q+(-1+\\beta _{1}+\\beta _{6})q^{3}+(\\beta _{2}+3\\beta _{3}+\\beta _{9}+\\cdots)q^{5}+\\cdots"
"72.6.l.a"	4	11.547635026534605	"4.0.576.1"	[-8]	[]	[0, 2, 0, 0]	NULL	"q+4\\beta _{1}q^{2}+(1+11\\beta _{1}-\\beta _{2})q^{3}+2^{5}\\beta _{2}q^{4}+\\cdots"
"72.6.l.b"	112	11.547635026534605	NULL	[]	[]	[-3, -6, 0, 0]	NULL	NULL
"72.6.n.a"	116	11.547635026534605	NULL	[]	[]	[-1, 0, 0, -2]	NULL	NULL
"72.7.b.a"	1	16.56389402062927	"1.1.1.1"	[-8]	[]	[8, 0, 0, 0]	NULL	"q+8q^{2}+2^{6}q^{4}+2^{9}q^{8}+2338q^{11}+\\cdots"
"72.7.b.b"	4	16.56389402062927	"4.0.3803625.2"	[]	[]	[-2, 0, 0, 0]	NULL	"q-\\beta _{2}q^{2}+(-11+\\beta _{1}+\\beta _{2}-\\beta _{3})q^{4}+\\cdots"
"72.7.b.c"	12	16.56389402062927	NULL	[]	[]	[-10, 0, 0, 0]	NULL	"q+(-1-\\beta _{1})q^{2}+(2+\\beta _{1}+\\beta _{5})q^{4}+\\cdots"
"72.7.b.d"	12	16.56389402062927	NULL	[]	[]	[0, 0, 0, 0]	NULL	"q+\\beta _{1}q^{2}+(-13+\\beta _{3})q^{4}+(-2\\beta _{1}+\\cdots)q^{5}+\\cdots"
"72.7.e.a"	2	16.56389402062927	"2.0.8.1"	[]	[]	[0, 0, 0, 120]	NULL	"q+5\\beta q^{5}+60q^{7}+236\\beta q^{11}+1192q^{13}+\\cdots"
"72.7.e.b"	4	16.56389402062927	"4.0.1345600.3"	[]	[]	[0, 0, 0, -432]	NULL	"q+(-5^{2}\\beta _{1}-\\beta _{3})q^{5}+(-108-\\beta _{2}+\\cdots)q^{7}+\\cdots"
"72.7.h.a"	24	16.56389402062927	NULL	[]	[]	[0, 0, 0, 0]	NULL	NULL
"72.7.j.a"	140	16.56389402062927	NULL	[]	[]	[-3, 0, 0, -2]	NULL	NULL
"72.7.m.a"	36	16.56389402062927	NULL	[]	[]	[0, 10, 0, 0]	NULL	NULL
"72.7.p.a"	4	16.56389402062927	"4.0.576.1"	[-8]	[]	[16, -46, 0, 0]	NULL	"q+8\\beta _{2}q^{2}+(-\\beta _{1}-23\\beta _{2}+\\beta _{3})q^{3}+\\cdots"
"72.7.p.b"	136	16.56389402062927	NULL	[]	[]	[-17, 42, 0, 0]	NULL	NULL
"72.8.a.a"	1	22.491721834856765	"1.1.1.1"	[]	[]	[0, 0, -430, -1224]	1	"q-430q^{5}-1224q^{7}+3164q^{11}+\\cdots"
"72.8.a.b"	1	22.491721834856765	"1.1.1.1"	[]	[]	[0, 0, -110, 504]	-1	"q-110q^{5}+504q^{7}-3812q^{11}+9574q^{13}+\\cdots"
"72.8.a.c"	1	22.491721834856765	"1.1.1.1"	[]	[]	[0, 0, 26, 1056]	1	"q+26q^{5}+1056q^{7}-6412q^{11}+5206q^{13}+\\cdots"
"72.8.a.d"	1	22.491721834856765	"1.1.1.1"	[]	[]	[0, 0, 82, -456]	-1	"q+82q^{5}-456q^{7}+2524q^{11}-10778q^{13}+\\cdots"
"72.8.a.e"	1	22.491721834856765	"1.1.1.1"	[]	[]	[0, 0, 530, 120]	1	"q+530q^{5}+120q^{7}+7196q^{11}-9626q^{13}+\\cdots"
"72.8.a.f"	2	22.491721834856765	"2.2.184.1"	[]	[]	[0, 0, -224, 840]	-1	"q+(-112+\\beta )q^{5}+(420-4\\beta )q^{7}+(320+\\cdots)q^{11}+\\cdots"
"72.8.a.g"	2	22.491721834856765	"2.2.184.1"	[]	[]	[0, 0, 224, 840]	1	"q+(112+\\beta )q^{5}+(420+4\\beta )q^{7}+(-320+\\cdots)q^{11}+\\cdots"
"72.8.d.a"	2	22.491721834856765	"2.0.8.1"	[-24]	[]	[0, 0, 0, -1508]	NULL	"q+4\\beta q^{2}-2^{7}q^{4}+197\\beta q^{5}-754q^{7}+\\cdots"
"72.8.d.b"	6	22.491721834856765	NULL	[]	[]	[-6, 0, 0, -688]	NULL	"q+(-1-\\beta _{1})q^{2}+(19+\\beta _{1}+\\beta _{3})q^{4}+\\cdots"
"72.8.d.c"	12	22.491721834856765	NULL	[]	[]	[0, 0, 0, 136]	NULL	"q+\\beta _{1}q^{2}+(34+\\beta _{3})q^{4}+(-3\\beta _{1}+\\beta _{5}+\\cdots)q^{5}+\\cdots"
"72.8.d.d"	14	22.491721834856765	NULL	[]	[]	[14, 0, 0, 1372]	NULL	"q+(1+\\beta _{1})q^{2}+(-15+\\beta _{1}-\\beta _{2})q^{4}+\\cdots"
"72.8.f.a"	28	22.491721834856765	NULL	[]	[]	[0, 0, 0, 0]	NULL	NULL
"72.8.i.a"	20	22.491721834856765	NULL	[]	[]	[0, 57, -125, 1245]	NULL	"q+(3+\\beta _{5})q^{3}+(13\\beta _{2}-\\beta _{3}-\\beta _{4}-\\beta _{5}+\\cdots)q^{5}+\\cdots"
"72.8.i.b"	22	22.491721834856765	NULL	[]	[]	[0, -44, -125, -1245]	NULL	NULL
"72.8.l.a"	4	22.491721834856765	"4.0.576.1"	[-8]	[]	[0, 86, 0, 0]	NULL	"q+(8\\beta _{1}-8\\beta _{3})q^{2}+(13\\beta _{1}+43\\beta _{2}-13\\beta _{3})q^{3}+\\cdots"
"72.8.l.b"	160	22.491721834856765	NULL	[]	[]	[-3, -90, 0, 0]	NULL	NULL
"72.8.n.a"	164	22.491721834856765	NULL	[]	[]	[-1, 0, 0, -2]	NULL	NULL
"72.9.b.a"	1	29.33125992440116	"1.1.1.1"	[-8]	[]	[-16, 0, 0, 0]	NULL	"q-2^{4}q^{2}+2^{8}q^{4}-2^{12}q^{8}+27166q^{11}+\\cdots"
