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

$R= 31.8145560802$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 0.774352400
4 0.5
5 -0.447213595
6 -0.547549833
7 1.068963415
8 -0.353553390
9 -0.400378359
10 0.316227766
11 -0.202590862
12 0.387176200
13 1.032574037
14 -0.755871280
15 -0.346300921
16 0.250000000
17 -0.0460539848
18 0.283110252
19 -0.180477360
20 -0.223606797
21 0.827754387
22 0.143253372
23 0.821890943
24 -0.273774916
25 0.200000000
26 -0.730140104
27 -1.084386344
28 0.534481707
29 -0.890737959
30 0.244871729
31 1.589012145
32 -0.176776695
33 -0.156876721
34 0.0325650849
35 -0.478054972
36 -0.200189179
37 1.456729338
38 0.127616765
39 0.799576185
40 0.158113883
41 -0.865962609
42 -0.585310740
43 -0.120445476
44 -0.101295431
45 0.179054645
46 -0.581164659
47 -1.586019611
48 0.193588100
49 0.142682784
50 -0.141421356
51 -0.0356620137
52 0.516287018
53 -0.223018354
54 0.766776937
55 0.0906013881
56 -0.377935640
57 -0.139753077
58 0.629846851
59 0.528040480
60 -0.173150460
61 -0.285924824
62 -1.123601263
63 -0.427989818
64 0.125000000
65 -0.461781147
66 0.110928593
67 1.476179462
68 -0.0230269924
69 0.636433225
70 0.338035912
71 0.180143546
72 0.141555126
73 1.379118240
74 -1.030063193
75 0.154870480
76 -0.0902386803
77 -0.216562220
78 -0.565385742
79 1.708557701
80 -0.111803398
81 -0.439318810
82 0.612328033
83 -0.354575640
84 0.413877193
85 0.0205959681
86 0.0851678129
87 -0.689745077
88 0.0716266864
89 1.428464497
90 -0.126610754
91 1.103783870
92 0.410945471
93 1.230455369
94 1.121485222
95 0.0807119293
96 -0.136887458
97 -0.671814172
98 -0.100891964
99 0.0811129972
100 0.100000000
101 -0.234300672
102 0.0252168517
103 -0.906863905
104 -0.365070052
105 -0.370183015
106 0.157697790
107 -0.830010950
108 -0.542193172
109 -0.0947313514
110 -0.0640648559
111 1.128021860
112 0.267240853
113 0.403664992
114 0.0988203488
115 -0.367560804
116 -0.445368979
117 -0.413420298
118 -0.373381004
119 -0.0492300249
120 0.122435864
121 -0.958956942
122 0.202179382
123 -0.670560225
124 0.794506072
125 -0.0894427190
126 0.302634502
127 -1.653500981
128 -0.0883883476
129 -0.0932672436
130 0.326528581
131 -0.423126354
132 -0.0784383605
133 -0.192923695
134 -1.043816508
135 0.484952316
136 0.0162825424
137 -0.00332902805
138 -0.450026249
139 -1.057191446
140 -0.239027486
141 -1.228138094
142 -0.127380723
143 -0.209190065
144 -0.100094589
145 0.398350125
146 -0.975183859
147 0.110486756
148 0.728364669
149 1.792517684
150 -0.109509966
151 1.183238858
152 0.0638083827
153 0.0184390190
154 0.153132614
155 -0.710627834
156 0.399788092
157 1.778983708
158 -1.208132736
159 -0.172694798
160 0.0790569415
161 0.878571352
162 0.310645309
163 -0.547997227
164 -0.432981304
165 0.0701574024
166 0.250722840
167 0.107205614
168 -0.292655370
169 0.0662091492
170 -0.0145635487
171 0.0722592206
172 -0.0602227380
173 -0.903757672
174 0.487723421
175 0.213792683
176 -0.0506477157
177 0.408889434
178 -1.010076932
179 -0.304244996
180 0.0895273227
181 0.586787458
182 -0.780493059
183 -0.221406600
184 -0.290582329
185 -0.651469165
186 -0.870063335
187 0.00933036388
188 -0.793009805
189 -1.159168878
190 -0.0570719525
191 0.845195363
192 0.0967940501
193 0.276252945
194 0.475044356
195 -0.357581340
196 0.0713413921
197 -1.598350480
198 -0.0573555504
199 -0.937340492
200 -0.0707106781
201 1.143086179
202 0.165675594
203 -0.952162087
204 -0.0178310068
205 0.387270252
206 0.641249617
207 -0.329065080
208 0.258143509
209 0.0365590548
210 0.261758920
211 0.900770849
212 -0.111509177
213 0.139564069
214 0.586906371
215 0.0538648544
216 0.383388468
217 1.698654466
218 0.0669851810
219 1.067775070
220 0.0453006940
221 -0.0477582189
222 -0.797631906
223 -0.0527462865
224 -0.188967820
225 -0.0800756718
226 -0.285434253
227 0.839996577
228 -0.0698765387
229 -0.463879349
230 0.259904737
231 -0.168618483
232 0.314923425
233 1.707145089
234 0.292332296
235 0.709289533
236 0.264020240
237 1.313518003
238 0.0348108844
239 1.683199806
240 -0.0865752303
241 1.032707098
242 0.678084956
243 0.729077804
244 -0.142962412
245 -0.0638096809
246 0.474157682
247 -0.203807519
248 -0.561800631
249 -0.405759424
250 0.0632455532
251 1.408728786
252 -0.213994909
253 -0.190653915
254 1.169201756
255 0.0159485373
256 0.0625000000