# Classical modular forms downloaded from the LMFDB on 17 June 2026.
# Search link: https://www.lmfdb.org/ModularForm/GL2/Q/holomorphic/91/
# Query "{'level': 91}" returned 234 forms, sorted by analytic conductor.

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



"91.2.a.a"	1	0.7266386583936515	"1.1.1.1"	[]	[-2, 0, -3, -1]	1	"q-2q^{2}+2q^{4}-3q^{5}-q^{7}-3q^{9}+\\cdots"
"91.2.a.b"	1	0.7266386583936515	"1.1.1.1"	[]	[0, -2, -3, 1]	1	"q-2q^{3}-2q^{4}-3q^{5}+q^{7}+q^{9}+4q^{12}+\\cdots"
"91.2.a.c"	2	0.7266386583936515	"2.2.8.1"	[]	[0, 0, 6, 2]	-1	"q+\\beta q^{2}-\\beta q^{3}+(3+\\beta )q^{5}-2q^{6}+q^{7}+\\cdots"
"91.2.a.d"	3	0.7266386583936515	"3.3.316.1"	[]	[1, -2, 2, -3]	-1	"q+\\beta _{1}q^{2}+(-1+\\beta _{1}-\\beta _{2})q^{3}+(1+\\beta _{2})q^{4}+\\cdots"
"91.2.c.a"	6	0.7266386583936515	"6.0.350464.1"	[]	[0, 0, 0, 0]	NULL	"q+(-\\beta _{3}+\\beta _{4})q^{2}+\\beta _{1}q^{3}+(-1-\\beta _{1}+\\cdots)q^{4}+\\cdots"
"91.2.e.a"	2	0.7266386583936515	"2.0.3.1"	[]	[-1, 0, 0, 1]	NULL	"q-\\zeta_{6}q^{2}+(1-\\zeta_{6})q^{4}+(2-3\\zeta_{6})q^{7}+\\cdots"
"91.2.e.b"	4	0.7266386583936515	"4.0.225.1"	[]	[3, 0, 0, -8]	NULL	"q+(1+\\beta _{1}+\\beta _{3})q^{2}+(-2\\beta _{1}-2\\beta _{2}+\\cdots)q^{3}+\\cdots"
"91.2.e.c"	10	0.7266386583936515	NULL	[]	[-4, 0, -2, 1]	NULL	"q+(\\beta _{1}-\\beta _{7})q^{2}+(-\\beta _{4}+\\beta _{9})q^{3}+(-2+\\cdots)q^{4}+\\cdots"
"91.2.f.a"	4	0.7266386583936515	"4.0.225.1"	[]	[-3, 3, 6, -2]	NULL	"q+(-1-\\beta _{1}-\\beta _{3})q^{2}+(1+\\beta _{1}+\\beta _{3})q^{3}+\\cdots"
"91.2.f.b"	4	0.7266386583936515	"4.0.144.1"	[]	[0, -2, 0, -2]	NULL	"q-\\beta_{2} q^{2}+(-\\beta_{2}-\\beta_1)q^{3}+(\\beta_1-1)q^{4}+\\cdots"
"91.2.f.c"	8	0.7266386583936515	"8.0.59066497296.1"	[]	[1, -1, -14, 4]	NULL	"q+\\beta _{1}q^{2}-\\beta _{5}q^{3}+(-1+\\beta _{1}+\\beta _{2}+\\cdots)q^{4}+\\cdots"
"91.2.g.a"	2	0.7266386583936515	"2.0.3.1"	[]	[-1, -6, -3, -5]	NULL	"q-\\zeta_{6}q^{2}-3q^{3}+(1-\\zeta_{6})q^{4}+(-3+\\cdots)q^{5}+\\cdots"
"91.2.g.b"	12	0.7266386583936515	NULL	[]	[2, -2, 1, 9]	NULL	"q+(-\\beta _{1}-\\beta _{5}+\\beta _{11})q^{2}+(\\beta _{3}-\\beta _{11})q^{3}+\\cdots"
"91.2.h.a"	2	0.7266386583936515	"2.0.3.1"	[]	[2, 3, -3, 4]	NULL	"q+q^{2}+3\\zeta_{6}q^{3}-q^{4}-3\\zeta_{6}q^{5}+3\\zeta_{6}q^{6}+\\cdots"
"91.2.h.b"	12	0.7266386583936515	NULL	[]	[-4, 1, 1, -3]	NULL	"q+(\\beta _{3}+\\beta _{5}-\\beta _{11})q^{2}+\\beta _{11}q^{3}+(1+\\cdots)q^{4}+\\cdots"
"91.2.i.a"	12	0.7266386583936515	NULL	[]	[-4, 0, 0, -8]	NULL	"q-\\beta _{8}q^{2}+\\beta _{10}q^{3}+(-\\beta _{4}+\\beta _{6}+\\beta _{7}+\\cdots)q^{4}+\\cdots"
"91.2.k.a"	2	0.7266386583936515	"2.0.3.1"	[]	[0, 1, 3, -4]	NULL	"q+(1-2\\zeta_{6})q^{2}+\\zeta_{6}q^{3}-q^{4}+(2-\\zeta_{6})q^{5}+\\cdots"