"72.9.b.b"	6	29.33125992440116	NULL	[]	[]	[14, 0, 0, 0]	NULL	"q+(2+\\beta _{1})q^{2}+(-99+3\\beta _{1}+\\beta _{3}+\\beta _{4}+\\cdots)q^{4}+\\cdots"
"72.9.b.c"	16	29.33125992440116	NULL	[]	[]	[0, 0, 0, 0]	NULL	"q-\\beta _{1}q^{2}+(3+\\beta _{2})q^{4}+(-5\\beta _{1}+\\beta _{7}+\\cdots)q^{5}+\\cdots"
"72.9.b.d"	16	29.33125992440116	NULL	[]	[]	[6, 0, 0, 0]	NULL	"q+\\beta _{1}q^{2}+(3^{3}+\\beta _{4})q^{4}+(1-3\\beta _{1}+\\beta _{3}+\\cdots)q^{5}+\\cdots"
"72.9.e.a"	4	29.33125992440116	"4.0.246016.3"	[]	[]	[0, 0, 0, -2352]	NULL	"q+(-43\\beta _{1}+\\beta _{2})q^{5}+(-588+7\\beta _{3})q^{7}+\\cdots"
"72.9.e.b"	4	29.33125992440116	"4.0.57600.2"	[]	[]	[0, 0, 0, -816]	NULL	"q+(85\\beta _{1}-\\beta _{2})q^{5}+(-204+\\beta _{3})q^{7}+\\cdots"
"72.9.h.a"	32	29.33125992440116	NULL	[]	[]	[0, 0, 0, 0]	NULL	NULL
"72.9.j.a"	188	29.33125992440116	NULL	[]	[]	[-3, 0, 0, -2]	NULL	NULL
"72.9.m.a"	48	29.33125992440116	NULL	[]	[]	[0, -56, 0, 0]	NULL	NULL
"72.9.p.a"	4	29.33125992440116	"4.0.576.1"	[-8]	[]	[-32, -34, 0, 0]	NULL	"q-2^{4}\\beta _{2}q^{2}+(-\\beta _{1}-17\\beta _{2}+\\beta _{3})q^{3}+\\cdots"
"72.9.p.b"	184	29.33125992440116	NULL	[]	[]	[31, 30, 0, 0]	NULL	NULL
"72.10.a.a"	1	37.08258020379886	"1.1.1.1"	[]	[]	[0, 0, -1510, 10248]	-1	"q-1510q^{5}+10248q^{7}-3916q^{11}+\\cdots"
"72.10.a.b"	1	37.08258020379886	"1.1.1.1"	[]	[]	[0, 0, -830, 672]	1	"q-830q^{5}+672q^{7}+73468q^{11}+\\cdots"
"72.10.a.c"	1	37.08258020379886	"1.1.1.1"	[]	[]	[0, 0, -614, 2184]	1	"q-614q^{5}+2184q^{7}-4940q^{11}+\\cdots"
"72.10.a.d"	1	37.08258020379886	"1.1.1.1"	[]	[]	[0, 0, 794, -5880]	-1	"q+794q^{5}-5880q^{7}+30644q^{11}+\\cdots"
"72.10.a.e"	1	37.08258020379886	"1.1.1.1"	[]	[]	[0, 0, 2074, -4344]	1	"q+2074q^{5}-4344q^{7}-93644q^{11}+\\cdots"
"72.10.a.f"	2	37.08258020379886	"2.2.3544.1"	[]	[]	[0, 0, -736, -2952]	-1	"q+(-368+\\beta )q^{5}+(-1476+4\\beta )q^{7}+\\cdots"
"72.10.a.g"	2	37.08258020379886	"2.2.3544.1"	[]	[]	[0, 0, 736, -2952]	1	"q+(368+\\beta )q^{5}+(-1476-4\\beta )q^{7}+\\cdots"
"72.10.a.h"	2	37.08258020379886	"2.2.109.1"	[]	[]	[0, 0, 772, -2880]	-1	"q+(386+\\beta )q^{5}+(-1440+5\\beta )q^{7}+\\cdots"
"72.10.d.a"	2	37.08258020379886	"2.0.8.1"	[-24]	[]	[0, 0, 0, -8636]	NULL	"q-8\\beta q^{2}-2^{9}q^{4}+119\\beta q^{5}-4318q^{7}+\\cdots"
"72.10.d.b"	8	37.08258020379886	NULL	[]	[]	[18, 0, 0, 4800]	NULL	"q+(2+\\beta _{1})q^{2}+(-54+3\\beta _{1}+\\beta _{2})q^{4}+\\cdots"
"72.10.d.c"	16	37.08258020379886	NULL	[]	[]	[0, 0, 0, 18240]	NULL	"q+\\beta _{1}q^{2}+(75+\\beta _{2})q^{4}+(2\\beta _{1}+\\beta _{6}+\\cdots)q^{5}+\\cdots"
"72.10.d.d"	18	37.08258020379886	NULL	[]	[]	[-34, 0, 0, -9604]	NULL	"q+(-2-\\beta _{1})q^{2}+(29+2\\beta _{1}+\\beta _{5})q^{4}+\\cdots"
"72.10.f.a"	36	37.08258020379886	NULL	[]	[]	[0, 0, 0, 0]	NULL	NULL
"72.10.i.a"	26	37.08258020379886	NULL	[]	[]	[0, 60, 625, 2811]	NULL	NULL
"72.10.i.b"	28	37.08258020379886	NULL	[]	[]	[0, 13, 625, -2811]	NULL	NULL
"72.10.l.a"	4	37.08258020379886	"4.0.576.1"	[-8]	[]	[0, -190, 0, 0]	NULL	"q+(-2^{4}\\beta _{1}+2^{4}\\beta _{3})q^{2}+(73\\beta _{1}-95\\beta _{2}+\\cdots)q^{3}+\\cdots"
"72.10.l.b"	208	37.08258020379886	NULL	[]	[]	[-3, 186, 0, 0]	NULL	NULL
"72.10.n.a"	212	37.08258020379886	NULL	[]	[]	[-1, 0, 0, -2]	NULL	NULL
"72.11.b.a"	1	45.74572219250813	"1.1.1.1"	[-8]	[]	[32, 0, 0, 0]	NULL	"q+2^{5}q^{2}+2^{10}q^{4}+2^{15}q^{8}+97426q^{11}+\\cdots"
"72.11.b.b"	8	45.74572219250813	NULL	[]	[]	[-42, 0, 0, 0]	NULL	"q+(-5+\\beta _{1})q^{2}+(5^{2}-5\\beta _{1}+\\beta _{2}+\\beta _{3}+\\cdots)q^{4}+\\cdots"
"72.11.b.c"	20	45.74572219250813	NULL	[]	[]	[0, 0, 0, 0]	NULL	"q-\\beta _{1}q^{2}+(2^{5}-\\beta _{2})q^{4}+(15\\beta _{1}+\\beta _{5}+\\cdots)q^{5}+\\cdots"
"72.11.b.d"	20	45.74572219250813	NULL	[]	[]	[22, 0, 0, 0]	NULL	"q+(1+\\beta _{1})q^{2}+(-93+\\beta _{1}-\\beta _{4})q^{4}+\\cdots"
