# Classical modular forms downloaded from the LMFDB on 31 May 2026.
# Search link: https://www.lmfdb.org/ModularForm/GL2/Q/holomorphic/273/
# Query "{'level': 273}" returned 226 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.



"273.1.o.a"	2	0.13624474844880965	"2.0.4.1"	[-3]	[]	[0, 0, 0, 0]	NULL	"q+i q^{3}+i q^{4}-i q^{7}-q^{9}-q^{12}+\\cdots"
"273.1.o.b"	2	0.13624474844880965	"2.0.4.1"	[-3]	[]	[0, 0, 0, 2]	NULL	"q-i q^{3}+i q^{4}+q^{7}-q^{9}+q^{12}+\\cdots"
"273.1.s.a"	2	0.13624474844880965	"2.0.3.1"	[-3]	[]	[0, -1, 0, -1]	NULL	"q+\\zeta_{6}^{2}q^{3}+q^{4}+\\zeta_{6}^{2}q^{7}-\\zeta_{6}q^{9}+\\cdots"
"273.1.s.b"	4	0.13624474844880965	"4.0.144.1"	[]	[]	[0, 0, 0, -2]	NULL	"q-\\zeta_{12}^{3}q^{2}-\\zeta_{12}^{5}q^{3}+\\zeta_{12}^{5}q^{5}+\\cdots"
"273.1.x.a"	2	0.13624474844880965	"2.0.3.1"	[-3]	[]	[0, -2, 0, -1]	NULL	"q-q^{3}-\\zeta_{6}^{2}q^{4}-\\zeta_{6}q^{7}+q^{9}+\\zeta_{6}^{2}q^{12}+\\cdots"
"273.1.bm.a"	2	0.13624474844880965	"2.0.3.1"	[-3]	[]	[0, 2, 0, -1]	NULL	"q+q^{3}+\\zeta_{6}^{2}q^{4}-\\zeta_{6}q^{7}+q^{9}+\\zeta_{6}^{2}q^{12}+\\cdots"
"273.1.bm.b"	4	0.13624474844880965	"4.0.144.1"	[]	[]	[0, 0, 0, 4]	NULL	"q-\\zeta_{12}q^{2}-\\zeta_{12}^{3}q^{3}-\\zeta_{12}^{5}q^{5}+\\zeta_{12}^{4}q^{6}+\\cdots"
"273.1.bp.a"	2	0.13624474844880965	"2.0.3.1"	[-3]	[]	[0, 1, 0, 1]	NULL	"q-\\zeta_{6}^{2}q^{3}-q^{4}-\\zeta_{6}^{2}q^{7}-\\zeta_{6}q^{9}+\\cdots"
"273.1.bs.a"	4	0.13624474844880965	"4.0.144.1"	[-3]	[]	[0, 0, 0, 0]	NULL	"q+\\zeta_{12}q^{3}-\\zeta_{12}^{3}q^{4}-\\zeta_{12}q^{7}+\\zeta_{12}^{2}q^{9}+\\cdots"
"273.1.ch.a"	4	0.13624474844880965	"4.0.144.1"	[-3]	[]	[0, 0, 0, -2]	NULL	"q-\\zeta_{12}^{3}q^{3}-\\zeta_{12}^{5}q^{4}+\\zeta_{12}^{4}q^{7}+\\cdots"
"273.2.a.a"	1	2.1799159751809545	"1.1.1.1"	[]	[]	[-2, -1, -1, 1]	1	"q-2q^{2}-q^{3}+2q^{4}-q^{5}+2q^{6}+q^{7}+\\cdots"
"273.2.a.b"	1	2.1799159751809545	"1.1.1.1"	[]	[]	[2, 1, 1, -1]	-1	"q+2q^{2}+q^{3}+2q^{4}+q^{5}+2q^{6}-q^{7}+\\cdots"
"273.2.a.c"	2	2.1799159751809545	"2.2.8.1"	[]	[]	[2, -2, 0, 2]	-1	"q+(1+\\beta )q^{2}-q^{3}+(1+2\\beta )q^{4}+(-1+\\cdots)q^{6}+\\cdots"
"273.2.a.d"	3	2.1799159751809545	"3.3.316.1"	[]	[]	[-2, -3, -3, -3]	1	"q+(-1+\\beta _{1})q^{2}-q^{3}+(2-2\\beta _{1}+\\beta _{2})q^{4}+\\cdots"
"273.2.a.e"	4	2.1799159751809545	"4.4.17428.1"	[]	[]	[1, 4, -3, 4]	-1	"q+\\beta _{1}q^{2}+q^{3}+(2+\\beta _{2})q^{4}+(-1-\\beta _{2}+\\cdots)q^{5}+\\cdots"
"273.2.c.a"	2	2.1799159751809545	"2.0.4.1"	[]	[]	[0, 2, 0, 0]	NULL	"q+2 i q^{2}+q^{3}-2 q^{4}+3 i q^{5}+2 i q^{6}+\\cdots"
"273.2.c.b"	6	2.1799159751809545	"6.0.350464.1"	[]	[]	[0, 6, 0, 0]	NULL	"q-\\beta _{4}q^{2}+q^{3}+(-\\beta _{1}+\\beta _{2})q^{4}+(-\\beta _{3}+\\cdots)q^{5}+\\cdots"
"273.2.c.c"	8	2.1799159751809545	"8.0.265727878144.1"	[]	[]	[0, -8, 0, 0]	NULL	"q+\\beta _{1}q^{2}-q^{3}+(-2+\\beta _{2})q^{4}+(-\\beta _{3}+\\cdots)q^{5}+\\cdots"
"273.2.e.a"	32	2.1799159751809545	NULL	[]	[]	[0, 0, 0, 4]	NULL	NULL
"273.2.g.a"	32	2.1799159751809545	NULL	[]	[]	[0, 0, 0, 0]	NULL	NULL
"273.2.i.a"	2	2.1799159751809545	"2.0.3.1"	[]	[]	[1, -1, -4, -5]	NULL	"q+\\zeta_{6}q^{2}+(-1+\\zeta_{6})q^{3}+(1-\\zeta_{6})q^{4}+\\cdots"
"273.2.i.b"	6	2.1799159751809545	"6.0.19683.1"	[]	[]	[0, 3, -3, 0]	NULL	"q+(-\\zeta_{18}+\\zeta_{18}^{2}+\\zeta_{18}^{4}-\\zeta_{18}^{5})q^{2}+\\cdots"
"273.2.i.c"	6	2.1799159751809545	"6.0.64827.1"	[]	[]	[2, -3, 3, 0]	NULL	"q+(\\beta _{1}+\\beta _{4})q^{2}-\\beta _{5}q^{3}+(2\\beta _{1}-2\\beta _{2}+\\cdots)q^{4}+\\cdots"