"91.2.k.b"	12	0.7266386583936515	"12.0.2346760387617129.1"	[]	[0, -3, -3, -3]	NULL	"q+\\beta _{9}q^{2}+(\\beta _{1}+\\beta _{4}+\\beta _{6})q^{3}+(-1+\\cdots)q^{4}+\\cdots"
"91.2.q.a"	12	0.7266386583936515	"12.0.58891012706304.1"	[]	[0, 0, 0, 0]	NULL	"q+(-\\beta _{1}-\\beta _{4}-\\beta _{6}+\\beta _{10})q^{2}+(-\\beta _{2}+\\cdots)q^{3}+\\cdots"
"91.2.r.a"	16	0.7266386583936515	NULL	[]	[0, -4, 0, 0]	NULL	"q+\\beta _{11}q^{2}+(-1+\\beta _{3}+\\beta _{6})q^{3}+(1+\\cdots)q^{4}+\\cdots"
"91.2.u.a"	2	0.7266386583936515	"2.0.3.1"	[]	[-3, -2, -3, -5]	NULL	"q+(-2+\\zeta_{6})q^{2}-q^{3}+(1-\\zeta_{6})q^{4}+\\cdots"
"91.2.u.b"	12	0.7266386583936515	"12.0.2346760387617129.1"	[]	[0, 6, 3, 3]	NULL	"q-\\beta _{10}q^{2}+(1-\\beta _{1}+\\beta _{3}+\\beta _{8})q^{3}+\\cdots"
"91.2.w.a"	28	0.7266386583936515	NULL	[]	[-2, 0, -6, 2]	NULL	NULL
"91.2.ba.a"	28	0.7266386583936515	NULL	[]	[-2, -6, -6, -6]	NULL	NULL
"91.2.bb.a"	32	0.7266386583936515	NULL	[]	[-2, -12, -6, -6]	NULL	NULL
"91.2.bc.a"	32	0.7266386583936515	NULL	[]	[-8, 0, 0, 0]	NULL	NULL
"91.3.b.a"	1	2.479570405678702	"1.1.1.1"	[-91]	[0, 0, -3, 7]	NULL	"q+4q^{4}-3q^{5}+7q^{7}+9q^{9}-13q^{13}+\\cdots"
"91.3.b.b"	1	2.479570405678702	"1.1.1.1"	[-91]	[0, 0, 3, -7]	NULL	"q+4q^{4}+3q^{5}-7q^{7}+9q^{9}+13q^{13}+\\cdots"
"91.3.b.c"	4	2.479570405678702	"4.0.43264.3"	[]	[0, 0, 0, 0]	NULL	"q+\\beta _{2}q^{2}+(\\beta _{1}+\\beta _{3})q^{3}+3q^{4}+(\\beta _{1}+\\cdots)q^{5}+\\cdots"
"91.3.b.d"	6	2.479570405678702	NULL	[]	[0, 0, -8, 7]	NULL	"q+\\beta _{1}q^{2}+\\beta _{1}q^{3}+(-5+\\beta _{2})q^{4}+(-2+\\cdots)q^{5}+\\cdots"
"91.3.b.e"	6	2.479570405678702	NULL	[]	[0, 0, 8, -7]	NULL	"q+\\beta _{1}q^{2}-\\beta _{1}q^{3}+(-5+\\beta _{2})q^{4}+(2+\\cdots)q^{5}+\\cdots"
"91.3.d.a"	16	2.479570405678702	NULL	[]	[2, 0, 0, 2]	NULL	"q-\\beta _{2}q^{2}+\\beta _{1}q^{3}+(2+\\beta _{4})q^{4}+\\beta _{3}q^{5}+\\cdots"
"91.3.j.a"	28	2.479570405678702	NULL	[]	[4, 0, -20, 0]	NULL	NULL
"91.3.l.a"	34	2.479570405678702	NULL	[]	[0, -6, 0, -19]	NULL	NULL
"91.3.m.a"	34	2.479570405678702	NULL	[]	[1, 0, -6, 14]	NULL	NULL
"91.3.n.a"	4	2.479570405678702	"4.0.24336.3"	[]	[-2, 0, 0, -14]	NULL	"q+(-1+\\beta _{2})q^{2}-\\beta _{1}q^{3}+3\\beta _{2}q^{4}+\\cdots"
"91.3.n.b"	28	2.479570405678702	NULL	[]	[0, 0, 0, 12]	NULL	NULL
"91.3.o.a"	32	2.479570405678702	NULL	[]	[-2, 0, -6, -2]	NULL	NULL
"91.3.p.a"	34	2.479570405678702	NULL	[]	[-3, 0, 0, -8]	NULL	NULL
"91.3.s.a"	32	2.479570405678702	NULL	[]	[0, -12, 0, 0]	NULL	NULL
"91.3.t.a"	32	2.479570405678702	NULL	[]	[-6, 0, 0, 18]	NULL	NULL
"91.3.v.a"	34	2.479570405678702	NULL	[]	[-2, 0, -6, -7]	NULL	NULL
"91.3.x.a"	68	2.479570405678702	NULL	[]	[-2, 2, -2, -26]	NULL	NULL
