Properties

Level 10
Symmetry even
Weight 0
Character \( \chi_{10}(1,\cdot) \)
Multiplicity 1
Precision 0
Fricke Eigenvalue 1
Atkin-Lehner Eigenvalues n/a

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Spectral parameter

$R= 15.2144704333$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -1.397646029
4 0.5
5 -0.447213595
6 0.988284985
7 1.721595566
8 -0.353553390
9 0.953414424
10 0.316227766
11 1.167843123
12 -0.698823014
13 1.035417293
14 -1.217351899
15 0.625046306
16 0.250000000
17 -1.149975153
18 -0.674165804
19 0.717670424
20 -0.223606797
21 -2.406181207
22 -0.825789792
23 0.570245441
24 0.494142492
25 0.200000000
26 -0.732150589
27 0.0651101449
28 0.860797783
29 -1.887463088
30 -0.441974481
31 0.114975178
32 -0.176776695
33 -1.632231305
34 0.813155228
35 -0.769920943
36 0.476707212
37 0.212696596
38 -0.507469624
39 -1.447146869
40 0.158113883
41 -0.101233291
42 1.701427048
43 -0.648265949
44 0.583921561
45 -0.426379892
46 -0.403224418
47 1.737502123
48 -0.349411507
49 1.963891293
50 -0.141421356
51 1.607258206
52 0.517708646
53 0.376352077
54 -0.0460398250
55 -0.522275322
56 -0.608675949
57 -1.003049219
58 1.334637949
59 0.544862457
60 0.312523153
61 0.727513574
62 -0.0812997287
63 1.641394045
64 0.125000000
65 -0.463052690
66 1.154161824
67 1.091081157
68 -0.574987576
69 -0.797001277
70 0.544416319
71 -1.195093306
72 -0.337082902
73 -0.640505623
74 -0.150399205
75 -0.279529205
76 0.358835212
77 2.010553544
78 1.023287364
79 0.303077888
80 -0.111803398
81 -1.044415359
82 0.0715827471
83 -1.055439192
84 -1.203090603
85 0.514284522
86 0.458393248
87 2.638005291
88 -0.412894896
89 -1.905710209
90 0.301496113
91 1.782569822
92 0.285122720
93 -0.160694595
94 -1.228599533
95 -0.320951971
96 0.247071246
97 0.0239198673
98 -1.388680851
99 1.113438463
100 0.100000000
101 -0.486301876
102 -1.136503177
103 0.329210417
104 -0.366075294
105 1.076076949
106 -0.266121106
107 0.915637976
108 0.0325550724
109 -0.555184104
110 0.369304422
111 -0.297274542
112 0.430398891
113 1.532611509
114 0.709262905
115 -0.255021514
116 -0.943731544
117 0.987181686
118 -0.385275938
119 -1.979791905
120 -0.220987240
121 0.363858357
122 -0.514429782
123 0.141488068
124 0.0574875894
125 -0.0894427190
126 -1.160640860
127 0.684033902
128 -0.0883883476
129 0.906041518
130 0.327427697
131 -0.940761507
132 -0.816115652
133 1.235526118
134 -0.771510885
135 -0.0291181420
136 0.406577614
137 1.557907336
138 0.563565007
139 0.271466135
140 -0.384960471
141 -2.428679581
142 0.845058581
143 1.209216284
144 0.238353606
145 0.844099154
146 0.452905869
147 -2.744393768
148 0.106348298
149 1.623616202
150 0.197656997
151 0.562609714
152 -0.253734812
153 -1.099761565
154 -1.421676044
155 -0.0514184631
156 -0.723573434
157 -0.468474635
158 -0.214308429
159 -0.521964063
160 0.0790569415
161 0.970619558
162 0.738513183
163 -0.940783198
164 -0.0506166459
165 0.729956030
166 0.746308210
167 0.459898058
168 0.850713524
169 0.221189350
170 -0.363654073
171 0.519858279
172 -0.324132974