"273.2.i.d"	8	2.1799159751809545	"8.0.4868829729.1"	[]	[]	[1, -4, -3, 9]	NULL	"q+(-\\beta _{1}+\\beta _{3}+\\beta _{6})q^{2}+\\beta _{4}q^{3}+(\\beta _{3}+\\cdots)q^{4}+\\cdots"
"273.2.i.e"	10	2.1799159751809545	NULL	[]	[]	[0, 5, 3, 4]	NULL	"q+(\\beta _{4}-\\beta _{8})q^{2}+(1-\\beta _{2})q^{3}+(-1-\\beta _{1}+\\cdots)q^{4}+\\cdots"
"273.2.j.a"	2	2.1799159751809545	"2.0.3.1"	[]	[]	[0, 2, 0, 5]	NULL	"q+q^{3}+(2-2\\zeta_{6})q^{4}+(3-\\zeta_{6})q^{7}+q^{9}+\\cdots"
"273.2.j.b"	16	2.1799159751809545	NULL	[]	[]	[0, -16, 0, 1]	NULL	"q+\\beta _{1}q^{2}-q^{3}+(-\\beta _{3}+\\beta _{5}-\\beta _{9}+\\beta _{14}+\\cdots)q^{4}+\\cdots"
"273.2.j.c"	20	2.1799159751809545	NULL	[]	[]	[0, 20, 0, -9]	NULL	"q+(\\beta _{1}+\\beta _{4})q^{2}+q^{3}+(-\\beta _{2}-2\\beta _{7}+\\cdots)q^{4}+\\cdots"
"273.2.k.a"	6	2.1799159751809545	"6.0.19683.1"	[]	[]	[0, -3, 12, 3]	NULL	"q+(\\zeta_{18}-\\zeta_{18}^{2}-\\zeta_{18}^{4}+\\zeta_{18}^{5})q^{2}+\\cdots"
"273.2.k.b"	6	2.1799159751809545	"6.0.6040683.1"	[]	[]	[0, 3, 4, -3]	NULL	"q+(\\beta _{1}+\\beta _{2})q^{2}+(1-\\beta _{4})q^{3}+(\\beta _{3}-\\beta _{4}+\\cdots)q^{4}+\\cdots"
"273.2.k.c"	6	2.1799159751809545	"6.0.64827.1"	[]	[]	[2, -3, 0, -3]	NULL	"q+(\\beta _{1}+\\beta _{4})q^{2}+(-1+\\beta _{5})q^{3}+(2\\beta _{1}+\\cdots)q^{4}+\\cdots"
"273.2.k.d"	6	2.1799159751809545	"6.0.771147.1"	[]	[]	[2, 3, 0, 3]	NULL	"q+(1+\\beta _{1}-\\beta _{2}-\\beta _{3}+\\beta _{5})q^{2}-\\beta _{4}q^{3}+\\cdots"
"273.2.l.a"	2	2.1799159751809545	"2.0.3.1"	[]	[]	[0, -1, 0, -4]	NULL	"q-\\zeta_{6}q^{3}-2q^{4}+(-3+2\\zeta_{6})q^{7}+(-1+\\cdots)q^{9}+\\cdots"
"273.2.l.b"	16	2.1799159751809545	NULL	[]	[]	[0, 8, 0, 1]	NULL	"q+(-\\beta _{1}-\\beta _{2})q^{2}+\\beta _{9}q^{3}+(1+\\beta _{3}+\\cdots)q^{4}+\\cdots"
"273.2.l.c"	20	2.1799159751809545	NULL	[]	[]	[0, -10, 0, 3]	NULL	"q-\\beta _{4}q^{2}+(-1+\\beta _{7})q^{3}+(2+\\beta _{2})q^{4}+\\cdots"
"273.2.n.a"	4	2.1799159751809545	"4.0.256.1"	[]	[]	[-4, -4, -8, 0]	NULL	"q+(-1-\\zeta_{8}^{2})q^{2}+(-1+\\zeta_{8}+\\zeta_{8}^{2}+\\cdots)q^{3}+\\cdots"
"273.2.n.b"	4	2.1799159751809545	"4.0.256.1"	[]	[]	[4, -4, 8, 0]	NULL	"q+(1-\\zeta_{8}^{2})q^{2}+(-1+\\zeta_{8}+\\zeta_{8}^{2})q^{3}+\\cdots"
"273.2.n.c"	48	2.1799159751809545	NULL	[]	[]	[0, 8, 0, 0]	NULL	NULL
"273.2.p.a"	4	2.1799159751809545	"4.0.2304.2"	[]	[]	[0, 0, -8, 4]	NULL	"q+\\beta _{1}q^{2}+\\beta _{2}q^{3}+\\beta _{2}q^{4}+(-2+2\\beta _{2}+\\cdots)q^{5}+\\cdots"
"273.2.p.b"	4	2.1799159751809545	"4.0.6400.3"	[]	[]	[0, 0, -4, -4]	NULL	"q-\\beta _{2}q^{3}+2\\beta _{2}q^{4}+(-1+\\beta _{1}-\\beta _{2}+\\cdots)q^{5}+\\cdots"
"273.2.p.c"	4	2.1799159751809545	"4.0.6400.3"	[]	[]	[0, 0, 4, -4]	NULL	"q-\\beta _{2}q^{3}-2\\beta _{2}q^{4}+(1-\\beta _{2}+\\beta _{3})q^{5}+\\cdots"
"273.2.p.d"	4	2.1799159751809545	"4.0.2304.2"	[]	[]	[0, 0, 8, 0]	NULL	"q+\\beta _{1}q^{2}-\\beta _{2}q^{3}+\\beta _{2}q^{4}+(2-2\\beta _{2}+\\cdots)q^{5}+\\cdots"
"273.2.p.e"	12	2.1799159751809545	NULL	[]	[]	[0, 0, -12, 12]	NULL	"q+\\beta _{8}q^{2}-\\beta _{4}q^{3}+(3\\beta _{4}-\\beta _{6}-\\beta _{11})q^{4}+\\cdots"
"273.2.p.f"	12	2.1799159751809545	NULL	[]	[]	[0, 0, 12, -4]	NULL	"q+\\beta _{8}q^{2}+\\beta _{4}q^{3}+(3\\beta _{4}-\\beta _{6}-\\beta _{11})q^{4}+\\cdots"
"273.2.r.a"	2	2.1799159751809545	"2.0.3.1"	[-3]	[]	[0, -3, 0, 4]	NULL	"q+(-1-\\zeta_{6})q^{3}+2q^{4}+(1+2\\zeta_{6})q^{7}+\\cdots"
"273.2.r.b"	64	2.1799159751809545	NULL	[]	[]	[0, 0, 0, -10]	NULL	NULL