"91.3.y.a"	56	2.479570405678702	NULL	[]	[-4, 0, 20, 0]	NULL	NULL
"91.3.z.a"	64	2.479570405678702	NULL	[]	[-2, -4, -2, -2]	NULL	NULL
"91.3.bd.a"	68	2.479570405678702	NULL	[]	[-2, -4, -2, 6]	NULL	NULL
"91.4.a.a"	3	5.369173810522396	"3.3.1384.1"	[]	[1, 1, -22, -21]	-1	"q+\\beta _{1}q^{2}+(1-\\beta _{1}-\\beta _{2})q^{3}+(-1-\\beta _{1}+\\cdots)q^{4}+\\cdots"
"91.4.a.b"	4	5.369173810522396	"4.4.5364412.1"	[]	[-4, -5, -36, 28]	-1	"q+(-1+\\beta _{1})q^{2}+(-1-\\beta _{1}-\\beta _{2})q^{3}+\\cdots"
"91.4.a.c"	5	5.369173810522396	NULL	[]	[7, -5, 16, -35]	1	"q+(1+\\beta _{4})q^{2}+(-1-\\beta _{3})q^{3}+(10-\\beta _{2}+\\cdots)q^{4}+\\cdots"
"91.4.a.d"	6	5.369173810522396	NULL	[]	[2, 13, 26, 42]	1	"q+\\beta _{1}q^{2}+(2-\\beta _{4})q^{3}+(2+\\beta _{2})q^{4}+\\cdots"
"91.4.c.a"	22	5.369173810522396	NULL	[]	[0, 0, 0, 0]	NULL	NULL
"91.4.e.a"	22	5.369173810522396	NULL	[]	[7, 0, -2, 28]	NULL	NULL
"91.4.e.b"	26	5.369173810522396	NULL	[]	[-5, 0, 14, -20]	NULL	NULL
"91.4.f.a"	2	5.369173810522396	"2.0.3.1"	[]	[5, -2, -38, -7]	NULL	"q+(5-5\\zeta_{6})q^{2}+(-2+2\\zeta_{6})q^{3}-17\\zeta_{6}q^{4}+\\cdots"
"91.4.f.b"	18	5.369173810522396	NULL	[]	[-3, 6, -6, -63]	NULL	"q-\\beta _{1}q^{2}+(1+\\beta _{6}-\\beta _{8}+\\beta _{11})q^{3}+\\cdots"
"91.4.f.c"	20	5.369173810522396	NULL	[]	[-6, -4, 28, 70]	NULL	"q+(-1-\\beta _{1}-\\beta _{4}-\\beta _{5})q^{2}-\\beta _{9}q^{3}+\\cdots"
"91.4.g.a"	52	5.369173810522396	NULL	[]	[1, 10, -2, 1]	NULL	NULL
"91.4.h.a"	52	5.369173810522396	NULL	[]	[-2, -5, -2, -17]	NULL	NULL
"91.4.i.a"	52	5.369173810522396	NULL	[]	[-4, 0, 0, -22]	NULL	NULL
"91.4.k.a"	52	5.369173810522396	NULL	[]	[0, 7, 0, -39]	NULL	NULL
"91.4.q.a"	44	5.369173810522396	NULL	[]	[0, 0, 0, 0]	NULL	NULL
"91.4.r.a"	52	5.369173810522396	NULL	[]	[0, 10, 0, 0]	NULL	NULL
"91.4.u.a"	52	5.369173810522396	NULL	[]	[-3, -14, 0, 15]	NULL	NULL
"91.4.w.a"	104	5.369173810522396	NULL	[]	[-2, 0, -6, 16]	NULL	NULL
"91.4.ba.a"	104	5.369173810522396	NULL	[]	[-2, -6, -6, -56]	NULL	NULL
"91.4.bb.a"	104	5.369173810522396	NULL	[]	[-2, -12, -6, 64]	NULL	NULL
"91.4.bc.a"	104	5.369173810522396	NULL	[]	[-8, 0, 0, -20]	NULL	NULL
"91.5.b.a"	1	9.406666640629833	"1.1.1.1"	[-91]	[0, 0, -41, 49]	NULL	"q+2^{4}q^{4}-41q^{5}+7^{2}q^{7}+3^{4}q^{9}+\\cdots"
"91.5.b.b"	1	9.406666640629833	"1.1.1.1"	[-91]	[0, 0, 41, -49]	NULL	"q+2^{4}q^{4}+41q^{5}-7^{2}q^{7}+3^{4}q^{9}+\\cdots"
"91.5.b.c"	32	9.406666640629833	NULL	[]	[0, 0, 0, 0]	NULL	NULL
"91.5.d.a"	32	9.406666640629833	NULL	[]	[-6, 0, 0, -50]	NULL	NULL
"91.5.j.a"	56	9.406666640629833	NULL	[]	[0, 0, 24, 0]	NULL	NULL
"91.5.l.a"	70	9.406666640629833	NULL	[]	[0, -12, 0, -35]	NULL	NULL
