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

$R= 29.6238435169$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -1.728464029
4 0.5
5 -0.447213595
6 1.222208636
7 -1.591276423
8 -0.353553390
9 1.987587900
10 0.316227766
11 -0.374229500
12 -0.864232014
13 0.767009832
14 1.125202349
15 0.772992613
16 0.250000000
17 0.735607965
18 -1.405436882
19 -1.337389648
20 -0.223606797
21 2.750464058
22 0.264620217
23 1.453240905
24 0.611104318
25 0.200000000
26 -0.542357853
27 -1.707010161
28 -0.795638211
29 1.487343955
30 -0.546588318
31 -0.927615334
32 -0.176776695
33 0.646842230
34 -0.520153380
35 0.711640450
36 0.993793950
37 0.0801767765
38 0.945677289
39 -1.325748905
40 0.158113883
41 0.0301188627
42 -1.944871787
43 1.640377125
44 -0.187114750
45 -0.888876331
46 -1.027596499
47 1.115743895
48 -0.432116007
49 1.532160655
50 -0.141421356
51 -1.271471907
52 0.383504916
53 1.220969775
54 1.207038460
55 0.167360520
56 0.562601174
57 2.311629901
58 -1.051710997
59 0.0930459251
60 0.386496306
61 -1.355674256
62 0.655923093
63 -3.162801765
64 0.125000000
65 -0.343017225
66 -0.457386527
67 -1.001415648
68 0.367803982
69 -2.511874631
70 -0.503205788
71 -0.100177569
72 -0.702718441
73 0.504927675
74 -0.0566935424
75 -0.345692805
76 -0.668694824
77 0.595502581
78 0.937446041
79 -1.304073388
80 -0.111803398
81 0.962917761
82 -0.0212972520
83 -1.068544459
84 1.375232029
85 -0.328973882
86 -1.159921788
87 -2.570820526
88 0.132310108
89 0.446206723
90 0.628530481
91 -1.220524663
92 0.726620452
93 1.603349739
94 -0.788950074
95 0.598098833
96 0.305552159
97 -1.709251367
98 -1.083401189
99 -0.743814027
100 0.100000000
101 0.960406647
102 0.899066407
103 1.498876374
104 -0.271178926
105 -1.230044920
106 -0.863356007
107 -1.405297354
108 -0.853505080
109 -0.783876160
110 -0.118341758
111 -0.138582674
112 -0.397819105
113 0.772979794
114 -1.634569178
115 -0.649909090
116 0.743671977
117 1.524499462
118 -0.0657934046
119 -1.170555611
120 -0.273294159
121 -0.859952280
122 0.958606459
123 -0.0520593708
124 -0.463807667
125 -0.0894427190
126 2.236438575
127 -1.474176995
128 -0.0883883476
129 -2.835332855
130 0.242549805
131 0.908857095
132 0.323421115
133 2.128156616
134 0.708107796
135 0.763398151
136 -0.260076690
137 0.0339481386
138 1.776163585
139 0.626145288
140 0.355820225
141 -1.928523189
142 0.0708362385
143 -0.287037706
144 0.496896975
145 -0.665160438
146 -0.357037783
147 -2.648284579
148 0.0400883882
149 -0.629629083
150 0.244441727
151 -0.734175319
152 0.472838644
153 1.462085492
154 -0.421083913
155 0.414842189
156 -0.662874452
157 1.571813225
158 0.922119135
159 -2.110402337
160 0.0790569415
161 -2.312507997
162 -0.680885678
163 -0.122905057
164 0.0150594313
165 -0.289276639
166 0.755575033
167 0.929483914
168 -0.972435893
169 -0.411695910
170 0.232619663
171 -2.658179476
172 0.820188562
173 0.372894395
174 1.817844627
175 -0.318255284
176 -0.0935573751
177 -0.160826543
178 -0.315515800
179 -0.406496625
180 -0.444438165
181 0.354762873
182 0.863041265
183 2.343234379
184 -0.513798249
185 -0.0358561445
186 -1.133739473
187 -0.275286336
188 0.557871947
189 2.716322965
190 -0.422919740
191 -1.059888116
192 -0.216058003
193 1.738089926
194 1.208623232
195 0.592892934
196 0.766080327
197 -0.0173397182
198 0.525955942
199 0.511862321
200 -0.0707106781
201 1.730907057
202 -0.679110052
203 -2.366810453
204 -0.635735953
205 -0.0134695648
206 -1.059865648
207 2.888383657
208 0.191752458
209 0.500589572
210 0.869773104
211 0.788226045
212 0.610484887
213 0.173273824
214 0.993695289
215 -0.733598952
216 0.603519230
217 1.476045450
218 0.554284148
219 -0.873221961
220 0.0836802602
221 0.565029514
222 0.0979927487
223 0.0562213364
224 0.281300587
225 0.397517580
226 -0.546579254
227 0.832800513
228 1.155814950
229 0.376123980
230 0.459555125
231 -1.025930081
232 -0.525855498
233 -0.00470923185
234 -1.077983908
235 -0.498975839
236 0.0465229625
237 2.268552689
238 0.827707810
239 -0.780252835
240 0.193248153