"273.2.t.a"	2	2.1799159751809545	"2.0.3.1"	[]	[]	[0, 1, -6, 5]	NULL	"q+(-1+2\\zeta_{6})q^{2}+\\zeta_{6}q^{3}-q^{4}+(-4+\\cdots)q^{5}+\\cdots"
"273.2.t.b"	4	2.1799159751809545	"4.0.441.1"	[]	[]	[0, -2, 6, 0]	NULL	"q+(\\beta _{1}-\\beta _{3})q^{2}+(-1+\\beta _{2})q^{3}+(-1+\\cdots)q^{4}+\\cdots"
"273.2.t.c"	12	2.1799159751809545	"12.0.2346760387617129.1"	[]	[]	[0, -6, -6, -3]	NULL	"q+(\\beta _{1}+\\beta _{3}+\\beta _{6})q^{2}+(-1-\\beta _{4})q^{3}+\\cdots"
"273.2.t.d"	20	2.1799159751809545	NULL	[]	[]	[0, 10, 6, 2]	NULL	"q+(\\beta _{2}+\\beta _{3})q^{2}+\\beta _{11}q^{3}+(-1+\\beta _{1}+\\cdots)q^{4}+\\cdots"
"273.2.u.a"	2	2.1799159751809545	"2.0.3.1"	[-3]	[]	[0, -3, 0, -4]	NULL	"q+(-1-\\zeta_{6})q^{3}+2\\zeta_{6}q^{4}+(-3+2\\zeta_{6})q^{7}+\\cdots"
"273.2.u.b"	2	2.1799159751809545	"2.0.3.1"	[-3]	[]	[0, 3, 0, -5]	NULL	"q+(1+\\zeta_{6})q^{3}+2\\zeta_{6}q^{4}+(-3+\\zeta_{6})q^{7}+\\cdots"
"273.2.u.c"	64	2.1799159751809545	NULL	[]	[]	[0, 0, 0, 0]	NULL	NULL
"273.2.y.a"	2	2.1799159751809545	"2.0.3.1"	[-3]	[]	[0, 0, 0, 5]	NULL	"q+(1-2\\zeta_{6})q^{3}+(2-2\\zeta_{6})q^{4}+(3-\\zeta_{6})q^{7}+\\cdots"
"273.2.y.b"	64	2.1799159751809545	NULL	[]	[]	[0, 0, 0, -12]	NULL	NULL
"273.2.ba.a"	2	2.1799159751809545	"2.0.3.1"	[-3]	[]	[0, 3, 0, -1]	NULL	"q+(1+\\zeta_{6})q^{3}+(2-2\\zeta_{6})q^{4}+(-2+3\\zeta_{6})q^{7}+\\cdots"
"273.2.ba.b"	2	2.1799159751809545	"2.0.3.1"	[-3]	[]	[0, 3, 0, 1]	NULL	"q+(1+\\zeta_{6})q^{3}+(2-2\\zeta_{6})q^{4}+(2-3\\zeta_{6})q^{7}+\\cdots"
"273.2.ba.c"	64	2.1799159751809545	NULL	[]	[]	[0, -12, 0, 0]	NULL	NULL
"273.2.bd.a"	16	2.1799159751809545	NULL	[]	[]	[0, -8, 0, 0]	NULL	"q+\\beta _{2}q^{2}+(-1+\\beta _{12})q^{3}+(1+\\beta _{3}+\\cdots)q^{4}+\\cdots"
"273.2.bd.b"	16	2.1799159751809545	NULL	[]	[]	[0, 8, 0, 0]	NULL	"q-\\beta _{14}q^{2}-\\beta _{5}q^{3}+(2+2\\beta _{5}+\\beta _{7}+\\cdots)q^{4}+\\cdots"
"273.2.bf.a"	2	2.1799159751809545	"2.0.3.1"	[-3]	[]	[0, 0, 0, -5]	NULL	"q+(1-2\\zeta_{6})q^{3}-2\\zeta_{6}q^{4}+(-2-\\zeta_{6})q^{7}+\\cdots"
"273.2.bf.b"	64	2.1799159751809545	NULL	[]	[]	[0, 0, 0, -4]	NULL	NULL
"273.2.bh.a"	64	2.1799159751809545	NULL	[]	[]	[0, 0, 0, -4]	NULL	NULL
"273.2.bj.a"	2	2.1799159751809545	"2.0.3.1"	[]	[]	[-3, 1, -6, 1]	NULL	"q+(-1-\\zeta_{6})q^{2}+\\zeta_{6}q^{3}+\\zeta_{6}q^{4}+(-2+\\cdots)q^{5}+\\cdots"
"273.2.bj.b"	2	2.1799159751809545	"2.0.3.1"	[]	[]	[3, 1, 6, -1]	NULL	"q+(1+\\zeta_{6})q^{2}+\\zeta_{6}q^{3}+\\zeta_{6}q^{4}+(2+2\\zeta_{6})q^{5}+\\cdots"
"273.2.bj.c"	16	2.1799159751809545	NULL	[]	[]	[0, -8, 0, 0]	NULL	"q+(\\beta _{1}+\\beta _{9})q^{2}-\\beta _{10}q^{3}+(\\beta _{10}-\\beta _{11}+\\cdots)q^{4}+\\cdots"
"273.2.bj.d"	16	2.1799159751809545	NULL	[]	[]	[0, 8, 0, 0]	NULL	"q-\\beta _{8}q^{2}+\\beta _{3}q^{3}+(\\beta _{2}+\\beta _{3}+\\beta _{5}-\\beta _{6}+\\cdots)q^{4}+\\cdots"
"273.2.bl.a"	2	2.1799159751809545	"2.0.3.1"	[]	[]	[3, -2, 6, 1]	NULL	"q+(2-\\zeta_{6})q^{2}-q^{3}+(1-\\zeta_{6})q^{4}+(2+\\cdots)q^{5}+\\cdots"
"273.2.bl.b"	4	2.1799159751809545	"4.0.441.1"	[]	[]	[3, 4, -6, 0]	NULL	"q+(1-\\beta _{3})q^{2}+q^{3}+(\\beta _{1}+\\beta _{2}-2\\beta _{3})q^{4}+\\cdots"
"273.2.bl.c"	12	2.1799159751809545	"12.0.2346760387617129.1"	[]	[]	[-3, 12, 6, 3]	NULL	"q+(-\\beta _{1}-\\beta _{6}+\\beta _{8})q^{2}+q^{3}+(-1+\\cdots)q^{4}+\\cdots"
"273.2.bl.d"	20	2.1799159751809545	NULL	[]	[]	[-3, -20, -6, -5]	NULL	"q+\\beta _{3}q^{2}-q^{3}+(\\beta _{11}+\\beta _{17})q^{4}+\\beta _{8}q^{5}+\\cdots"
