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

$R= 26.2206008714$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 1.987819760
4 0.5
5 0.447213595
6 -1.405600832
7 -0.711218692
8 -0.353553390
9 2.951427400
10 -0.316227766
11 -1.373733771
12 0.993909880
13 -0.432589095
14 0.502907560
15 0.888980022
16 0.250000000
17 -1.514558445
18 -2.086974328
19 0.174389107
20 0.223606797
21 -1.413774570
22 0.971376465
23 0.437464155
24 -0.702800416
25 0.200000000
26 0.305886682
27 3.879085947
28 -0.355609346
29 0.155533732
30 -0.628603802
31 0.892494246
32 -0.176776695
33 -2.730735136
34 1.070954547
35 -0.318066668
36 1.475713700
37 -0.167801200
38 -0.123311720
39 -0.859909152
40 -0.158113883
41 0.865760920
42 0.999689585
43 -1.217777648
44 -0.686866885
45 1.319918459
46 -0.309333870
47 -0.755743044
48 0.496954940
49 -0.494167971
50 -0.141421356
51 -3.010669206
52 -0.216294547
53 0.212260130
54 -2.742927977
55 -0.614352419
56 0.251453780
57 0.346654113
58 -0.109978956
59 -1.176289064
60 0.444490011
61 -1.394134085
62 -0.631088733
63 -2.099110335
64 0.125000000
65 -0.193459724
66 1.930921332
67 0.0461597718
68 -0.757279222
69 0.869599892
70 0.224907098
71 -1.046555508
72 -1.043487164
73 -0.672246730
74 0.118653366
75 0.397563952
76 0.0871945536
77 0.977025136
78 0.608047592
79 -1.805998951
80 0.111803398
81 4.759496298
82 -0.612185417
83 1.806715810
84 -0.706887285
85 -0.677331128
86 0.861098832
87 0.309173026
88 0.485688232
89 -1.619979912
90 -0.933323293
91 0.307665450
92 0.218732077
93 1.774117698
94 0.534391031
95 0.0779891796
96 -0.351400208
97 0.235451580
98 0.349429524
99 -4.054475493
100 0.100000000
101 -0.355691066
102 2.128864611
103 -0.562611573
104 0.152943341
105 -0.632259208
106 -0.150090577
107 -0.476732139
108 1.939542973
109 0.0200882567
110 0.434412761
111 -0.333558541
112 -0.177804673
113 -0.104568474
114 -0.245121474
115 0.195639917
116 0.0777668660
117 -1.276755309
118 0.831761974
119 1.077182276
120 -0.314301901
121 0.887144475
122 0.985801665
123 1.720976665
124 0.446247123
125 0.0894427190
126 1.484295152
127 -0.543818671
128 -0.0883883476
129 -2.420722472
130 0.136796683
131 0.819661755
132 -1.365367568
133 -0.124028792
134 -0.0326398876
135 1.734779973
136 0.535477273
137 -0.450620014
138 -0.614899981
139 -1.628691117
140 -0.159033334
141 -1.502280957
142 0.740026496
143 0.594262248
144 0.737856850
145 0.0695567995
146 0.475350221
147 -0.982316866
148 -0.0839006001
149 -0.583327392
150 -0.281120166
151 1.050109323
152 -0.0616558601
153 -4.470109290
154 -0.690861099
155 0.399135560
156 -0.429954576
157 -0.398351692
158 1.277034105
159 0.421934909
160 -0.0790569415
161 -0.311132852
162 -3.365472107
163 0.492967350
164 0.432880460
165 -1.221221878
166 -1.277541001
167 -0.0404094680
168 0.499844792
169 -0.812867330
170 0.478945433
171 0.514696535
172 -0.608888824
173 0.294917168
174 -0.218618343
175 -0.142243738
176 -0.343433442
177 -2.338252879
178 1.145498781
179 0.542113786
180 0.659959229
181 1.898343960
182 -0.217552326
183 -2.771282834
184 -0.154666935
185 -0.0750429781
186 -1.254490655
187 2.080608121
188 -0.377871522
189 -2.758862031
190 -0.0551466777
191 -1.217271386
192 0.248477470
193 -1.067734381
194 -0.166489408
195 -0.384563063
196 -0.247083985
197 1.541833201
198 2.866947115
199 -0.937253830
200 -0.0707106781
201 0.0918471138
202 0.251511565
203 -0.110054812
204 -1.505334603
205 0.387180054
206 0.397826458
207 1.290394281
208 -0.108147273
209 -0.239014871
210 0.447074773
211 1.021161815
212 0.106130065
213 -2.081686252
214 0.337100528
215 -0.544606720
216 -1.371463988
217 -0.634106473
218 -0.0142045425
219 -1.325127526
220 -0.307176209
221 0.657434288
222 0.235861506
223 -0.180175490
224 0.125726890
225 0.590285480
226 0.0739410775