"91.5.m.a"	70	9.406666640629833	NULL	[]	[1, 0, -6, 4]	NULL	NULL
"91.5.n.a"	72	9.406666640629833	NULL	[]	[-2, 0, 0, -28]	NULL	NULL
"91.5.o.a"	64	9.406666640629833	NULL	[]	[6, 0, 54, 50]	NULL	NULL
"91.5.p.a"	70	9.406666640629833	NULL	[]	[-3, 0, 0, -58]	NULL	NULL
"91.5.s.a"	72	9.406666640629833	NULL	[]	[0, -24, 0, 0]	NULL	NULL
"91.5.t.a"	72	9.406666640629833	NULL	[]	[-6, 0, 0, 84]	NULL	NULL
"91.5.v.a"	70	9.406666640629833	NULL	[]	[-2, 6, -6, -83]	NULL	NULL
"91.5.x.a"	140	9.406666640629833	NULL	[]	[-2, 2, -2, -118]	NULL	NULL
"91.5.y.a"	112	9.406666640629833	NULL	[]	[0, 0, -24, 0]	NULL	NULL
"91.5.z.a"	144	9.406666640629833	NULL	[]	[-2, -4, -2, 50]	NULL	NULL
"91.5.bd.a"	140	9.406666640629833	NULL	[]	[-2, -4, -2, -54]	NULL	NULL
"91.6.a.a"	6	14.594927602981238	NULL	[]	[-13, -26, -130, 294]	1	"q+(-2-\\beta _{1})q^{2}+(-4-\\beta _{3})q^{3}+(8+\\cdots)q^{4}+\\cdots"
"91.6.a.b"	7	14.594927602981238	NULL	[]	[-2, 28, -62, -343]	1	"q-\\beta _{1}q^{2}+(4+\\beta _{1}+\\beta _{3})q^{3}+(14+2\\beta _{1}+\\cdots)q^{4}+\\cdots"
"91.6.a.c"	8	14.594927602981238	NULL	[]	[-1, 28, 219, 392]	-1	"q-\\beta _{1}q^{2}+(4-\\beta _{1}-\\beta _{4})q^{3}+(31+\\beta _{2}+\\cdots)q^{4}+\\cdots"
"91.6.a.d"	9	14.594927602981238	NULL	[]	[10, 10, 89, -441]	-1	"q+(1+\\beta _{1})q^{2}+(1+\\beta _{4})q^{3}+(7+2\\beta _{1}+\\cdots)q^{4}+\\cdots"
"91.6.c.a"	34	14.594927602981238	NULL	[]	[0, 0, 0, 0]	NULL	NULL
"91.6.e.a"	38	14.594927602981238	NULL	[]	[13, 0, -40, 317]	NULL	NULL
"91.6.e.b"	42	14.594927602981238	NULL	[]	[-11, 0, -38, -123]	NULL	NULL
"91.6.f.a"	36	14.594927602981238	NULL	[]	[-4, -5, 154, -882]	NULL	NULL
"91.6.f.b"	36	14.594927602981238	NULL	[]	[12, 5, -122, 882]	NULL	NULL
"91.6.g.a"	90	14.594927602981238	NULL	[]	[1, -56, -2, -56]	NULL	NULL
"91.6.h.a"	90	14.594927602981238	NULL	[]	[-2, 28, -2, 217]	NULL	NULL
"91.6.i.a"	92	14.594927602981238	NULL	[]	[-4, 0, 0, -96]	NULL	NULL
"91.6.k.a"	90	14.594927602981238	NULL	[]	[0, -26, 0, 121]	NULL	NULL
"91.6.q.a"	68	14.594927602981238	NULL	[]	[0, 0, 0, 0]	NULL	NULL
"91.6.r.a"	88	14.594927602981238	NULL	[]	[0, -20, 0, 0]	NULL	NULL
"91.6.u.a"	90	14.594927602981238	NULL	[]	[-3, 52, 0, 146]	NULL	NULL
"91.6.w.a"	180	14.594927602981238	NULL	[]	[-2, 0, -6, 90]	NULL	NULL
"91.6.ba.a"	180	14.594927602981238	NULL	[]	[-2, -6, -6, 338]	NULL	NULL
"91.6.bb.a"	176	14.594927602981238	NULL	[]	[-2, -12, -6, -142]	NULL	NULL
"91.6.bc.a"	176	14.594927602981238	NULL	[]	[-8, 0, 0, -208]	NULL	NULL
"91.7.b.a"	1	20.93492160940644	"1.1.1.1"	[-91]	[0, 0, -198, -343]	NULL	"q+2^{6}q^{4}-198q^{5}-7^{3}q^{7}+3^{6}q^{9}+\\cdots"
"91.7.b.b"	1	20.93492160940644	"1.1.1.1"	[-91]	[0, 0, 198, 343]	NULL	"q+2^{6}q^{4}+198q^{5}+7^{3}q^{7}+3^{6}q^{9}+\\cdots"