"273.2.bn.a"	2	2.1799159751809545	"2.0.3.1"	[-3]	[]	[0, -3, 0, -5]	NULL	"q+(-2+\\zeta_{6})q^{3}+(-2+2\\zeta_{6})q^{4}+(-2+\\cdots)q^{7}+\\cdots"
"273.2.bn.b"	2	2.1799159751809545	"2.0.3.1"	[-3]	[]	[0, 3, 0, 4]	NULL	"q+(2-\\zeta_{6})q^{3}+(-2+2\\zeta_{6})q^{4}+(1+2\\zeta_{6})q^{7}+\\cdots"
"273.2.bn.c"	64	2.1799159751809545	NULL	[]	[]	[0, 0, 0, -4]	NULL	NULL
"273.2.br.a"	2	2.1799159751809545	"2.0.3.1"	[-3]	[]	[0, 3, 0, 4]	NULL	"q+(2-\\zeta_{6})q^{3}-2q^{4}+(3-2\\zeta_{6})q^{7}+\\cdots"
"273.2.br.b"	64	2.1799159751809545	NULL	[]	[]	[0, -6, 0, -6]	NULL	NULL
"273.2.bt.a"	36	2.1799159751809545	NULL	[]	[]	[0, 0, 0, 6]	NULL	NULL
"273.2.bt.b"	40	2.1799159751809545	NULL	[]	[]	[0, 0, 0, -2]	NULL	NULL
"273.2.bv.a"	4	2.1799159751809545	"4.0.144.1"	[-3]	[]	[0, 0, 0, 8]	NULL	"q+(\\zeta_{12}-2\\zeta_{12}^{3})q^{3}-2\\zeta_{12}^{3}q^{4}+(1+\\cdots)q^{7}+\\cdots"
"273.2.bv.b"	128	2.1799159751809545	NULL	[]	[]	[0, 2, 0, -16]	NULL	NULL
"273.2.bw.a"	4	2.1799159751809545	"4.0.144.1"	[-3]	[]	[0, 0, 0, 0]	NULL	"q+(-2\\zeta_{12}+\\zeta_{12}^{3})q^{3}+(-2\\zeta_{12}+2\\zeta_{12}^{3})q^{4}+\\cdots"
"273.2.bw.b"	128	2.1799159751809545	NULL	[]	[]	[0, -4, 0, -16]	NULL	NULL
"273.2.by.a"	4	2.1799159751809545	"4.0.144.1"	[]	[]	[2, 0, -2, -2]	NULL	"q+(1-\\zeta_{12}^{2}+\\zeta_{12}^{3})q^{2}+(\\zeta_{12}-\\zeta_{12}^{3})q^{3}+\\cdots"
"273.2.by.b"	4	2.1799159751809545	"4.0.144.1"	[]	[]	[2, 0, 2, 0]	NULL	"q+(1-\\zeta_{12}^{2}+\\zeta_{12}^{3})q^{2}+(-\\zeta_{12}+\\zeta_{12}^{3})q^{3}+\\cdots"
"273.2.by.c"	32	2.1799159751809545	NULL	[]	[]	[-2, 0, -2, -2]	NULL	NULL
"273.2.by.d"	32	2.1799159751809545	NULL	[]	[]	[-2, 0, 2, 2]	NULL	NULL
"273.2.bz.a"	36	2.1799159751809545	NULL	[]	[]	[0, 0, 0, -6]	NULL	NULL
"273.2.bz.b"	36	2.1799159751809545	NULL	[]	[]	[0, 0, 0, 4]	NULL	NULL
"273.2.cc.a"	112	2.1799159751809545	NULL	[]	[]	[0, 0, 0, 0]	NULL	NULL
"273.2.cd.a"	4	2.1799159751809545	"4.0.144.1"	[-3]	[]	[0, 0, 0, 0]	NULL	"q+(-\\zeta_{12}-\\zeta_{12}^{3})q^{3}+(2\\zeta_{12}-2\\zeta_{12}^{3})q^{4}+\\cdots"
"273.2.cd.b"	4	2.1799159751809545	"4.0.144.1"	[-3]	[]	[0, 0, 0, 2]	NULL	"q+(\\zeta_{12}+\\zeta_{12}^{3})q^{3}+(2\\zeta_{12}-2\\zeta_{12}^{3})q^{4}+\\cdots"
"273.2.cd.c"	8	2.1799159751809545	"8.0.5308416.1"	[]	[]	[0, 4, -4, 0]	NULL	"q+\\zeta_{24}^{7}q^{2}+(1-\\zeta_{24}^{2}+\\zeta_{24}^{3}-\\zeta_{24}^{4}+\\cdots)q^{3}+\\cdots"
"273.2.cd.d"	8	2.1799159751809545	"8.0.5308416.1"	[]	[]	[0, 4, 4, 0]	NULL	"q+\\zeta_{24}^{7}q^{2}+(1+\\zeta_{24}^{2}-\\zeta_{24}^{4}+\\zeta_{24}^{5}+\\cdots)q^{3}+\\cdots"
"273.2.cd.e"	112	2.1799159751809545	NULL	[]	[]	[0, -12, 0, -4]	NULL	NULL
"273.2.cg.a"	36	2.1799159751809545	NULL	[]	[]	[0, 0, 0, 4]	NULL	NULL
"273.2.cg.b"	40	2.1799159751809545	NULL	[]	[]	[0, 0, 0, -8]	NULL	NULL
"273.3.b.a"	48	7.438711217036105	NULL	[]	[]	[0, 4, 0, 0]	NULL	NULL
"273.3.d.a"	36	7.438711217036105	NULL	[]	[]	[0, 0, 0, 0]	NULL	NULL
"273.3.f.a"	32	7.438711217036105	NULL	[]	[]	[-4, 0, 0, 4]	NULL	NULL
"273.3.h.a"	56	7.438711217036105	NULL	[]	[]	[0, 0, 0, 0]	NULL	NULL
"273.3.m.a"	56	7.438711217036105	NULL	[]	[]	[-8, 0, 40, 0]	NULL	NULL
"273.3.o.a"	144	7.438711217036105	NULL	[]	[]	[0, 0, 0, 8]	NULL	NULL
"273.3.q.a"	36	7.438711217036105	NULL	[]	[]	[0, -54, 0, -9]	NULL	NULL
"273.3.q.b"	38	7.438711217036105	NULL	[]	[]	[0, 57, 0, 25]	NULL	NULL
"273.3.s.a"	2	7.438711217036105	"2.0.3.1"	[-3]	[]	[0, 3, 0, 2]	NULL	"q+(3-3\\zeta_{6})q^{3}+4q^{4}+(5-8\\zeta_{6})q^{7}+\\cdots"
"273.3.s.b"	140	7.438711217036105	NULL	[]	[]	[0, -2, 0, 0]	NULL	NULL
