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

$R= 26.4536952758$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 1.684415559
4 0.5
5 -0.447213595
6 -1.191061664
7 0.657303325
8 -0.353553390
9 1.837255776
10 0.316227766
11 0.242992369
12 0.842207779
13 0.123935205
14 -0.464783638
15 -0.753293538
16 0.250000000
17 -0.311753117
18 -1.299136018
19 -1.263942561
20 -0.223606797
21 1.107171948
22 -0.171821552
23 -1.905507331
24 -0.595530832
25 0.200000000
26 -0.0876354244
27 1.410286656
28 0.328651662
29 1.561436698
30 0.532658969
31 -0.983160076
32 -0.176776695
33 0.409300127
34 0.220442743
35 -0.293954983
36 0.918627888
37 -1.032938236
38 0.893742356
39 0.208758388
40 0.158113883
41 0.199373163
42 -0.782888792
43 0.684691796
44 0.121496184
45 -0.821645761
46 1.347397155
47 -1.606279507
48 0.421103889
49 -0.567952338
50 -0.141421356
51 -0.525121802
52 0.0619676028
53 -1.172995887
54 -0.997223258
55 -0.108669491
56 -0.232391819
57 -2.129004516
58 -1.104102477
59 -0.272676179
60 -0.376646769
61 -1.009166996
62 0.695199156
63 1.207634331
64 0.125000000
65 -0.0554255089
66 -0.289418895
67 -0.719273421
68 -0.155876558
69 -3.209666197
70 0.207857562
71 0.672984542
72 -0.649568009
73 1.594983598
74 0.730397631
75 0.336883111
76 -0.631971280
77 0.159719692
78 -0.147614472
79 1.208717721
80 -0.111803398
81 0.538253010
82 -0.140978116
83 -0.324918227
84 0.553585974
85 0.139420232
86 -0.484150212
87 2.630108269
88 -0.0859107761
89 1.633227994
90 0.580991289
91 0.0814630228
92 -0.952753665
93 -1.656050129
94 1.135811132
95 0.565252297
96 -0.297765416
97 -1.786727190
98 0.401602949
99 0.446439134
100 0.100000000
101 0.270069511
102 0.371317187
103 -1.411617244
104 -0.0438177122
105 -0.495142347
106 0.829433346
107 -1.725034812
108 0.705143328
109 -0.0245209353
110 0.0768409341
111 -1.739897237
112 0.164325831
113 1.134311778
114 1.505433531
115 0.852168784
116 0.780718349
117 0.227700672
118 0.192811175
119 -0.204916361
120 0.266329484
121 -0.940954708
122 0.713588826
123 0.335827259
124 -0.491580038
125 -0.0894427190
126 -0.853926424
127 1.557633594
128 -0.0883883476
129 1.153305516
130 0.0391917532
131 0.351165789
132 0.204650063
133 -0.830793648
134 0.508603113
135 -0.630699366
136 0.110221371
137 0.157626436
138 2.269576733
139 0.931625937
140 -0.146977491
141 -2.705642195
142 -0.475871933
143 0.0301153109
144 0.459313944
145 -0.698295720
146 -1.127823718
147 -0.956667750
148 -0.516469118
149 -0.772596512
150 -0.238212332
151 0.395663589
152 0.446871178
153 -0.572770211
154 -0.112938877
155 0.439682552
156 0.104379194
157 -0.473710297
158 -0.854692497
159 -1.975812480
160 0.0790569415
161 -1.252496194
162 -0.380602353
163 0.774455144
164 0.0996865819
165 -0.183044581
166 0.229751881
167 1.411288273
168 -0.391444396
169 -0.984640045
170 -0.0985849920
171 -2.322186411
172 0.342345898
173 0.0450200989
174 -1.859767392
175 0.131460665
176 0.0607480923
177 -0.459298881
178 -1.154866590
179 0.565699187
180 -0.410822880
181 -0.978533217
182 -0.0576030558
183 -1.699856066
184 0.673698577
185 0.461944022
186 1.171004276
187 -0.0757591381
188 -0.803139753
189 0.926965946
190 -0.399693732
191 -0.222029452
192 0.210551944
193 0.528675668
194 1.263406912
195 -0.0933595896
196 -0.283976169
197 -1.086006789
198 -0.315680139
199 -0.610357999
200 -0.0707106781
201 -1.211673713
202 -0.190967983
203 1.025926481
204 -0.262560901
205 -0.0891623894
206 0.998164125
207 -3.503315824
208 0.0309838014
209 -0.309708438
210 0.350118511
211 0.0738112244
212 -0.586497943
213 1.127795636
214 1.219783813
215 -0.306203480
216 -0.498611629
217 -0.658752572
218 0.0173389196
219 2.687308441
220 -0.0543347456
221 -0.0677971265
222 1.230293135
223 -0.981037286
224 -0.116195909
225 0.367451155
226 -0.802079550
227 0.392304642
228 -1.064502258