"91.7.b.c"	52	20.93492160940644	NULL	[]	[0, 0, 0, 0]	NULL	NULL
"91.7.d.a"	48	20.93492160940644	NULL	[]	[10, 0, 0, 552]	NULL	NULL
"91.7.j.a"	84	20.93492160940644	NULL	[]	[-16, 0, -220, 0]	NULL	NULL
"91.7.l.a"	108	20.93492160940644	NULL	[]	[0, -3, 0, 717]	NULL	NULL
"91.7.m.a"	108	20.93492160940644	NULL	[]	[1, 0, -6, -41]	NULL	NULL
"91.7.n.a"	108	20.93492160940644	NULL	[]	[-2, 0, 0, 679]	NULL	NULL
"91.7.o.a"	96	20.93492160940644	NULL	[]	[-10, 0, -336, -552]	NULL	NULL
"91.7.p.a"	108	20.93492160940644	NULL	[]	[-3, 0, 0, -363]	NULL	NULL
"91.7.s.a"	108	20.93492160940644	NULL	[]	[0, -6, 0, 0]	NULL	NULL
"91.7.t.a"	108	20.93492160940644	NULL	[]	[-6, 0, 0, -363]	NULL	NULL
"91.7.v.a"	108	20.93492160940644	NULL	[]	[-2, -3, -6, 319]	NULL	NULL
"91.7.x.a"	216	20.93492160940644	NULL	[]	[-2, 2, -2, 1036]	NULL	NULL
"91.7.y.a"	168	20.93492160940644	NULL	[]	[16, 0, 220, 0]	NULL	NULL
"91.7.z.a"	216	20.93492160940644	NULL	[]	[-2, -4, -2, -1364]	NULL	NULL
"91.7.bd.a"	216	20.93492160940644	NULL	[]	[-2, -4, -2, -404]	NULL	NULL
"91.8.a.a"	1	28.42703731905508	"1.1.1.1"	[]	[22, 21, 140, -343]	1	"q+22q^{2}+21q^{3}+356q^{4}+140q^{5}+\\cdots"
"91.8.a.b"	9	28.42703731905508	NULL	[]	[-5, -26, -181, -3087]	-1	"q+(-1+\\beta _{1})q^{2}+(-3+\\beta _{2})q^{3}+(43+\\cdots)q^{4}+\\cdots"
"91.8.a.c"	10	28.42703731905508	NULL	[]	[-18, -80, -927, 3430]	-1	"q+(-2+\\beta _{1})q^{2}+(-8-\\beta _{1}+\\beta _{3})q^{3}+\\cdots"
"91.8.a.d"	10	28.42703731905508	NULL	[]	[-3, -101, 226, -3430]	1	"q-\\beta _{1}q^{2}+(-10-\\beta _{1}-\\beta _{3})q^{3}+(6^{2}+\\cdots)q^{4}+\\cdots"
"91.8.a.e"	12	28.42703731905508	NULL	[]	[6, 82, 1026, 4116]	1	"q+(1-\\beta _{1})q^{2}+(7+\\beta _{3})q^{3}+(82+\\beta _{2}+\\cdots)q^{4}+\\cdots"
"91.8.c.a"	50	28.42703731905508	NULL	[]	[0, 0, 0, 0]	NULL	NULL
"91.8.e.a"	54	28.42703731905508	NULL	[]	[17, 0, 454, -1827]	NULL	NULL
"91.8.e.b"	58	28.42703731905508	NULL	[]	[-31, 0, 48, 85]	NULL	NULL
"91.8.f.a"	48	28.42703731905508	NULL	[]	[-8, 41, 526, 8232]	NULL	NULL
"91.8.f.b"	48	28.42703731905508	NULL	[]	[24, -41, -1302, -8232]	NULL	NULL
"91.8.g.a"	126	28.42703731905508	NULL	[]	[1, 160, -2, -1816]	NULL	NULL
"91.8.h.a"	126	28.42703731905508	NULL	[]	[-2, -80, -2, 953]	NULL	NULL
"91.8.i.a"	124	28.42703731905508	NULL	[]	[-4, 0, 0, 1056]	NULL	NULL
"91.8.k.a"	126	28.42703731905508	NULL	[]	[0, 82, 0, 2009]	NULL	NULL
"91.8.q.a"	100	28.42703731905508	NULL	[]	[0, 0, 0, 0]	NULL	NULL
"91.8.r.a"	128	28.42703731905508	NULL	[]	[0, 52, 0, 0]	NULL	NULL
"91.8.u.a"	126	28.42703731905508	NULL	[]	[-3, -164, 0, 754]	NULL	NULL
"91.8.w.a"	252	28.42703731905508	NULL	[]	[-2, 0, -6, -1062]	NULL	NULL
"91.8.ba.a"	252	28.42703731905508	NULL	[]	[-2, -6, -6, 2962]	NULL	NULL
