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

$R= 28.8500871556$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 0.677270750
4 0.5
5 -0.447213595
6 0.478902740
7 1.562310273
8 0.353553390
9 -0.541304330
10 -0.316227766
11 -0.546616241
12 0.338635375
13 -1.344744128
14 1.104720188
15 -0.302884687
16 0.250000000
17 -0.163531127
18 -0.382759962
19 1.532705855
20 -0.223606797
21 1.058107051
22 -0.386516051
23 0.518564034
24 0.239451370
25 0.200000000
26 -0.950877692
27 -1.043880340
28 0.781155136
29 -1.508406790
30 -0.214171816
31 -1.727417593
32 0.176776695
33 -0.370207192
34 -0.115633969
35 -0.698686394
36 -0.270652165
37 1.681664149
38 1.083786704
39 -0.910755865
40 -0.158113883
41 0.137795771
42 0.748194671
43 -1.762963776
44 -0.273308120
45 0.242078655
46 0.366680145
47 -0.705844810
48 0.169317687
49 1.440813390
50 0.141421356
51 -0.110754849
52 -0.672372064
53 -0.615992274
54 -0.738134867
55 0.244454214
56 0.552360094
57 1.038056845
58 -1.066604670
59 0.438494731
60 -0.151442343
61 -0.729003186
62 -1.221468694
63 -0.845685315
64 0.125000000
65 0.601387856
66 -0.261776016
67 -1.299515142
68 -0.0817655638
69 0.351208253
70 -0.494045887
71 -0.264681639
72 -0.191379981
73 -0.409833662
74 1.189116123
75 0.135454150
76 0.766352927
77 -0.853984170
78 -0.644001648
79 1.127772533
80 -0.111803398
81 -0.165685292
82 0.0974363243
83 1.440065217
84 0.529053525
85 0.0731333436
86 -1.246603641
87 -1.021599799
88 -0.193258025
89 -0.0385594646
90 0.171175459
91 -2.100907566
92 0.259282017
93 -1.169929410
94 -0.499107652
95 -0.685446896
96 0.119725685
97 -1.087833554
98 1.018808918
99 0.295885738
100 0.100000000
101 1.184322147
102 -0.0783155052
103 -0.0254698172
104 -0.475438846
105 -0.473199859
106 -0.435572314
107 0.472314856
108 -0.521940170
109 -1.152410788
110 0.172855233
111 1.138941941
112 0.390577568
113 -1.159449544
114 0.734017034
115 -0.231908886
116 -0.754203395
117 0.727915819
118 0.310062597
119 -0.255486360
120 -0.107085908
121 -0.701210684
122 -0.515483096
123 0.0933250455
124 -0.863708796
125 -0.0894427190
126 -0.597989821
127 -0.434452565
128 0.0883883476
129 -1.194003800
130 0.425245431
131 -1.183239676
132 -0.185103596
133 2.394562104
134 -0.918895969
135 0.466837480
136 -0.0578169846
137 -0.680943973
138 0.248341737
139 1.674526966
140 -0.349343197
141 -0.478048045
142 -0.187158182
143 0.735058982
144 -0.135326082
145 0.674580024
146 -0.289796161
147 0.975820767
148 0.840832074
149 0.342962161
150 0.0957805481
151 0.0706694464
152 0.541893352
153 0.0885201074
154 -0.603857997
155 0.772524633
156 -0.455377932
157 -0.510754127
158 0.797455605
159 -0.417193569
160 -0.0790569415
161 0.810157933
162 -0.117157193
163 -0.310627588
164 0.0688978856
165 0.165561689
166 1.018279880
167 -1.232606670
168 0.374097335
169 0.808336727
170 0.0517130831
171 -0.829660328
172 -0.881481888
173 0.389865194
174 -0.722380145
175 0.312462054
176 -0.136654060
177 0.296979817
178 -0.0272656589
179 -0.468291841
180 0.121039327
181 -1.798695144
182 -1.485565987
183 -0.493731360
184 0.183340072
185 -0.752063070
186 -0.827265019
187 0.0893880000
188 -0.352922405
189 -1.630863718
190 -0.484684148
191 1.138016708
192 0.0846588438
193 0.301204641
194 -0.769214483
195 0.407302405
196 0.720406695
197 -0.957874753
198 0.209222812
199 -0.632714414
200 0.0707106781
201 -0.880109892
202 0.837442221
203 -2.356596646
204 -0.0553774248
205 -0.0616241423
206 -0.0180098804
207 -0.280587343
208 -0.336186032
209 -0.837650103
210 -0.334602829
211 -0.701113025
212 -0.307996137
213 -0.179144810
214 0.333977037
215 0.788421369
216 -0.369067433
217 -2.696170274
218 -0.814877483
219 -0.278319673
220 0.122227107
221 0.219126105
222 0.805353570
223 1.000329848
224 0.276180047
225 -0.108260866
226 -0.819854635
227 1.211960027
228 0.519028422
229 -0.738878377
230 -0.163984346
231 -0.587291500
232 -0.533302335
233 -1.420892000
234 0.514714212
235 0.315663395
236 0.219247365
237 0.875418502
238 -0.180656138