Properties

Level 10
Symmetry odd
Weight 0
Character \( \chi_{10}(1,\cdot) \)
Multiplicity 1
Precision 0
Fricke Eigenvalue -1
Atkin-Lehner Eigenvalues n/a

Related objects

Downloads

Learn more about

Spectral parameter

$R= 26.671211243$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 1.065480741
4 0.5
5 0.447213595
6 -0.753408657
7 -1.516246480
8 -0.353553390
9 0.135249210
10 -0.316227766
11 1.035386169
12 0.532740370
13 1.155845689
14 1.072148168
15 0.476497473
16 0.250000000
17 0.0977805498
18 -0.0956356335
19 1.694079683
20 0.223606797
21 -1.615531423
22 -0.732128581
23 -0.323893236
24 -0.376704328
25 0.200000000
26 -0.817306325
27 -0.921375312
28 -0.758123240
29 -1.303730047
30 -0.336934594
31 0.893858890
32 -0.176776695
33 1.103184023
34 -0.0691412898
35 -0.678086040
36 0.0676246050
37 1.047506225
38 -1.197895232
39 1.231531322
40 -0.158113883
41 -1.255700657
42 1.142353225
43 0.0933833235
44 0.517693084
45 0.0604852855
46 0.229027104
47 -1.175424689
48 0.266370185
49 1.299003389
50 -0.141421356
51 0.104183292
52 0.577922844
53 -1.302010012
54 0.651510731
55 0.463038771
56 0.536074084
57 1.805009277
58 0.921876357
59 1.160238005
60 0.238248736
61 -0.616580877
62 -0.632053682
63 -0.205071138
64 0.125000000
65 0.516909906
66 -0.780068904
67 1.310186549
68 0.0488902749
69 -0.345102005
70 0.479479237
71 1.638017239
72 -0.0478178167
73 -0.350289582
74 -0.740698755
75 0.213096148
76 0.847039841
77 -1.569900636
78 -0.870824149
79 0.180580865
80 0.111803398
81 -1.116956861
82 0.887914450
83 0.321203147
84 -0.807765711
85 0.0437287912
86 -0.0660319813
87 -1.389099257
88 -0.366064290
89 -1.157368280
90 -0.0427695555
91 -1.752546958
92 -0.161946618
93 0.952389433
94 0.831150768
95 0.757615466
96 -0.188352164
97 -0.818049094
98 -0.918534105
99 0.140035161
100 0.100000000
101 1.627528371
102 -0.0736687127
103 0.521264633
104 -0.408653162
105 -0.722487616
106 0.920660108
107 0.313145588
108 -0.460687656
109 1.788894116
110 -0.327417855
111 1.116097709
112 -0.379061620
113 -0.760789738
114 -1.276334300
115 -0.144849458
116 -0.651865023
117 0.156327216
118 -0.820412161
119 -0.148259414
120 -0.168467297
121 0.0720245209
122 0.435988519
123 -1.337924867
124 0.446929445
125 0.0894427190
126 0.145007192
127 -0.320462997
128 -0.0883883476
129 0.0994981327
130 -0.365510500
131 0.276199788
132 0.551592011
133 -2.568642357
134 -0.926441793
135 -0.412051566
136 -0.0345706449
137 1.363496505
138 0.244023968
139 1.169690480
140 -0.339043020
141 -1.252392370
142 -1.158253097
143 1.196746641
144 0.0338123025
145 -0.583045802
146 0.247692139
147 1.384063092
148 0.523753112
149 1.668055194
150 -0.150681731
151 0.746991179
152 -0.598947616
153 0.0132247247
154 1.110087385
155 0.399745848
156 0.615765661
157 1.135812442
158 -0.127689954
159 -1.387266574
160 -0.0790569415
161 0.491102011
162 0.789807770
163 0.938850967
164 -0.627850328
165 0.493358893
166 -0.227124923
167 0.667795335
168 0.571176612
169 0.335979295
170 -0.0309209248
171 0.229122954
172 0.0466916617
173 0.586882297
174 0.982241504
175 -0.303249296
176 0.258846542
177 1.236210229
178 0.818382959
179 0.0223913900
180 0.0302426427
181 1.263386627
182 1.239237838
183 -0.656953882
184 0.114513552
185 0.468459025
186 -0.673441026
187 0.101238620
188 -0.587712344
189 1.397029027
190 -0.535715033
191 -1.053510791
192 0.133185092
193 -1.598051761
194 0.578448062
195 0.550757550
196 0.649501694
197 0.0374146815
198 -0.0990198123
199 0.265519563
200 -0.0707106781
201 1.395806126
202 -1.150836347
203 1.976643734
204 0.0520916463
205 -0.561566405
206 -0.368589756
207 -0.0440147592
208 0.288961422
209 1.753423015
210 0.510875893
211 -0.570763602
212 -0.651005006
213 1.746596592
214 -0.221427369
215 0.0417622918
216 0.325755365
217 -1.353869208
218 -1.264939160
219 -0.373181141
220 0.231519385
221 0.117158436
222 -0.789200259
223 -1.066685015
224 0.268037042
225 0.0270498420
226 0.537959583