"91.8.bb.a"	256	28.42703731905508	NULL	[]	[-2, -12, -6, -398]	NULL	NULL
"91.8.bc.a"	256	28.42703731905508	NULL	[]	[-8, 0, 0, -2576]	NULL	NULL
"91.9.b.a"	1	37.071453515562574	"1.1.1.1"	[-91]	[0, 0, -431, -2401]	NULL	"q+2^{8}q^{4}-431q^{5}-7^{4}q^{7}+3^{8}q^{9}+\\cdots"
"91.9.b.b"	1	37.071453515562574	"1.1.1.1"	[-91]	[0, 0, 431, 2401]	NULL	"q+2^{8}q^{4}+431q^{5}+7^{4}q^{7}+3^{8}q^{9}+\\cdots"
"91.9.b.c"	72	37.071453515562574	NULL	[]	[0, 0, 0, 0]	NULL	NULL
"91.9.d.a"	64	37.071453515562574	NULL	[]	[-6, 0, 0, -2350]	NULL	NULL
"91.9.j.a"	112	37.071453515562574	NULL	[]	[0, 0, -336, 0]	NULL	NULL
"91.9.l.a"	146	37.071453515562574	NULL	[]	[0, 78, 0, 3005]	NULL	NULL
"91.9.m.a"	146	37.071453515562574	NULL	[]	[1, 0, -6, -4046]	NULL	NULL
"91.9.n.a"	144	37.071453515562574	NULL	[]	[-2, 0, 0, -1038]	NULL	NULL
"91.9.o.a"	128	37.071453515562574	NULL	[]	[6, 0, 1674, 2350]	NULL	NULL
"91.9.p.a"	146	37.071453515562574	NULL	[]	[-3, 0, 0, -1268]	NULL	NULL
"91.9.s.a"	144	37.071453515562574	NULL	[]	[0, 156, 0, 0]	NULL	NULL
"91.9.t.a"	144	37.071453515562574	NULL	[]	[-6, 0, 0, -1746]	NULL	NULL
"91.9.v.a"	146	37.071453515562574	NULL	[]	[-2, -84, -6, -2303]	NULL	NULL
"91.9.x.a"	292	37.071453515562574	NULL	[]	[-2, 2, -2, 702]	NULL	NULL
"91.9.y.a"	224	37.071453515562574	NULL	[]	[0, 0, 336, 0]	NULL	NULL
"91.9.z.a"	288	37.071453515562574	NULL	[]	[-2, -4, -2, 2070]	NULL	NULL
"91.9.bd.a"	292	37.071453515562574	NULL	[]	[-2, -4, -2, -5314]	NULL	NULL
"91.10.a.a"	12	46.868261090912455	NULL	[]	[-21, -323, -5202, 28812]	1	"q+(-2+\\beta _{1})q^{2}+(-3^{3}-\\beta _{1}+\\beta _{3}+\\cdots)q^{3}+\\cdots"
"91.10.a.b"	13	46.868261090912455	NULL	[]	[-26, 163, -2640, -31213]	1	"q+(-2+\\beta _{1})q^{2}+(13-\\beta _{5})q^{3}+(253+\\cdots)q^{4}+\\cdots"
"91.10.a.c"	14	46.868261090912455	NULL	[]	[27, 163, 2964, 33614]	-1	"q+(2-\\beta _{1})q^{2}+(12-\\beta _{4})q^{3}+(171-6\\beta _{1}+\\cdots)q^{4}+\\cdots"
"91.10.a.d"	15	46.868261090912455	NULL	[]	[22, 1, 1694, -36015]	-1	"q+(1+\\beta _{1})q^{2}-\\beta _{3}q^{3}+(427+\\beta _{2})q^{4}+\\cdots"
"91.10.c.a"	62	46.868261090912455	NULL	[]	[0, 0, 0, 0]	NULL	NULL
"91.10.e.a"	70	46.868261090912455	NULL	[]	[65, 0, -2118, -8764]	NULL	NULL
"91.10.e.b"	74	46.868261090912455	NULL	[]	[-31, 0, -950, 14708]	NULL	NULL
"91.10.f.a"	64	46.868261090912455	NULL	[]	[-48, 4, 8568, -76832]	NULL	NULL
"91.10.f.b"	64	46.868261090912455	NULL	[]	[16, -4, -4016, 76832]	NULL	NULL
"91.10.g.a"	164	46.868261090912455	NULL	[]	[1, -326, -2, 113]	NULL	NULL
"91.10.h.a"	164	46.868261090912455	NULL	[]	[-2, 163, -2, -913]	NULL	NULL
"91.10.i.a"	164	46.868261090912455	NULL	[]	[-4, 0, 0, -1142]	NULL	NULL
"91.10.k.a"	164	46.868261090912455	NULL	[]	[0, -161, 0, -2055]	NULL	NULL
