Properties

Level 10
Symmetry odd
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

$R= 28.7503926305$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -1.724976045
4 0.5
5 0.447213595
6 1.219742258
7 -1.743768733
8 -0.353553390
9 1.975542355
10 -0.316227766
11 -0.0724752302
12 -0.862488022
13 -0.204222371
14 1.233030696
15 -0.771432739
16 0.250000000
17 -1.570379947
18 -1.396919396
19 1.113727741
20 0.223606797
21 3.007959293
22 0.0512477267
23 -1.475706061
24 0.609871129
25 0.200000000
26 0.144407023
27 -1.682787194
28 -0.871884366
29 -0.747098063
30 0.545485321
31 0.475181172
32 -0.176776695
33 0.125018036
34 1.110426309
35 -0.779837085
36 0.987771177
37 1.009449990
38 -0.787524438
39 0.352278698
40 -0.158113883
41 0.913639029
42 -2.126948414
43 0.817307442
44 -0.0362376151
45 0.883489400
46 1.043481763
47 -1.164048502
48 -0.431244011
49 2.040729396
50 -0.141421356
51 2.708867790
52 -0.102111185
53 -0.434003038
54 1.189910236
55 -0.0324119083
56 0.616515348
57 -1.921153674
58 0.528278106
59 -1.448947034
60 -0.385716369
61 -0.587437624
62 -0.336003829
63 -3.444888992
64 0.125000000
65 -0.0913310208
66 -0.0884011010
67 -1.024053038
68 -0.785189973
69 2.545557605
70 0.551428091
71 -1.149961433
72 -0.698459698
73 -0.527991323
74 -0.713788933
75 -0.344995209
76 0.556863870
77 0.126380040
78 -0.249098656
79 -1.367473224
80 0.111803398
81 0.927225244
82 -0.646040353
83 -0.969861899
84 1.503979646
85 -0.702295262
86 -0.577923635
87 1.288726262
88 0.0256238633
89 -1.218302166
90 -0.624721345
91 0.356116585
92 -0.737853030
93 -0.819676139
94 0.823106589
95 0.498074187
96 0.304935564
97 0.931587769
98 -1.443013595
99 -0.143177887
100 0.100000000
101 -1.925127046
102 -1.915458784
103 -0.364605299
104 0.0722035117
105 1.345200290
106 0.306886491
107 -0.898260680
108 -0.841393597
109 0.537831773
110 0.0229186801
111 -1.741277052
112 -0.435942183
113 -0.653441542
114 1.358460791
115 -0.659955813
116 -0.373549031
117 -0.403449944
118 1.024560273
119 2.738379452
120 0.272742660
121 -0.994747341
122 0.415381127
123 -1.576005439
124 0.237590586
125 0.0894427190
126 2.435904367
127 1.600495247
128 -0.0883883476
129 -1.409835760
130 0.0645807841
131 -1.029006794
132 0.0625090180
133 -1.942083613
134 0.724114848
135 -0.752565311
136 0.555213154
137 0.764175710
138 -1.799981045
139 0.530373574
140 -0.389918542
141 2.007955781
142 0.813145527
143 0.0148010633
144 0.493885588
145 -0.334112411
146 0.373346245
147 -3.520209324
148 0.504724995
149 -1.025338242
150 0.243948451
151 -0.898412502
152 -0.393762219
153 -3.102352098
154 -0.0893641836
155 0.212507480
156 0.176139349
157 -0.0239696161
158 0.966949589
159 0.748644838
160 -0.0790569415
161 2.573290073
162 -0.655647257
163 -1.114520837
164 0.456819514
165 0.0559097654
166 0.685795925
167 -0.581479620
168 -1.063474207
169 -0.958293260
170 0.496597742
171 2.200216373
172 0.408653721
173 0.147698973
174 -0.911267079
175 -0.348753746
176 -0.0181188075
177 2.499399371
178 0.861469723
179 -1.546113090
180 0.441744700
181 -0.409195316
182 -0.251812452
183 1.013315533
184 0.521740881
185 0.451439759
186 0.579598556
187 0.113811936
188 -0.582024251
189 2.934388450
190 -0.352191635
191 0.370198362
192 -0.215622005
193 0.960610642
194 -0.658732029
195 0.157543823
196 1.020364698
197 -0.131385709
198 0.101242054
199 -0.175664357
200 -0.0707106781
201 1.766432355
202 1.361270389
203 1.302781249
204 1.354433895
205 0.408591795
206 0.257814880
207 -2.915146173
208 -0.0510555927
209 -0.0805709499
210 -0.951200247
211 -0.467893265
212 -0.217001519
213 1.983444857
214 0.635166218
215 0.365511000
216 0.594955118
217 -0.827313919
218 -0.380304493
219 0.912389344
220 -0.0162059541
221 0.319559918
222 1.231268811
223 -1.077914117
224 0.308257674
225 0.395108471
226 0.462052945
227 1.320766132
228 -0.960576837
229 0.675732517
230 0.466659231
231 -0.219812427
232 0.264139053
233 0.571187109
234 0.285282191
235 -0.520578316
236 -0.724473517
237 2.370848404
238 -1.936326680