"273.3.v.a"	2	7.438711217036105	"2.0.3.1"	[]	[]	[-1, -3, 0, -7]	NULL	"q-\\zeta_{6}q^{2}+(-2+\\zeta_{6})q^{3}+(3-3\\zeta_{6})q^{4}+\\cdots"
"273.3.v.b"	2	7.438711217036105	"2.0.3.1"	[]	[]	[-1, 3, 0, -7]	NULL	"q-\\zeta_{6}q^{2}+(2-\\zeta_{6})q^{3}+(3-3\\zeta_{6})q^{4}+\\cdots"
"273.3.v.c"	36	7.438711217036105	NULL	[]	[]	[1, -54, 0, -8]	NULL	NULL
"273.3.v.d"	36	7.438711217036105	NULL	[]	[]	[1, 54, 0, 25]	NULL	NULL
"273.3.w.a"	2	7.438711217036105	"2.0.3.1"	[-3]	[]	[0, -3, 0, -13]	NULL	"q-3\\zeta_{6}q^{3}+4\\zeta_{6}q^{4}+(-5-3\\zeta_{6})q^{7}+\\cdots"
"273.3.w.b"	2	7.438711217036105	"2.0.3.1"	[-3]	[]	[0, -3, 0, 13]	NULL	"q-3\\zeta_{6}q^{3}+4\\zeta_{6}q^{4}+(5+3\\zeta_{6})q^{7}+\\cdots"
"273.3.w.c"	16	7.438711217036105	NULL	[]	[]	[0, 0, 0, 0]	NULL	"q+(-\\beta _{1}-\\beta _{10})q^{2}+(\\beta _{4}-\\beta _{9})q^{3}+(\\beta _{4}+\\cdots)q^{4}+\\cdots"
"273.3.w.d"	120	7.438711217036105	NULL	[]	[]	[0, 4, 0, 0]	NULL	NULL
"273.3.x.a"	2	7.438711217036105	"2.0.3.1"	[-3]	[]	[0, 6, 0, -11]	NULL	"q+3q^{3}+(4-4\\zeta_{6})q^{4}+(-3-5\\zeta_{6})q^{7}+\\cdots"
"273.3.x.b"	140	7.438711217036105	NULL	[]	[]	[0, -8, 0, 10]	NULL	NULL
"273.3.z.a"	2	7.438711217036105	"2.0.3.1"	[]	[]	[-1, 0, 12, -7]	NULL	"q+(-1+\\zeta_{6})q^{2}+(-1+2\\zeta_{6})q^{3}+3\\zeta_{6}q^{4}+\\cdots"
"273.3.z.b"	34	7.438711217036105	NULL	[]	[]	[1, 0, -12, 0]	NULL	NULL
"273.3.z.c"	38	7.438711217036105	NULL	[]	[]	[0, 0, 0, -6]	NULL	NULL
"273.3.bb.a"	4	7.438711217036105	"4.0.24336.3"	[]	[]	[2, 6, -6, -26]	NULL	"q+(1-\\beta _{2})q^{2}+(2-\\beta _{2})q^{3}+3\\beta _{2}q^{4}+\\cdots"
"273.3.bb.b"	28	7.438711217036105	NULL	[]	[]	[0, 42, 24, 24]	NULL	NULL
"273.3.bb.c"	32	7.438711217036105	NULL	[]	[]	[2, -48, -6, -2]	NULL	NULL
"273.3.bc.a"	112	7.438711217036105	NULL	[]	[]	[0, 0, 0, 0]	NULL	NULL
"273.3.be.a"	112	7.438711217036105	NULL	[]	[]	[0, 0, 0, 0]	NULL	NULL
"273.3.bg.a"	36	7.438711217036105	NULL	[]	[]	[0, 0, 0, -21]	NULL	NULL
"273.3.bg.b"	38	7.438711217036105	NULL	[]	[]	[0, 0, 0, 26]	NULL	NULL
"273.3.bi.a"	36	7.438711217036105	NULL	[]	[]	[0, -54, 0, 0]	NULL	NULL
"273.3.bi.b"	40	7.438711217036105	NULL	[]	[]	[0, 60, 0, 0]	NULL	NULL
"273.3.bk.a"	128	7.438711217036105	NULL	[]	[]	[0, 0, 0, -8]	NULL	NULL
"273.3.bm.a"	2	7.438711217036105	"2.0.3.1"	[-3]	[]	[0, -6, 0, 11]	NULL	"q-3q^{3}-4\\zeta_{6}q^{4}+(8-5\\zeta_{6})q^{7}+9q^{9}+\\cdots"
"273.3.bm.b"	140	7.438711217036105	NULL	[]	[]	[0, 4, 0, -30]	NULL	NULL
"273.3.bo.a"	2	7.438711217036105	"2.0.3.1"	[]	[]	[0, -3, 4, -14]	NULL	"q+(-1-\\zeta_{6})q^{3}-4\\zeta_{6}q^{4}+2q^{5}-7q^{7}+\\cdots"
"273.3.bo.b"	2	7.438711217036105	"2.0.3.1"	[]	[]	[0, 3, -4, -7]	NULL	"q+(1+\\zeta_{6})q^{3}-4\\zeta_{6}q^{4}-2q^{5}+(-7+\\cdots)q^{7}+\\cdots"
"273.3.bo.c"	36	7.438711217036105	NULL	[]	[]	[0, -54, -4, 10]	NULL	NULL
"273.3.bo.d"	36	7.438711217036105	NULL	[]	[]	[0, 54, 4, -10]	NULL	NULL
"273.3.bp.a"	2	7.438711217036105	"2.0.3.1"	[-3]	[]	[0, -3, 0, 2]	NULL	"q-3\\zeta_{6}q^{3}-4q^{4}+(-3+8\\zeta_{6})q^{7}+\\cdots"
"273.3.bp.b"	140	7.438711217036105	NULL	[]	[]	[0, 4, 0, 8]	NULL	NULL
"273.3.bq.a"	2	7.438711217036105	"2.0.3.1"	[]	[]	[2, 3, 12, -7]	NULL	"q+q^{2}+(1+\\zeta_{6})q^{3}-3q^{4}+(4+4\\zeta_{6})q^{5}+\\cdots"
"273.3.bq.b"	34	7.438711217036105	NULL	[]	[]	[-2, 51, -12, 18]	NULL	NULL
"273.3.bq.c"	38	7.438711217036105	NULL	[]	[]	[0, -57, 0, -3]	NULL	NULL
"273.3.bs.a"	4	7.438711217036105	"4.0.144.1"	[-3]	[]	[0, 0, 0, 4]	NULL	"q+3\\zeta_{12}q^{3}-4\\zeta_{12}^{3}q^{4}+(5-8\\zeta_{12}^{2}+\\cdots)q^{7}+\\cdots"