"72.11.e.a"	4	45.74572219250813	NULL	[]	[]	[0, 0, 0, 10320]	NULL	"q+(-1295\\beta _{1}-\\beta _{3})q^{5}+(2580+\\beta _{2}+\\cdots)q^{7}+\\cdots"
"72.11.e.b"	6	45.74572219250813	NULL	[]	[]	[0, 0, 0, 552]	NULL	"q+(-435\\beta _{1}+\\beta _{2})q^{5}+(92-2\\beta _{3}-\\beta _{4}+\\cdots)q^{7}+\\cdots"
"72.11.h.a"	40	45.74572219250813	NULL	[]	[]	[0, 0, 0, 0]	NULL	NULL
"72.11.j.a"	236	45.74572219250813	NULL	[]	[]	[-3, 0, 0, -2]	NULL	NULL
"72.11.m.a"	60	45.74572219250813	NULL	[]	[]	[0, 22, 0, 0]	NULL	NULL
"72.11.p.a"	4	45.74572219250813	"4.0.576.1"	[-8]	[]	[64, 482, 0, 0]	NULL	"q+2^{5}\\beta _{2}q^{2}+(11\\beta _{1}+241\\beta _{2}-11\\beta _{3})q^{3}+\\cdots"
"72.11.p.b"	232	45.74572219250813	NULL	[]	[]	[-65, -486, 0, 0]	NULL	NULL
"72.12.a.a"	1	55.3207090002904	"1.1.1.1"	[]	[]	[0, 0, -1870, -72312]	1	"q-1870q^{5}-72312q^{7}-147940q^{11}+\\cdots"
"72.12.a.b"	1	55.3207090002904	"1.1.1.1"	[]	[]	[0, 0, -1190, 18480]	-1	"q-1190q^{5}+18480q^{7}-135884q^{11}+\\cdots"
"72.12.a.c"	1	55.3207090002904	"1.1.1.1"	[]	[]	[0, 0, 3490, -55464]	-1	"q+3490q^{5}-55464q^{7}+597004q^{11}+\\cdots"
"72.12.a.d"	1	55.3207090002904	"1.1.1.1"	[]	[]	[0, 0, 7130, -19536]	1	"q+7130q^{5}-19536q^{7}+196148q^{11}+\\cdots"
"72.12.a.e"	2	55.3207090002904	"2.2.109.1"	[]	[]	[0, 0, -7868, 91056]	1	"q+(-3934-4\\beta )q^{5}+(45528-14\\beta )q^{7}+\\cdots"
"72.12.a.f"	2	55.3207090002904	"2.2.3061.1"	[]	[]	[0, 0, -1564, 37776]	-1	"q+(-782-\\beta )q^{5}+(18888-\\beta )q^{7}+\\cdots"
"72.12.a.g"	3	55.3207090002904	NULL	[]	[]	[0, 0, -1584, -17796]	1	"q+(-528-\\beta _{1})q^{5}+(-5932-\\beta _{1}+\\cdots)q^{7}+\\cdots"
"72.12.a.h"	3	55.3207090002904	NULL	[]	[]	[0, 0, 1584, -17796]	-1	"q+(528+\\beta _{1})q^{5}+(-5932-\\beta _{1}-\\beta _{2})q^{7}+\\cdots"
"72.12.d.a"	2	55.3207090002904	"2.0.8.1"	[-24]	[]	[0, 0, 0, 160252]	NULL	"q-2^{4}\\beta q^{2}-2^{11}q^{4}+4687\\beta q^{5}+80126q^{7}+\\cdots"
"72.12.d.b"	10	55.3207090002904	NULL	[]	[]	[-22, 0, 0, -33616]	NULL	"q+(-2-\\beta _{1})q^{2}+(43+2\\beta _{1}-\\beta _{2})q^{4}+\\cdots"
"72.12.d.c"	20	55.3207090002904	NULL	[]	[]	[0, 0, 0, -227480]	NULL	"q+\\beta _{1}q^{2}+(-48+\\beta _{2})q^{4}+(13\\beta _{1}-\\beta _{5}+\\cdots)q^{5}+\\cdots"
"72.12.d.d"	22	55.3207090002904	NULL	[]	[]	[46, 0, 0, 67228]	NULL	NULL
"72.12.f.a"	44	55.3207090002904	NULL	[]	[]	[0, 0, 0, 0]	NULL	NULL
"72.12.i.a"	32	55.3207090002904	NULL	[]	[]	[0, -207, -3125, 14187]	NULL	NULL
"72.12.i.b"	34	55.3207090002904	NULL	[]	[]	[0, -56, -3125, -14187]	NULL	NULL
"72.12.l.a"	4	55.3207090002904	"4.0.576.1"	[-8]	[]	[0, -394, 0, 0]	NULL	"q-2^{5}\\beta _{1}q^{2}+(-197+263\\beta _{1}+197\\beta _{2}+\\cdots)q^{3}+\\cdots"
"72.12.l.b"	256	55.3207090002904	NULL	[]	[]	[-3, 390, 0, 0]	NULL	NULL
"72.12.n.a"	260	55.3207090002904	NULL	[]	[]	[-1, 0, 0, -2]	NULL	NULL
"72.13.b.a"	1	65.80755484389256	"1.1.1.1"	[-8]	[]	[-64, 0, 0, 0]	NULL	"q-2^{6}q^{2}+2^{12}q^{4}-2^{18}q^{8}-1923122q^{11}+\\cdots"
"72.13.b.b"	10	65.80755484389256	NULL	[]	[]	[110, 0, 0, 0]	NULL	"q+(11-\\beta _{1})q^{2}+(-244-12\\beta _{1}-\\beta _{2}+\\cdots)q^{4}+\\cdots"
"72.13.b.c"	24	65.80755484389256	NULL	[]	[]	[-90, 0, 0, 0]	NULL	NULL
"72.13.b.d"	24	65.80755484389256	NULL	[]	[]	[0, 0, 0, 0]	NULL	NULL
"72.13.e.a"	6	65.80755484389256	NULL	[]	[]	[0, 0, 0, 143256]	NULL	"q+(987\\beta _{1}-\\beta _{4})q^{5}+(23876+\\beta _{2}+\\beta _{3}+\\cdots)q^{7}+\\cdots"
"72.13.e.b"	6	65.80755484389256	NULL	[]	[]	[0, 0, 0, 254424]	NULL	"q+(1845\\beta _{1}-\\beta _{3})q^{5}+(42404+\\beta _{2}+\\cdots)q^{7}+\\cdots"
"72.13.h.a"	48	65.80755484389256	NULL	[]	[]	[0, 0, 0, 0]	NULL	NULL
"72.13.m.a"	72	65.80755484389256	NULL	[]	[]	[0, 460, 0, 0]	NULL	NULL
"72.14.a.a"	1	77.20626884537714	"1.1.1.1"	[]	[]	[0, 0, 4330, -139992]	1	"q+4330q^{5}-139992q^{7}+6484324q^{11}+\\cdots"
"72.14.a.b"	1	77.20626884537714	"1.1.1.1"	[]	[]	[0, 0, 22490, 181272]	-1	"q+22490q^{5}+181272q^{7}+9261428q^{11}+\\cdots"