"91.10.q.a"	124	46.868261090912455	NULL	[]	[0, 0, 0, 0]	NULL	NULL
"91.10.r.a"	164	46.868261090912455	NULL	[]	[0, -326, 0, 0]	NULL	NULL
"91.10.u.a"	164	46.868261090912455	NULL	[]	[-3, 322, 0, 1023]	NULL	NULL
"91.10.w.a"	328	46.868261090912455	NULL	[]	[-2, 0, -6, 1136]	NULL	NULL
"91.10.ba.a"	328	46.868261090912455	NULL	[]	[-2, -6, -6, -2968]	NULL	NULL
"91.10.bb.a"	328	46.868261090912455	NULL	[]	[-2, -12, -6, 3872]	NULL	NULL
"91.10.bc.a"	328	46.868261090912455	NULL	[]	[-8, 0, 0, -916]	NULL	NULL
"91.11.b.a"	1	57.81750999330889	"1.1.1.1"	[-91]	[0, 0, -6243, 16807]	NULL	"q+2^{10}q^{4}-6243q^{5}+7^{5}q^{7}+3^{10}q^{9}+\\cdots"
"91.11.b.b"	1	57.81750999330889	"1.1.1.1"	[-91]	[0, 0, 6243, -16807]	NULL	"q+2^{10}q^{4}+6243q^{5}-7^{5}q^{7}+3^{10}q^{9}+\\cdots"
"91.11.b.c"	88	57.81750999330889	NULL	[]	[0, 0, 0, 0]	NULL	NULL
"91.11.d.a"	80	57.81750999330889	NULL	[]	[-22, 0, 0, -14498]	NULL	NULL
"91.11.j.a"	140	57.81750999330889	NULL	[]	[64, 0, 15580, 0]	NULL	NULL
"91.11.l.a"	182	57.81750999330889	NULL	[]	[0, 240, 0, -29267]	NULL	NULL
"91.11.m.a"	182	57.81750999330889	NULL	[]	[1, 0, -6, 34584]	NULL	NULL
"91.11.n.a"	184	57.81750999330889	NULL	[]	[-2, 0, 0, 5320]	NULL	NULL
"91.11.o.a"	160	57.81750999330889	NULL	[]	[22, 0, -6666, 14498]	NULL	NULL
"91.11.p.a"	182	57.81750999330889	NULL	[]	[-3, 0, 0, 3722]	NULL	NULL
"91.11.s.a"	184	57.81750999330889	NULL	[]	[0, 480, 0, 0]	NULL	NULL
"91.11.t.a"	184	57.81750999330889	NULL	[]	[-6, 0, 0, 25536]	NULL	NULL
"91.11.v.a"	182	57.81750999330889	NULL	[]	[-2, -246, -6, 9045]	NULL	NULL
"91.11.x.a"	364	57.81750999330889	NULL	[]	[-2, 2, -2, -20222]	NULL	NULL
"91.11.y.a"	280	57.81750999330889	NULL	[]	[-64, 0, -15580, 0]	NULL	NULL
"91.11.z.a"	368	57.81750999330889	NULL	[]	[-2, -4, -2, -10646]	NULL	NULL
"91.11.bd.a"	364	57.81750999330889	NULL	[]	[-2, -4, -2, 38306]	NULL	NULL
"91.12.a.a"	15	69.91922943092258	NULL	[]	[-77, 10, -13522, -252105]	-1	"q+(-5-\\beta _{1})q^{2}+(1+\\beta _{1}-\\beta _{3})q^{3}+\\cdots"
"91.12.a.b"	16	69.91922943092258	NULL	[]	[-10, -476, -19686, 268912]	-1	"q+(-1+\\beta _{1})q^{2}+(-30-\\beta _{3})q^{3}+(479+\\cdots)q^{4}+\\cdots"
"91.12.a.c"	17	69.91922943092258	NULL	[]	[19, -476, 8551, -285719]	1	"q+(1+\\beta _{1})q^{2}+(-28-\\beta _{1}-\\beta _{3})q^{3}+\\cdots"
"91.12.a.d"	18	69.91922943092258	NULL	[]	[86, 982, 20741, 302526]	1	"q+(5-\\beta _{1})q^{2}+(55-\\beta _{1}+\\beta _{3})q^{3}+(35^{2}+\\cdots)q^{4}+\\cdots"
"91.12.c.a"	78	69.91922943092258	NULL	[]	[0, 0, 0, 0]	NULL	NULL
"91.12.e.a"	86	69.91922943092258	NULL	[]	[73, 0, 5458, 38537]	NULL	NULL
"91.12.e.b"	90	69.91922943092258	NULL	[]	[-119, 0, 12104, -31679]	NULL	NULL
"91.12.f.a"	76	69.91922943092258	NULL	[]	[-96, -373, 41458, 638666]	NULL	NULL