"273.3.bs.b"	280	7.438711217036105	NULL	[]	[]	[0, -6, 0, 8]	NULL	NULL
"273.3.bu.a"	72	7.438711217036105	NULL	[]	[]	[0, 0, 0, 2]	NULL	NULL
"273.3.bu.b"	76	7.438711217036105	NULL	[]	[]	[0, 0, 0, 22]	NULL	NULL
"273.3.bx.a"	72	7.438711217036105	NULL	[]	[]	[0, 0, 0, 20]	NULL	NULL
"273.3.bx.b"	76	7.438711217036105	NULL	[]	[]	[0, 0, 0, -28]	NULL	NULL
"273.3.ca.a"	4	7.438711217036105	"4.0.144.1"	[-3]	[]	[0, 0, 0, 0]	NULL	"q+(3\\zeta_{12}-3\\zeta_{12}^{3})q^{3}+4\\zeta_{12}q^{4}+(8\\zeta_{12}+\\cdots)q^{7}+\\cdots"
"273.3.ca.b"	4	7.438711217036105	"4.0.144.1"	[-3]	[]	[0, 0, 0, 22]	NULL	"q+(-3\\zeta_{12}+3\\zeta_{12}^{3})q^{3}+4\\zeta_{12}q^{4}+\\cdots"
"273.3.ca.c"	272	7.438711217036105	NULL	[]	[]	[0, 0, 0, -52]	NULL	NULL
"273.3.cb.a"	4	7.438711217036105	"4.0.144.1"	[-3]	[]	[0, 0, 0, -26]	NULL	"q-3\\zeta_{12}q^{3}-4\\zeta_{12}q^{4}+(-8+3\\zeta_{12}^{2}+\\cdots)q^{7}+\\cdots"
"273.3.cb.b"	4	7.438711217036105	"4.0.144.1"	[-3]	[]	[0, 0, 0, 0]	NULL	"q+3\\zeta_{12}q^{3}-4\\zeta_{12}q^{4}+(3\\zeta_{12}+5\\zeta_{12}^{3})q^{7}+\\cdots"
"273.3.cb.c"	272	7.438711217036105	NULL	[]	[]	[0, -12, 0, 20]	NULL	NULL
"273.3.ce.a"	56	7.438711217036105	NULL	[]	[]	[4, 0, -32, 0]	NULL	NULL
"273.3.ce.b"	56	7.438711217036105	NULL	[]	[]	[4, 0, -8, 0]	NULL	NULL
"273.3.cf.a"	76	7.438711217036105	NULL	[]	[]	[0, 0, 0, -16]	NULL	NULL
"273.3.cf.b"	76	7.438711217036105	NULL	[]	[]	[0, 0, 0, 10]	NULL	NULL
"273.3.ch.a"	4	7.438711217036105	"4.0.144.1"	[-3]	[]	[0, 0, 0, 0]	NULL	"q+3\\zeta_{12}^{3}q^{3}+(-4\\zeta_{12}+4\\zeta_{12}^{3})q^{4}+\\cdots"
"273.3.ch.b"	280	7.438711217036105	NULL	[]	[]	[0, 0, 0, -20]	NULL	NULL
"273.4.a.a"	1	16.10752143156719	"1.1.1.1"	[]	[]	[-4, -3, 0, -7]	1	"q-4q^{2}-3q^{3}+8q^{4}+12q^{6}-7q^{7}+\\cdots"
"273.4.a.b"	1	16.10752143156719	"1.1.1.1"	[]	[]	[-1, 3, -5, 7]	-1	"q-q^{2}+3q^{3}-7q^{4}-5q^{5}-3q^{6}+\\cdots"
"273.4.a.c"	1	16.10752143156719	"1.1.1.1"	[]	[]	[-1, 3, 9, -7]	-1	"q-q^{2}+3q^{3}-7q^{4}+9q^{5}-3q^{6}+\\cdots"
"273.4.a.d"	2	16.10752143156719	"2.2.865.1"	[]	[]	[2, -6, 5, -14]	1	"q+q^{2}-3q^{3}-7q^{4}+(3-\\beta )q^{5}-3q^{6}+\\cdots"
"273.4.a.e"	4	16.10752143156719	"4.4.6295500.1"	[]	[]	[-3, -12, -3, 28]	-1	"q+(-1+\\beta _{1})q^{2}-3q^{3}+(3-2\\beta _{1}+\\beta _{2}+\\cdots)q^{4}+\\cdots"
"273.4.a.f"	4	16.10752143156719	"4.4.1038472.1"	[]	[]	[-3, 12, -24, -28]	-1	"q+(-1+\\beta _{1})q^{2}+3q^{3}+(4-\\beta _{1}+\\beta _{2}+\\cdots)q^{4}+\\cdots"
"273.4.a.g"	5	16.10752143156719	NULL	[]	[]	[5, -15, 15, 35]	1	"q+(1-\\beta _{1})q^{2}-3q^{3}+(7-\\beta _{1}+\\beta _{3}+\\cdots)q^{4}+\\cdots"
"273.4.a.h"	6	16.10752143156719	NULL	[]	[]	[-6, -18, 3, -42]	-1	"q+(-1+\\beta _{1})q^{2}-3q^{3}+(6-\\beta _{1}+\\beta _{2}+\\cdots)q^{4}+\\cdots"
"273.4.a.i"	6	16.10752143156719	NULL	[]	[]	[0, 18, 3, -42]	1	"q+\\beta _{1}q^{2}+3q^{3}+(7+\\beta _{1}+\\beta _{2})q^{4}+\\cdots"
"273.4.a.j"	6	16.10752143156719	NULL	[]	[]	[7, 18, -3, 42]	1	"q+(1+\\beta _{1})q^{2}+3q^{3}+(4+2\\beta _{1}+\\beta _{2}+\\cdots)q^{4}+\\cdots"
"273.4.c.a"	20	16.10752143156719	NULL	[]	[]	[0, -60, 0, 0]	NULL	"q+\\beta _{1}q^{2}-3q^{3}+(-3+\\beta _{2})q^{4}-\\beta _{13}q^{5}+\\cdots"
"273.4.c.b"	20	16.10752143156719	NULL	[]	[]	[0, 60, 0, 0]	NULL	"q+\\beta _{1}q^{2}+3q^{3}+(-4+\\beta _{2})q^{4}+(-\\beta _{1}+\\cdots)q^{5}+\\cdots"
"273.4.e.a"	96	16.10752143156719	NULL	[]	[]	[0, 0, 0, -12]	NULL	NULL
"273.4.i.a"	2	16.10752143156719	"2.0.3.1"	[]	[]	[5, -3, 3, 7]	NULL	"q+5\\zeta_{6}q^{2}+(-3+3\\zeta_{6})q^{3}+(-17+\\cdots)q^{4}+\\cdots"