"72.14.a.c"	2	77.20626884537714	"2.2.781.1"	[]	[]	[0, 0, -18476, 110928]	-1	"q+(-9238-4\\beta )q^{5}+(55464-74\\beta )q^{7}+\\cdots"
"72.14.a.d"	2	77.20626884537714	"2.2.62869.1"	[]	[]	[0, 0, -5068, 104880]	1	"q+(-2534-\\beta )q^{5}+(52440+5\\beta )q^{7}+\\cdots"
"72.14.a.e"	2	77.20626884537714	"2.2.1621.1"	[]	[]	[0, 0, 11204, 275808]	1	"q+(5602-\\beta )q^{5}+(137904-13\\beta )q^{7}+\\cdots"
"72.14.a.f"	2	77.20626884537714	"2.2.1624.1"	[]	[]	[0, 0, 30916, -532896]	-1	"q+(15458+7\\beta )q^{5}+(-266448-37\\beta )q^{7}+\\cdots"
"72.14.a.g"	3	77.20626884537714	NULL	[]	[]	[0, 0, -50256, 14532]	1	"q+(-16752+\\beta _{2})q^{5}+(4844-\\beta _{1}+\\cdots)q^{7}+\\cdots"
"72.14.a.h"	3	77.20626884537714	NULL	[]	[]	[0, 0, 50256, 14532]	-1	"q+(16752-\\beta _{2})q^{5}+(4844-\\beta _{1}-3\\beta _{2})q^{7}+\\cdots"
"72.14.d.a"	2	77.20626884537714	"2.0.8.1"	[-24]	[]	[0, 0, 0, -1179356]	NULL	"q+2^{5}\\beta q^{2}-2^{13}q^{4}+12349\\beta q^{5}+\\cdots"
"72.14.d.b"	2	77.20626884537714	"2.0.79.1"	[]	[]	[112, 0, 0, -351664]	NULL	"q+(56-4\\beta )q^{2}+(-1920-448\\beta )q^{4}+\\cdots"
"72.14.d.c"	10	77.20626884537714	NULL	[]	[]	[-110, 0, 0, 586960]	NULL	"q+(-11+\\beta _{1})q^{2}+(-472-12\\beta _{1}+\\cdots)q^{4}+\\cdots"
"72.14.d.d"	24	77.20626884537714	NULL	[]	[]	[0, 0, 0, 1649952]	NULL	NULL
"72.14.d.e"	26	77.20626884537714	NULL	[]	[]	[-2, 0, 0, -470596]	NULL	NULL
"72.14.f.a"	52	77.20626884537714	NULL	[]	[]	[0, 0, 0, 0]	NULL	NULL
"72.14.i.a"	38	77.20626884537714	NULL	[]	[]	[0, 12, 15625, 410565]	NULL	NULL
"72.14.i.b"	40	77.20626884537714	NULL	[]	[]	[0, -143, 15625, -410565]	NULL	NULL
"72.15.b.a"	1	89.5168570693723	"1.1.1.1"	[-8]	[]	[128, 0, 0, 0]	NULL	"q+2^{7}q^{2}+2^{14}q^{4}+2^{21}q^{8}-38712254q^{11}+\\cdots"
"72.15.b.b"	12	89.5168570693723	NULL	[]	[]	[-218, 0, 0, 0]	NULL	"q+(-18+\\beta _{1})q^{2}+(-2572-21\\beta _{1}+\\cdots)q^{4}+\\cdots"
"72.15.b.c"	28	89.5168570693723	NULL	[]	[]	[0, 0, 0, 0]	NULL	NULL
"72.15.b.d"	28	89.5168570693723	NULL	[]	[]	[182, 0, 0, 0]	NULL	NULL
"72.15.e.a"	6	89.5168570693723	NULL	[]	[]	[0, 0, 0, -528504]	NULL	"q+(-2595\\beta _{1}-\\beta _{3})q^{5}+(-88084+\\cdots)q^{7}+\\cdots"
"72.15.e.b"	8	89.5168570693723	NULL	[]	[]	[0, 0, 0, -1509984]	NULL	"q+(6985\\beta _{4}+\\beta _{5})q^{5}+(-188748+2\\beta _{1}+\\cdots)q^{7}+\\cdots"
"72.15.h.a"	56	89.5168570693723	NULL	[]	[]	[0, 0, 0, 0]	NULL	NULL
"72.15.m.a"	84	89.5168570693723	NULL	[]	[]	[0, -1118, 0, 0]	NULL	NULL
"72.16.a.a"	1	102.7393236719427	"1.1.1.1"	[]	[]	[0, 0, -313358, -2324616]	-1	"q-313358q^{5}-2324616q^{7}+55249084q^{11}+\\cdots"
"72.16.a.b"	1	102.7393236719427	"1.1.1.1"	[]	[]	[0, 0, 42010, 385728]	-1	"q+42010q^{5}+385728q^{7}-20444300q^{11}+\\cdots"
"72.16.a.c"	1	102.7393236719427	"1.1.1.1"	[]	[]	[0, 0, 251890, 1374072]	-1	"q+251890q^{5}+1374072q^{7}+43286716q^{11}+\\cdots"
"72.16.a.d"	2	102.7393236719427	"2.2.158701.1"	[]	[]	[0, 0, -291404, 1161216]	1	"q+(-145702-\\beta )q^{5}+(580608+7^{2}\\beta )q^{7}+\\cdots"
"72.16.a.e"	2	102.7393236719427	"2.2.1285.1"	[]	[]	[0, 0, -82780, -42192]	-1	"q+(-41390-\\beta )q^{5}+(-21096+23\\beta )q^{7}+\\cdots"
"72.16.a.f"	2	102.7393236719427	"2.2.88.1"	[]	[]	[0, 0, 18340, -680400]	1	"q+(9170+19\\beta )q^{5}+(-340200+203\\beta )q^{7}+\\cdots"
"72.16.a.g"	2	102.7393236719427	"2.2.232.1"	[]	[]	[0, 0, 140260, 126192]	1	"q+(70130+4\\beta )q^{5}+(63096-10\\beta )q^{7}+\\cdots"
"72.16.a.h"	4	102.7393236719427	NULL	[]	[]	[0, 0, -26944, 412176]	-1	"q+(-6736+\\beta _{1})q^{5}+(103044+\\beta _{1}+\\cdots)q^{7}+\\cdots"
"72.16.a.i"	4	102.7393236719427	NULL	[]	[]	[0, 0, 26944, 412176]	1	"q+(6736-\\beta _{1})q^{5}+(103044+\\beta _{1}+\\beta _{2}+\\cdots)q^{7}+\\cdots"
"72.16.d.a"	2	102.7393236719427	"2.0.8.1"	[-24]	[]	[0, 0, 0, 3941212]	NULL	"q+2^{6}\\beta q^{2}-2^{15}q^{4}+92477\\beta q^{5}+\\cdots"
"72.16.d.b"	14	102.7393236719427	NULL	[]	[]	[90, 0, 0, -1647088]	NULL	"q+(6+\\beta _{1})q^{2}+(3672+6\\beta _{1}+\\beta _{4})q^{4}+\\cdots"