"91.12.f.b"	76	69.91922943092258	NULL	[]	[32, 373, -20594, -638666]	NULL	NULL
"91.12.g.a"	202	69.91922943092258	NULL	[]	[1, 1456, -2, 99764]	NULL	NULL
"91.12.h.a"	202	69.91922943092258	NULL	[]	[-2, -728, -2, -28735]	NULL	NULL
"91.12.i.a"	204	69.91922943092258	NULL	[]	[-4, 0, 0, -73960]	NULL	NULL
"91.12.k.a"	202	69.91922943092258	NULL	[]	[0, 730, 0, -102695]	NULL	NULL
"91.12.q.a"	156	69.91922943092258	NULL	[]	[0, 0, 0, 0]	NULL	NULL
"91.12.r.a"	200	69.91922943092258	NULL	[]	[0, 484, 0, 0]	NULL	NULL
"91.12.u.a"	202	69.91922943092258	NULL	[]	[-3, -1460, 0, -25810]	NULL	NULL
"91.12.w.a"	404	69.91922943092258	NULL	[]	[-2, 0, -6, 73954]	NULL	NULL
"91.12.ba.a"	404	69.91922943092258	NULL	[]	[-2, -6, -6, -131430]	NULL	NULL
"91.12.bb.a"	400	69.91922943092258	NULL	[]	[-2, -12, -6, 5850]	NULL	NULL
"91.12.bc.a"	400	69.91922943092258	NULL	[]	[-8, 0, 0, 125568]	NULL	NULL
"91.13.d.a"	96	83.17343737214199	NULL	[]	[90, 0, 0, 279600]	NULL	NULL
"91.14.a.a"	18	97.58014534624056	NULL	[]	[-37, -2186, -97225, 2117682]	1	"q+(-2-\\beta _{1})q^{2}+(-122+\\beta _{1}-\\beta _{3}+\\cdots)q^{3}+\\cdots"
"91.14.a.b"	19	97.58014534624056	NULL	[]	[-218, 2188, -17267, -2235331]	1	"q+(-11-\\beta _{1})q^{2}+(115+\\beta _{2})q^{3}+(3147+\\cdots)q^{4}+\\cdots"
"91.14.a.c"	20	97.58014534624056	NULL	[]	[155, 2188, 146094, 2352980]	-1	"q+(8-\\beta _{1})q^{2}+(109-\\beta _{3})q^{3}+(4976+\\cdots)q^{4}+\\cdots"
"91.14.a.d"	21	97.58014534624056	NULL	[]	[-26, 730, 51914, -2470629]	-1	NULL
"91.14.c.a"	90	97.58014534624056	NULL	[]	[0, 0, 0, 0]	NULL	NULL
"91.16.a.a"	21	129.85108964092757	NULL	[]	[-221, -3347, -177766, -17294403]	-1	NULL
"91.16.a.b"	22	129.85108964092757	NULL	[]	[54, -7721, -596292, 18117946]	-1	NULL
"91.16.a.c"	23	129.85108964092757	NULL	[]	[163, -7721, 281616, -18941489]	1	NULL
"91.16.a.d"	24	129.85108964092757	NULL	[]	[438, 5401, 506826, 19765032]	1	NULL
"91.18.a.a"	24	166.7320994835493	NULL	[]	[-597, -23966, -2882682, 138355224]	1	NULL
"91.18.a.b"	25	166.7320994835493	NULL	[]	[-698, 15400, -2074710, -144120025]	1	NULL
"91.18.a.c"	26	166.7320994835493	NULL	[]	[171, 15400, 1943739, 149884826]	-1	NULL
"91.18.a.d"	27	166.7320994835493	NULL	[]	[70, 2278, 911369, -155649627]	-1	NULL
"91.20.a.a"	27	208.2231938663065	NULL	[]	[115, 30970, -5617237, -1089547389]	-1	NULL
"91.20.a.b"	28	208.2231938663065	NULL	[]	[-682, -8396, -13042671, 1129900996]	-1	NULL
"91.20.a.c"	29	208.2231938663065	NULL	[]	[1651, -8396, 4408726, -1170254603]	1	NULL
"91.20.a.d"	30	208.2231938663065	NULL	[]	[854, 109702, 15993866, 1210608210]	1	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.



#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.