"273.4.i.b"	6	16.10752143156719	"6.0.432216027.2"	[]	[]	[0, -9, 27, 38]	NULL	"q+\\beta _{1}q^{2}+(-3+3\\beta _{3})q^{3}+(1-\\beta _{1}+\\cdots)q^{4}+\\cdots"
"273.4.i.c"	14	16.10752143156719	NULL	[]	[]	[-8, -21, -21, -34]	NULL	"q+(-1+\\beta _{1}+\\beta _{2}+\\beta _{4})q^{2}-3\\beta _{4}q^{3}+\\cdots"
"273.4.i.d"	22	16.10752143156719	NULL	[]	[]	[1, 33, -17, 11]	NULL	NULL
"273.4.i.e"	26	16.10752143156719	NULL	[]	[]	[-3, -39, -15, -13]	NULL	NULL
"273.4.i.f"	26	16.10752143156719	NULL	[]	[]	[1, 39, 39, -13]	NULL	NULL
"273.4.k.a"	2	16.10752143156719	"2.0.3.1"	[]	[]	[-1, -3, -42, 7]	NULL	"q+(-1+\\zeta_{6})q^{2}+(-3+3\\zeta_{6})q^{3}+7\\zeta_{6}q^{4}+\\cdots"
"273.4.k.b"	2	16.10752143156719	"2.0.3.1"	[]	[]	[3, -3, -36, -7]	NULL	"q+(3-3\\zeta_{6})q^{2}+(-3+3\\zeta_{6})q^{3}-\\zeta_{6}q^{4}+\\cdots"
"273.4.k.c"	20	16.10752143156719	NULL	[]	[]	[-3, -30, 56, -70]	NULL	"q+(\\beta _{1}+\\beta _{2})q^{2}+(-3+3\\beta _{6})q^{3}+(\\beta _{5}+\\cdots)q^{4}+\\cdots"
"273.4.k.d"	20	16.10752143156719	NULL	[]	[]	[5, -30, 30, 70]	NULL	"q+(-1+\\beta _{1}-\\beta _{4}+\\beta _{5})q^{2}-3\\beta _{5}q^{3}+\\cdots"
"273.4.k.e"	22	16.10752143156719	NULL	[]	[]	[0, 33, 36, 77]	NULL	NULL
"273.4.k.f"	22	16.10752143156719	NULL	[]	[]	[4, 33, -12, -77]	NULL	NULL
"273.4.bd.a"	40	16.10752143156719	NULL	[]	[]	[0, -60, 0, 0]	NULL	NULL
"273.4.bd.b"	40	16.10752143156719	NULL	[]	[]	[0, 60, 0, 0]	NULL	NULL
"273.5.b.a"	96	28.2199999218895	NULL	[]	[]	[0, 4, 0, 0]	NULL	NULL
"273.5.d.a"	76	28.2199999218895	NULL	[]	[]	[0, 0, 0, 0]	NULL	NULL
"273.5.f.a"	64	28.2199999218895	NULL	[]	[]	[12, 0, 0, 20]	NULL	NULL
"273.6.a.a"	1	43.78478280894371	"1.1.1.1"	[]	[]	[-2, 9, -46, -49]	-1	"q-2q^{2}+9q^{3}-28q^{4}-46q^{5}-18q^{6}+\\cdots"
"273.6.a.b"	6	43.78478280894371	NULL	[]	[]	[-15, 54, 15, -294]	1	"q+(-3+\\beta _{1})q^{2}+9q^{3}+(14-3\\beta _{1}+\\cdots)q^{4}+\\cdots"
"273.6.a.c"	6	43.78478280894371	NULL	[]	[]	[-8, 54, -15, 294]	1	"q+(-1-\\beta _{1})q^{2}+9q^{3}+(2+2\\beta _{1}+\\beta _{3}+\\cdots)q^{4}+\\cdots"
"273.6.a.d"	6	43.78478280894371	NULL	[]	[]	[-5, 54, 112, -294]	-1	"q+(-1+\\beta _{1})q^{2}+9q^{3}+(18+\\beta _{1}+\\beta _{2}+\\cdots)q^{4}+\\cdots"
"273.6.a.e"	6	43.78478280894371	NULL	[]	[]	[3, -54, 15, -294]	-1	"q+(1-\\beta _{1})q^{2}-9q^{3}+(22+\\beta _{4})q^{4}+\\cdots"
"273.6.a.f"	7	43.78478280894371	NULL	[]	[]	[2, -63, -66, 343]	1	"q+\\beta _{1}q^{2}-9q^{3}+(19-2\\beta _{1}+\\beta _{2})q^{4}+\\cdots"
"273.6.a.g"	8	43.78478280894371	NULL	[]	[]	[18, -72, -15, 392]	-1	"q+(2+\\beta _{1})q^{2}-9q^{3}+(12+3\\beta _{1}+\\beta _{2}+\\cdots)q^{4}+\\cdots"
"273.6.a.h"	9	43.78478280894371	NULL	[]	[]	[-5, -81, -34, -441]	1	"q+(-1+\\beta _{1})q^{2}-9q^{3}+(19+\\beta _{2})q^{4}+\\cdots"
"273.6.a.i"	11	43.78478280894371	NULL	[]	[]	[8, 99, 34, 539]	-1	"q+(1-\\beta _{1})q^{2}+9q^{3}+(24+\\beta _{2})q^{4}+\\cdots"
"273.6.c.a"	36	43.78478280894371	NULL	[]	[]	[0, -324, 0, 0]	NULL	NULL
"273.6.c.b"	36	43.78478280894371	NULL	[]	[]	[0, 324, 0, 0]	NULL	NULL
"273.7.f.a"	96	62.80476482821932	NULL	[]	[]	[-20, 0, 0, -696]	NULL	NULL
"273.8.a.a"	7	85.28111195716524	NULL	[]	[]	[-5, 189, -330, 2401]	-1	"q+(-1+\\beta _{1})q^{2}+3^{3}q^{3}+(22+\\beta _{4}+\\cdots)q^{4}+\\cdots"
"273.8.a.b"	9	85.28111195716524	NULL	[]	[]	[4, -243, 330, -3087]	1	"q+\\beta _{1}q^{2}-3^{3}q^{3}+(40-\\beta _{1}+\\beta _{3})q^{4}+\\cdots"
"273.8.a.c"	10	85.28111195716524	NULL	[]	[]	[-7, -270, 123, 3430]	-1	"q+(-1+\\beta _{1})q^{2}-3^{3}q^{3}+(52+\\beta _{2}+\\cdots)q^{4}+\\cdots"