"72.16.d.c"	28	102.7393236719427	NULL	[]	[]	[0, 0, 0, -7235384]	NULL	NULL
"72.16.d.d"	30	102.7393236719427	NULL	[]	[]	[-178, 0, 0, 3294172]	NULL	NULL
"72.16.f.a"	60	102.7393236719427	NULL	[]	[]	[0, 0, 0, 0]	NULL	NULL
"72.16.i.a"	44	102.7393236719427	NULL	[]	[]	[0, -1443, -78125, 1897941]	NULL	NULL
"72.16.i.b"	46	102.7393236719427	NULL	[]	[]	[0, 4072, -78125, -1897941]	NULL	NULL
"72.17.b.a"	1	116.87367157677156	"1.1.1.1"	[-8]	[]	[-256, 0, 0, 0]	NULL	"q-2^{8}q^{2}+2^{16}q^{4}-2^{24}q^{8}-309273794q^{11}+\\cdots"
"72.17.b.b"	14	116.87367157677156	NULL	[]	[]	[350, 0, 0, 0]	NULL	"q+(5^{2}+\\beta _{1})q^{2}+(-3873+3^{3}\\beta _{1}+\\beta _{3}+\\cdots)q^{4}+\\cdots"
"72.17.b.c"	32	116.87367157677156	NULL	[]	[]	[-186, 0, 0, 0]	NULL	NULL
"72.17.b.d"	32	116.87367157677156	NULL	[]	[]	[0, 0, 0, 0]	NULL	NULL
"72.17.e.a"	8	116.87367157677156	NULL	[]	[]	[0, 0, 0, -8762976]	NULL	"q+(65659\\beta _{1}+\\beta _{3})q^{5}+(-1095372+\\cdots)q^{7}+\\cdots"
"72.17.e.b"	8	116.87367157677156	NULL	[]	[]	[0, 0, 0, -2603616]	NULL	"q+(-43525\\beta _{3}-\\beta _{5})q^{5}+(-325452+\\cdots)q^{7}+\\cdots"
"72.17.h.a"	64	116.87367157677156	NULL	[]	[]	[0, 0, 0, 0]	NULL	NULL
"72.17.m.a"	96	116.87367157677156	NULL	[]	[]	[0, -1904, 0, 0]	NULL	NULL
"72.18.a.a"	2	131.91990288808296	NULL	[]	[]	[0, 0, -1101004, 5453904]	1	"q+(-550502+\\beta )q^{5}+(2726952+19\\beta )q^{7}+\\cdots"
"72.18.a.b"	2	131.91990288808296	"2.2.1022389.1"	[]	[]	[0, 0, -354940, -7934208]	1	"q+(-177470-5\\beta )q^{5}+(-3967104+\\cdots)q^{7}+\\cdots"
"72.18.a.c"	2	131.91990288808296	"2.2.8584.1"	[]	[]	[0, 0, 53620, -333168]	-1	"q+(26810+20\\beta )q^{5}+(-166584-326\\beta )q^{7}+\\cdots"
"72.18.a.d"	2	131.91990288808296	"2.2.456.1"	[]	[]	[0, 0, 791924, -18932592]	1	"q+(395962+68\\beta )q^{5}+(-9466296+\\cdots)q^{7}+\\cdots"
"72.18.a.e"	2	131.91990288808296	"2.2.4524.1"	[]	[]	[0, 0, 1139764, 3021648]	-1	"q+(569882+13\\beta )q^{5}+(1510824+119\\beta )q^{7}+\\cdots"
"72.18.a.f"	3	131.91990288808296	NULL	[]	[]	[0, 0, -593658, 18724416]	-1	"q+(-197886-\\beta _{1})q^{5}+(6241472+\\cdots)q^{7}+\\cdots"
"72.18.a.g"	4	131.91990288808296	NULL	[]	[]	[0, 0, -677824, 9632880]	1	"q+(-169456-\\beta _{1})q^{5}+(2408220+\\cdots)q^{7}+\\cdots"
"72.18.a.h"	4	131.91990288808296	NULL	[]	[]	[0, 0, 677824, 9632880]	-1	"q+(169456+\\beta _{1})q^{5}+(2408220+\\beta _{2}+\\cdots)q^{7}+\\cdots"
"72.18.d.a"	2	131.91990288808296	"2.0.8.1"	[-24]	[]	[0, 0, 0, 18376324]	NULL	"q-2^{7}\\beta q^{2}-2^{17}q^{4}+493679\\beta q^{5}+\\cdots"
"72.18.d.b"	16	131.91990288808296	NULL	[]	[]	[-270, 0, 0, 11529600]	NULL	"q+(-17-\\beta _{1})q^{2}+(-1713+17\\beta _{1}+\\cdots)q^{4}+\\cdots"
"72.18.d.c"	32	131.91990288808296	NULL	[]	[]	[0, 0, 0, 4682880]	NULL	NULL
"72.18.d.d"	34	131.91990288808296	NULL	[]	[]	[542, 0, 0, -23059204]	NULL	NULL
"72.18.f.a"	68	131.91990288808296	NULL	[]	[]	[0, 0, 0, 0]	NULL	NULL
"72.19.b.a"	1	147.87801915102983	"1.1.1.1"	[-8]	[]	[512, 0, 0, 0]	NULL	"q+2^{9}q^{2}+2^{18}q^{4}+2^{27}q^{8}+354349618q^{11}+\\cdots"
"72.19.b.b"	16	147.87801915102983	NULL	[]	[]	[-426, 0, 0, 0]	NULL	"q+(-3^{3}+\\beta _{1})q^{2}+(-27760-30\\beta _{1}+\\cdots)q^{4}+\\cdots"
"72.19.b.c"	36	147.87801915102983	NULL	[]	[]	[-170, 0, 0, 0]	NULL	NULL
"72.19.b.d"	36	147.87801915102983	NULL	[]	[]	[0, 0, 0, 0]	NULL	NULL
"72.19.e.a"	8	147.87801915102983	NULL	[]	[]	[0, 0, 0, 112078752]	NULL	"q+(355105\\beta _{1}+\\beta _{5})q^{5}+(14009844+\\cdots)q^{7}+\\cdots"
"72.19.e.b"	10	147.87801915102983	NULL	[]	[]	[0, 0, 0, -44138184]	NULL	"q+(146357\\beta _{5}+\\beta _{6})q^{5}+(-4413818+\\cdots)q^{7}+\\cdots"
"72.19.h.a"	72	147.87801915102983	NULL	[]	[]	[0, 0, 0, 0]	NULL	NULL
"72.20.a.a"	2	164.74802152059414	"2.2.1453.1"	[]	[]	[0, 0, -1226620, 88510512]	-1	"q+(-613310-44\\beta )q^{5}+(44255256+\\cdots)q^{7}+\\cdots"
