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

$R= 31.933075041$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 0.444343452
4 0.5
5 0.447213595
6 0.314198268
7 0.383974693
8 0.353553390
9 -0.802558896
10 0.316227766
11 1.965482465
12 0.222171726
13 -0.415280687
14 0.271511109
15 0.198716432
16 0.250000000
17 -1.537503469
18 -0.567494838
19 1.281831033
20 0.223606797
21 0.170616640
22 1.389805979
23 0.808751252
24 0.157099134
25 0.200000000
26 -0.293647790
27 -0.800955242
28 0.191987346
29 0.549590065
30 0.140513737
31 -0.198182493
32 0.176776695
33 0.873349263
34 -1.087179129
35 0.171718703
36 -0.401279448
37 0.859167406
38 0.906391416
39 -0.184527254
40 0.158113883
41 0.219548440
42 0.120644183
43 -1.246265289
44 0.982741232
45 -0.358915249
46 0.571873494
47 1.361257327
48 0.111085863
49 -0.852563435
50 0.141421356
51 -0.683179599
52 -0.207640343
53 1.010349381
54 -0.566360883
55 0.878990480
56 0.135755554
57 0.569573226
58 0.388618861
59 1.718273028
60 0.0993582164
61 -1.405706855
62 -0.140136185
63 -0.308162306
64 0.125000000
65 -0.185719169
66 0.617551186
67 -0.244012067
68 -0.768751734
69 0.359363323
70 0.121423459
71 1.428927891
72 -0.283747419
73 -1.044510387
74 0.607523099
75 0.0888686904
76 0.640915516
77 0.754695526
78 -0.130480472
79 0.852147613
80 0.111803398
81 0.446659679
82 0.155244191
83 -0.268382597
84 0.0853083203
85 -0.687592454
86 -0.881242637
87 0.244206746
88 0.694902989
89 0.604581720
90 -0.253791406
91 -0.159457274
92 0.404375626
93 -0.0880610932
94 0.962554287
95 0.573252265
96 0.0785495670
97 -1.181937453
98 -0.602853386
99 -1.577415438
100 0.100000000
101 1.300111732
102 -0.483080927
103 -0.144771066
104 -0.146823895
105 0.0763020813
106 0.714424898
107 -1.758663642
108 -0.400477621
109 1.086916075
110 0.621540129
111 0.381765411
112 0.0959936732
113 0.670086093
114 0.402749090
115 0.361684555
116 0.274795032
117 0.333287210
118 1.215002510
119 -0.590362422
120 0.0702568685
121 2.863121322
122 -0.993984850
123 0.0975549119
124 -0.0990912467
125 0.0894427190
126 -0.217903656
127 0.268256180
128 0.0883883476
129 -0.553769821
130 -0.131323284
131 1.279864134
132 0.436674631
133 0.492190677
134 -0.172542587
135 -0.358198073
136 -0.543589564
137 -0.987255831
138 0.254108242
139 -0.700560940
140 0.0858593515
141 0.604865779
142 1.010404601
143 -0.816226909
144 -0.200639724
145 0.245784149
146 -0.738580377
147 -0.378830979
148 0.429583703
149 -0.874502576
150 0.0628396536
151 1.133649179
152 0.453195708
153 1.233937088
154 0.533650324
155 -0.0886299054
156 -0.0922636270
157 1.042650558
158 0.602559355
159 0.448942131
160 0.0790569415
161 0.310540014
162 0.315836088
163 -0.947623974
164 0.109774220
165 0.390573664
166 -0.189775154
167 0.0700894652
168 0.0603220917
169 -0.827541950
170 -0.486201287
171 -1.028744896
172 -0.623132644
173 1.297066464
174 0.172680246
175 0.0767949386
176 0.491370616
177 0.763503358
178 0.427503834
179 -1.030002862
180 -0.179457624
181 -0.438384459
182 -0.112753320
183 -0.624616593
184 0.285936747
185 0.384231344
186 -0.0622685962
187 -3.021936217
188 0.680628663
189 -0.307546616
190 0.405350564
191 -0.0920091411
192 0.0555429315
193 -1.381459806
194 -0.835755988
195 -0.0825230968
196 -0.426281717
197 0.720839912
198 -1.115401153
199 -0.108878997
200 0.0707106781
201 -0.108423570
202 0.919317822
203 0.211030118
204 -0.341589799
205 0.0981850474
206 -0.102368603
207 -0.649068365
208 -0.103820171
209 2.519419306
210 0.0539537191
211 0.997770301
212 0.505174690
213 0.634938885
214 -1.243562987
215 -0.557346781
216 -0.283180441
217 -0.0760757294
218 0.768565727
219 -0.464080799
220 0.439495240
221 0.638543821
222 0.269948911
223 0.930334225
224 0.0678777773
225 -0.160511779
226 0.473822421
227 -1.072591036
228 0.284786613
229 0.809447840
230 0.255749601
231 0.336213156
232 0.194309430
233 0.874421745
234 0.235669646
235 0.608772783
236 0.859136514
237 0.381221166
238 -0.417449272
239 1.357384899
240 0.0496791082
241 0.783713563
242 2.024532502
243 1.011723481
244 -0.702853427
245 -0.381277959
246 0.0689817397
247 -0.521015985
248 -0.0700680925
249 -0.0879268555
250 0.0632455532
251 0.631502237
252 -0.154081153
253 1.640811967
254 0.189685764
255 -0.305527204
256 0.0625000000
257 1.240396785
258 -0.391574395
259 0.628833331