"273.8.a.d"	11	85.28111195716524	NULL	[]	[]	[-10, 297, -170, -3773]	-1	"q+(-1+\\beta _{1})q^{2}+3^{3}q^{3}+(69-2\\beta _{1}+\\cdots)q^{4}+\\cdots"
"273.8.a.e"	11	85.28111195716524	NULL	[]	[]	[25, -297, 170, 3773]	1	"q+(2+\\beta _{1})q^{2}-3^{3}q^{3}+(58+4\\beta _{1}+\\beta _{2}+\\cdots)q^{4}+\\cdots"
"273.8.a.f"	12	85.28111195716524	NULL	[]	[]	[-12, -324, -123, -4116]	-1	"q+(-1-\\beta _{1})q^{2}-3^{3}q^{3}+(62+2\\beta _{1}+\\cdots)q^{4}+\\cdots"
"273.8.a.g"	12	85.28111195716524	NULL	[]	[]	[6, 324, -123, -4116]	1	"q+(1-\\beta _{1})q^{2}+3^{3}q^{3}+(85+\\beta _{2})q^{4}+\\cdots"
"273.8.a.h"	12	85.28111195716524	NULL	[]	[]	[27, 324, 123, 4116]	1	"q+(2+\\beta _{1})q^{2}+3^{3}q^{3}+(76+3\\beta _{1}+\\beta _{2}+\\cdots)q^{4}+\\cdots"
"273.8.c.a"	48	85.28111195716524	NULL	[]	[]	[0, -1296, 0, 0]	NULL	NULL
"273.8.c.b"	48	85.28111195716524	NULL	[]	[]	[0, 1296, 0, 0]	NULL	NULL
"273.10.a.a"	12	140.60478327273736	NULL	[]	[]	[-24, 972, 615, 28812]	1	"q+(-2-\\beta _{1})q^{2}+3^{4}q^{3}+(240+6\\beta _{1}+\\cdots)q^{4}+\\cdots"
"273.10.a.b"	12	140.60478327273736	NULL	[]	[]	[-9, -972, -615, -28812]	-1	"q+(-1+\\beta _{1})q^{2}-3^{4}q^{3}+(186+2\\beta _{1}+\\cdots)q^{4}+\\cdots"
"273.10.a.c"	12	140.60478327273736	NULL	[]	[]	[-3, 972, -615, -28812]	1	"q-\\beta _{1}q^{2}+3^{4}q^{3}+(115-\\beta _{1}+\\beta _{2}+\\cdots)q^{4}+\\cdots"
"273.10.a.d"	13	140.60478327273736	NULL	[]	[]	[-62, -1053, -1219, 31213]	1	"q+(-5+\\beta _{1})q^{2}-3^{4}q^{3}+(219-5\\beta _{1}+\\cdots)q^{4}+\\cdots"
"273.10.a.e"	13	140.60478327273736	NULL	[]	[]	[29, 1053, 1219, -31213]	-1	"q+(2+\\beta _{1})q^{2}+3^{4}q^{3}+(255+\\beta _{1}+\\beta _{2}+\\cdots)q^{4}+\\cdots"
"273.10.a.f"	14	140.60478327273736	NULL	[]	[]	[2, -1134, 615, 33614]	-1	"q+\\beta _{1}q^{2}-3^{4}q^{3}+(304-\\beta _{1}+\\beta _{2}+\\cdots)q^{4}+\\cdots"
"273.10.a.g"	15	140.60478327273736	NULL	[]	[]	[-41, -1215, -1281, -36015]	1	"q+(-3+\\beta _{1})q^{2}-3^{4}q^{3}+(314-3\\beta _{1}+\\cdots)q^{4}+\\cdots"
"273.10.a.h"	17	140.60478327273736	NULL	[]	[]	[40, 1377, 1281, 40817]	-1	"q+(2+\\beta _{1})q^{2}+3^{4}q^{3}+(295+3\\beta _{1}+\\cdots)q^{4}+\\cdots"
"273.12.a.a"	13	209.75768829276777	NULL	[]	[]	[-109, 3159, -6095, 218491]	-1	"q+(-8-\\beta _{1})q^{2}+3^{5}q^{3}+(567+20\\beta _{1}+\\cdots)q^{4}+\\cdots"
"273.12.a.b"	15	209.75768829276777	NULL	[]	[]	[100, -3645, 6095, -252105]	1	"q+(7-\\beta _{1})q^{2}-3^{5}q^{3}+(1174-10\\beta _{1}+\\cdots)q^{4}+\\cdots"
"273.12.a.c"	16	209.75768829276777	NULL	[]	[]	[-63, -3888, -3168, 268912]	-1	"q+(-4+\\beta _{1})q^{2}-3^{5}q^{3}+(1298-4\\beta _{1}+\\cdots)q^{4}+\\cdots"
"273.12.a.d"	17	209.75768829276777	NULL	[]	[]	[-10, 4131, -6405, -285719]	-1	"q+(-1+\\beta _{1})q^{2}+3^{5}q^{3}+(1246-\\beta _{1}+\\cdots)q^{4}+\\cdots"
"273.12.a.e"	17	209.75768829276777	NULL	[]	[]	[65, -4131, 6405, 285719]	1	"q+(4-\\beta _{1})q^{2}-3^{5}q^{3}+(1071-4\\beta _{1}+\\cdots)q^{4}+\\cdots"
"273.12.a.f"	18	209.75768829276777	NULL	[]	[]	[19, 4374, -3168, 302526]	1	"q+(1+\\beta _{1})q^{2}+3^{5}q^{3}+(1354-\\beta _{1}+\\cdots)q^{4}+\\cdots"
"273.12.a.g"	18	209.75768829276777	NULL	[]	[]	[36, -4374, 3168, -302526]	-1	"q+(2-\\beta _{1})q^{2}-3^{5}q^{3}+(1060-3\\beta _{1}+\\cdots)q^{4}+\\cdots"
"273.12.a.h"	18	209.75768829276777	NULL	[]	[]	[54, 4374, 3168, -302526]	1	"q+(3-\\beta _{1})q^{2}+3^{5}q^{3}+(1147-2\\beta _{1}+\\cdots)q^{4}+\\cdots"


# 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.