"72.20.a.b"	2	164.74802152059414	NULL	[]	[]	[0, 0, 957620, -77881440]	-1	"q+(478810+\\beta )q^{5}+(-38940720+\\cdots)q^{7}+\\cdots"
"72.20.a.c"	2	164.74802152059414	"2.2.7996.1"	[]	[]	[0, 0, 1780660, 16959648]	1	"q+(890330+23\\beta )q^{5}+(8479824-479\\beta )q^{7}+\\cdots"
"72.20.a.d"	2	164.74802152059414	"2.2.619789.1"	[]	[]	[0, 0, 2327140, -27922992]	1	"q+(1163570-5\\beta )q^{5}+(-13961496+\\cdots)q^{7}+\\cdots"
"72.20.a.e"	3	164.74802152059414	NULL	[]	[]	[0, 0, -2237994, -55517448]	-1	"q+(-745998+\\beta _{1})q^{5}+(-18505816+\\cdots)q^{7}+\\cdots"
"72.20.a.f"	3	164.74802152059414	NULL	[]	[]	[0, 0, -2140218, 55851720]	1	"q+(-713406+8\\beta _{1}-\\beta _{2})q^{5}+(18617240+\\cdots)q^{7}+\\cdots"
"72.20.a.g"	5	164.74802152059414	NULL	[]	[]	[0, 0, -167696, -72181116]	-1	"q+(-33539+\\beta _{1})q^{5}+(-14436222+\\cdots)q^{7}+\\cdots"
"72.20.a.h"	5	164.74802152059414	NULL	[]	[]	[0, 0, 167696, -72181116]	1	"q+(33539-\\beta _{1})q^{5}+(-14436222+\\cdots)q^{7}+\\cdots"
"72.20.d.a"	2	164.74802152059414	"2.0.8.1"	[-24]	[]	[0, 0, 0, -376882628]	NULL	"q-2^{8}\\beta q^{2}-2^{19}q^{4}+1324567\\beta q^{5}+\\cdots"
"72.20.d.b"	18	164.74802152059414	NULL	[]	[]	[458, 0, 0, -80707216]	NULL	"q+(5^{2}-\\beta _{1})q^{2}+(-22907-3^{3}\\beta _{1}+\\cdots)q^{4}+\\cdots"
"72.20.d.c"	36	164.74802152059414	NULL	[]	[]	[0, 0, 0, 215468200]	NULL	NULL
"72.20.d.d"	38	164.74802152059414	NULL	[]	[]	[-914, 0, 0, 161414428]	NULL	NULL
"72.20.f.a"	76	164.74802152059414	NULL	[]	[]	[0, 0, 0, 0]	NULL	NULL
"72.21.b.a"	1	182.52991087391638	"1.1.1.1"	[-8]	[]	[-1024, 0, 0, 0]	NULL	"q-2^{10}q^{2}+2^{20}q^{4}-2^{30}q^{8}+42383023726q^{11}+\\cdots"
"72.21.b.b"	18	182.52991087391638	NULL	[]	[]	[398, 0, 0, 0]	NULL	"q+(22+\\beta _{1})q^{2}+(40275+21\\beta _{1}-\\beta _{2}+\\cdots)q^{4}+\\cdots"
"72.21.b.c"	40	182.52991087391638	NULL	[]	[]	[0, 0, 0, 0]	NULL	NULL
"72.21.b.d"	40	182.52991087391638	NULL	[]	[]	[1254, 0, 0, 0]	NULL	NULL
"72.21.e.a"	10	182.52991087391638	NULL	[]	[]	[0, 0, 0, -489367704]	NULL	"q+(732773\\beta _{5}+\\beta _{6})q^{5}+(-48936770+\\cdots)q^{7}+\\cdots"
"72.21.e.b"	10	182.52991087391638	NULL	[]	[]	[0, 0, 0, 676694952]	NULL	"q+(-806622\\beta _{5}+\\beta _{6})q^{5}+(67669493+\\cdots)q^{7}+\\cdots"
"72.21.h.a"	80	182.52991087391638	NULL	[]	[]	[0, 0, 0, 0]	NULL	NULL
"72.22.a.a"	2	201.2236878866847	"2.2.537541.1"	[]	[]	[0, 0, -21948620, -659451408]	-1	"q+(-10974310-5\\beta )q^{5}+(-329725704+\\cdots)q^{7}+\\cdots"
"72.22.a.b"	2	201.2236878866847	"2.2.358549.1"	[]	[]	[0, 0, -2108140, 444771792]	1	"q+(-1054070-20\\beta )q^{5}+(222385896+\\cdots)q^{7}+\\cdots"
"72.22.a.c"	3	201.2236878866847	NULL	[]	[]	[0, 0, -5280498, 852542376]	1	"q+(-1760166+\\beta _{1})q^{5}+(284180792+\\cdots)q^{7}+\\cdots"
"72.22.a.d"	3	201.2236878866847	NULL	[]	[]	[0, 0, -2080026, -1205282064]	1	"q+(-693342-\\beta _{1})q^{5}+(-401760688+\\cdots)q^{7}+\\cdots"
"72.22.a.e"	3	201.2236878866847	NULL	[]	[]	[0, 0, 4833126, 271431024]	-1	"q+(1611042+\\beta _{1})q^{5}+(90477008+\\cdots)q^{7}+\\cdots"
"72.22.a.f"	3	201.2236878866847	NULL	[]	[]	[0, 0, 24111774, 295988280]	-1	"q+(8037258-\\beta _{2})q^{5}+(98662760+\\cdots)q^{7}+\\cdots"
"72.22.a.g"	5	201.2236878866847	NULL	[]	[]	[0, 0, -10324496, -370380036]	1	"q+(-2064899+\\beta _{1})q^{5}+(-74076006+\\cdots)q^{7}+\\cdots"
"72.22.a.h"	5	201.2236878866847	NULL	[]	[]	[0, 0, 10324496, -370380036]	-1	"q+(2064899-\\beta _{1})q^{5}+(-74076006+\\cdots)q^{7}+\\cdots"
"72.22.f.a"	84	201.2236878866847	NULL	[]	[]	[0, 0, 0, 0]	NULL	NULL
"72.23.e.a"	10	220.82935308613236	NULL	[]	[]	[0, 0, 0, 165396888]	NULL	"q+(-716395\\beta _{5}+\\beta _{6})q^{5}+(16539689+\\cdots)q^{7}+\\cdots"
"72.23.e.b"	12	220.82935308613236	NULL	[]	[]	[0, 0, 0, 2386734576]	NULL	"q+(-6524295\\beta _{6}+\\beta _{7})q^{5}+(198894548+\\cdots)q^{7}+\\cdots"
"72.23.h.a"	88	220.82935308613236	NULL	[]	[]	[0, 0, 0, 0]	NULL	NULL


