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

$R= 27.5537953828$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -0.892505841
4 0.5
5 -0.447213595
6 0.631096933
7 -0.843897313
8 -0.353553390
9 -0.203433322
10 0.316227766
11 1.128946502
12 -0.446252920
13 1.739479777
14 0.596725512
15 0.399140746
16 0.250000000
17 1.052721992
18 0.143849081
19 0.706002799
20 -0.223606797
21 0.753183281
22 -0.798285727
23 -1.660102280
24 0.315548466
25 0.200000000
26 -1.229997946
27 1.074071270
28 -0.421948656
29 0.391538669
30 -0.282235128
31 1.162407045
32 -0.176776695
33 -1.007591348
34 -0.744386859
35 0.377402351
36 -0.101716661
37 1.369248195
38 -0.499219367
39 -1.552495862
40 0.158113883
41 -0.683393682
42 -0.532581006
43 1.579213698
44 0.564473251
45 0.0909781474
46 1.173869579
47 1.653377920
48 -0.223126460
49 -0.287837324
50 -0.141421356
51 -0.939560527
52 0.869739888
53 -0.989129371
54 -0.759483078
55 -0.504880224
56 0.298362756
57 -0.630111622
58 -0.276859648
59 -0.613309753
60 0.199570373
61 0.427027302
62 -0.821945904
63 0.171676834
64 0.125000000
65 -0.777919005
66 0.712474675
67 -1.081391252
68 0.526360996
69 1.481650983
70 -0.266863762
71 -1.578465799
72 0.0719245408
73 0.248297781
74 -0.968204684
75 -0.178501168
76 0.353001399
77 -0.952714919
78 1.097780352
79 0.532715929
80 -0.111803398
81 -0.755181561
82 0.483232307
83 0.256717146
84 0.376591640
85 -0.470791587
86 -1.116672714
87 -0.349450549
88 -0.399142863
89 0.958058832
90 -0.0643312650
91 -1.467942310
92 -0.830051140
93 -1.037455078
94 -1.169114739
95 -0.315734050
96 0.157774233
97 0.383692147
98 0.203531724
99 -0.229665337
100 0.100000000
101 0.0673365625
102 0.664369620
103 -1.414694753
104 -0.614998973
105 -0.336833803
106 0.699420086
107 0.227708642
108 0.537035635
109 0.944950722
110 0.357004230
111 -1.222062013
112 -0.210974328
113 0.569027539
114 0.445556201
115 0.742420309
116 0.195769334
117 -0.353868149
118 0.433675485
119 -0.888389260
120 -0.141117564
121 0.274520204
122 -0.301953901
123 0.609932853
124 0.581203522
125 -0.0894427190
126 -0.121393853
127 0.0315223515
128 -0.0883883476
129 -1.409457451
130 0.550071803
131 -1.639503729
132 -0.503795674
133 -0.595793865
134 0.764659087
135 -0.480339274
136 -0.372193429
137 0.205445411
138 -1.047685457
139 -1.477798122
140 0.188701175
141 -1.475649453
142 1.116143870
143 1.963779609
144 -0.0508583305
145 -0.175101416
146 -0.175573045
147 0.256896493
148 0.684624097
149 0.222353295
150 0.126219386
151 -0.135679613
152 -0.249609683
153 -0.214158734
154 0.673671180
155 -0.519844234
156 -0.776247931
157 -1.625470373
158 -0.376687046
159 0.882803736
160 0.0790569415
161 1.400955844
162 0.533994002
163 1.653572245
164 -0.341696841
165 0.450608549
166 -0.181526435
167 1.474903172
168 -0.266290503
169 2.025789900
170 0.332899923
171 -0.143624483
172 0.789606849
173 0.442126579
174 0.247098853
175 -0.168779462
176 0.282236625
177 0.547382654
178 -0.677449897
179 0.301654658
180 0.0454890737
181 -0.0448627871
182 1.037991961
183 -0.381124260
184 0.586934789
185 -0.612346408
186 0.733591521
187 1.188465826
188 0.826688960
189 -0.906402182
190 0.223257688
191 -0.0506836829
192 -0.111563230
193 1.840622086
194 -0.271311319
195 0.694297256
196 -0.143918662
197 0.00483034481
198 0.162397917
199 0.686630703
200 -0.0707106781
201 0.965127636
202 -0.0476141399
203 -0.330428715
204 -0.469780263
205 0.305622945
206 1.000340253
207 0.337597476
208 0.434869944
209 0.797120048
210 0.238177466
211 -1.247750908
212 -0.494564685
213 1.408326343
214 -0.161014325
215 -0.706245835
216 -0.379741539
217 -0.980166521
218 -0.668181063
219 -0.221771832
220 -0.252440112
221 1.830704671
222 0.864128337
223 0.239601847
224 0.149181378
225 -0.0406866644
226 -0.402363231
227 0.166298652
228 -0.315055811
229 0.0399361761
230 -0.524970435
231 0.848600672
232 -0.138429824
233 1.864723970
234 0.250222568
235 -0.739413084
236 -0.306654876
237 -0.375434349
238 0.628186070