# Label --
#    The **label** of a newform $f\in S_k^{\rm new}(N,\chi)$ has the format \( N.k.a.x \), where

#    -  \( N\) is the level;

#    - \(k\) is the weight;

#    - \(N.a\) is the label of the Galois orbit of the Dirichlet character $\chi$;

#    - \(x\) is the label of the Galois orbit of the newform $f$.

#    For each embedding of the coefficient field of $f$ into the complex numbers, the corresponding modular form over $\C$ has a label of the form \(N.k.a.x.n.i\), where

#    - \(n\) determines the Conrey label \(N.n\) of the Dirichlet character \(\chi\);

#    - \(i\) is an integer ranging from 1 to the relative dimension of the newform that distinguishes embeddings with the same character $\chi$.


# Dim --
#    The **dimension** of a space of modular forms is its dimension as a complex vector space; for spaces of newforms $S_k^{\rm new}(N,\chi)$ this is the same as the dimension of the $\Q$-vector space spanned by its eigenforms.

#    The **dimension** of a newform refers to the dimension of its newform subspace, equivalently, the cardinality of its newform orbit.  This is equal to the degree of its coefficient field (as an extension of $\Q$).

#    The **relative dimension** of $S_k^{\rm new}(N,\chi)$  is its dimension as a $\Q(\chi)$-vector space, where $\Q(\chi)$ is the field generated by the values of $\chi$, and similarly for newform subspaces.


#$A$ (analytic_conductor) --
#    The **analytic conductor** of a newform $f \in S_k^{\mathrm{new}}(N,\chi)$ is the positive real number
#    \[
#    N\left(\frac{\exp(\psi(k/2))}{2\pi}\right)^2,
#    \]
#    where $\psi(x):=\Gamma'(x)/\Gamma(x)$ is the logarithmic derivative of the Gamma function.


#Field (nf_label) --
#    The **coefficient field** of a modular form is the subfield of $\C$ generated by the coefficients $a_n$ of its $q$-expansion $\sum a_nq^n$.  The space of cusp forms $S_k^\mathrm{new}(N,\chi)$ has a basis of modular forms that are simultaneous eigenforms for all Hecke operators and with algebraic Fourier coefficients.  For such eigenforms the coefficient field will be a number field, and Galois conjugate eigenforms will share the same coefficient field.  Moreover, if $m$ is the smallest positive integer such that the values of the character $\chi$ are contained in the cyclotomic field $\Q(\zeta_m)$, the coefficient field will contain $\Q(\zeta_m)$
#    For eigenforms, the coefficient field is also known as the **Hecke field**.


#CM (cm_discs) --
#    A newform $f$ admits a **self-twist** by a primitive
#     Dirichlet character $\chi$ if the equality
#    \[
#    a_p(f) = \chi(p)a_p(f)
#    \]
#    holds for all but finitely many primes $p$.

#    For non-trivial $\chi$ this can hold only when $\chi$ has order $2$ and $a_p=0$ for all primes $p$ not dividing the level of $f$ for which $\chi(p)=-1$.
#    The character $\chi$ is then the Kronecker character of a quadratic field $K$ and may be identified by the discriminant $D$ of $K$.

#    If $D$ is negative, the modular form $f$ is said to have complex multiplication (CM) by $K$, and if $D$ is positive, $f$ is said to have real multiplication (RM) by $K$.  The latter can occur only when $f$ is a modular form of weight $1$ whose projective image is dihedral.

#    It is possible for a modular form to have multiple non-trivial self twists; this occurs precisely when $f$ is a modular form of weight one whose projective image is isomorphic to $D_2:=C_2\times C_2$; in this case $f$ admits three non-trivial self twists, two of which are CM and one of which is RM.



#RM (rm_discs) --
#    A newform $f$ admits a **self-twist** by a primitive
#     Dirichlet character $\chi$ if the equality
#    \[
#    a_p(f) = \chi(p)a_p(f)
#    \]
#    holds for all but finitely many primes $p$.

#    For non-trivial $\chi$ this can hold only when $\chi$ has order $2$ and $a_p=0$ for all primes $p$ not dividing the level of $f$ for which $\chi(p)=-1$.
#    The character $\chi$ is then the Kronecker character of a quadratic field $K$ and may be identified by the discriminant $D$ of $K$.

#    If $D$ is negative, the modular form $f$ is said to have complex multiplication (CM) by $K$, and if $D$ is positive, $f$ is said to have real multiplication (RM) by $K$.  The latter can occur only when $f$ is a modular form of weight $1$ whose projective image is dihedral.

#    It is possible for a modular form to have multiple non-trivial self twists; this occurs precisely when $f$ is a modular form of weight one whose projective image is isomorphic to $D_2:=C_2\times C_2$; in this case $f$ admits three non-trivial self twists, two of which are CM and one of which is RM.



#Traces (trace_display) --
#    For a newform $f \in S_k^{\rm new}(\Gamma_1(N))$, its **trace form** $\mathrm{Tr}(f)$ is the sum of its distinct conjugates under $\mathrm{Aut}(\C)$ (equivalently, the sum under all embeddings of the coefficient field into $\C$).  The trace form is a modular form $\mathrm{Tr}(f) \in S_k^{\rm new}(\Gamma_1(N))$ whose $q$-expansion has integral coefficients $a_n(\mathrm{Tr}(f)) \in \Z$.

#    The coefficient $a_1$ is equal to the dimension of the newform.

#    For $p$ prime, the coefficient $a_p$ is the trace of Frobenius in the direct sum of the $\ell$-adic Galois representations attached to the conjugates of $f$ (for any prime $\ell$).  When $f$ has weight $k=2$, the coefficient $a_p(f)$ is the trace of Frobenius acting on the modular abelian variety associated to $f$.

#    For a newspace $S_k^{\rm new}(N,\chi)$, its trace form is the sum of the trace forms $\mathrm{Tr}(f)$ over all newforms $f\in S_k^{\rm new}(N,k)$; it is also a modular form in $S_k^{\rm new}(\Gamma_1(N))$.

#    The graphical plot displayed in the properties box on the home page of each newform or newspace is computed using the trace form.


#Fricke sign (fricke_eigenval) --
#    The **Fricke involution** is the Atkin-Lehner involution $w_N$ on the space $S_k(\Gamma_0(N))$ (induced by the corresponding involution on the modular curve $X_0(N)$).

#    For a newform $f \in S_k^{\textup{new}}(\Gamma_0(N))$, the sign of the functional equation satisfied by the L-function attached to $f$ is $i^{-k}$ times the eigenvalue of $\omega_N$ on $f$.  So, for example when $k=2$, the signs swap, and the analytic rank of $f$ is even when $w_N f = -f$ and odd when $w_N f = +f$.


#$q$-expansion (qexp_display) --
#    The **$q$-expansion** of a modular form $f(z)$ is its Fourier expansion at the cusp $z=i\infty$, expressed as a power series $\sum_{n=0}^{\infty} a_n q^n$ in the variable $q=e^{2\pi iz}$.

#    For cusp forms, the constant coefficient $a_0$ of the $q$-expansion is zero.

#    For newforms, we have $a_1=1$ and the coefficients $a_n$ are algebraic integers in a number field $K \subseteq \C$.

#    Accordingly, we define the **$q$-expansion** of a newform orbit $[f]$ to be the $q$-expansion of any newform $f$ in the orbit, but with coefficients $a_n \in K$ (without an embedding into $\C$).  Each embedding $K \hookrightarrow \C$ then gives rise to an embedded newform whose $q$-expansion has $a_n \in \C$, as above.