Properties

Level 10
Symmetry even
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

$R= 28.3486863507$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 1.140801869
4 0.5
5 0.447213595
6 0.806668738
7 0.740059958
8 0.353553390
9 0.301428906
10 0.316227766
11 -0.512139031
12 0.570400934
13 1.005614456
14 0.523301415
15 0.510182105
16 0.250000000
17 0.382661722
18 0.213142423
19 -0.499963194
20 0.223606797
21 0.844261784
22 -0.362136981
23 0.0204269381
24 0.403334369
25 0.200000000
26 0.711076801
27 -0.796931210
28 0.370029979
29 1.193127890
30 0.360753226
31 1.179530914
32 0.176776695
33 -0.584249164
34 0.270582699
35 0.330964874
36 0.150714453
37 -0.365080921
38 -0.353527365
39 1.147206852
40 0.158113883
41 1.758964211
42 0.596983232
43 -0.580017177
44 -0.256069515
45 0.134803104
46 0.0144440265
47 -0.708827303
48 0.285200467
49 -0.452311257
50 0.141421356
51 0.436541208
52 0.502807228
53 0.285935446
54 -0.563515462
55 -0.229035537
56 0.261650707
57 -0.570358947
58 0.843668822
59 1.362002676
60 0.255091052
61 1.298648581
62 0.834054308
63 0.223075463
64 0.125000000
65 0.449724456
66 -0.413126545
67 0.880109363
68 0.191330861
69 0.0233030892
70 0.234027507
71 0.518800548
72 0.106571211
73 -1.125905532
74 -0.258151195
75 0.228160373
76 -0.249981597
77 -0.379013590
78 0.811197744
79 -0.888672794
80 0.111803398
81 -1.210569520
82 1.243775521
83 0.816937139
84 0.422130892
85 0.171131524
86 -0.410134079
87 1.361122528
88 -0.181068490
89 1.693323769
90 0.0953201895
91 0.744214993
92 0.0102134690
93 1.345611072
94 -0.501216593
95 -0.223590337
96 0.201667184
97 -1.170353472
98 -0.319832357
99 -0.154373507
100 0.100000000
101 -0.0232505105
102 0.308681248
103 -0.487845507
104 0.355538400
105 0.377565348
106 0.202186893
107 1.548274059
108 -0.398465605
109 0.820824870
110 -0.161952581
111 -0.416484997
112 0.185014989
113 -1.057390450
114 -0.403304679
115 0.00913520446
116 0.596563945
117 0.303121265
118 0.963081328
119 0.283192618
120 0.180376613
121 -0.737713612
122 0.918283218
123 2.006629660
124 0.589765457
125 0.0894427190
126 0.157738173
127 -0.553715391
128 0.0883883476
129 -0.661684679
130 0.318003213
131 -0.993988170
132 -0.292124582
133 -0.370002741
134 0.622331299
135 -0.356398471
136 0.135291349
137 -0.542902064
138 0.0164777724
139 -0.997743376
140 0.165482437
141 -0.808631513
142 0.366847385
143 -0.515014413
144 0.0753572265
145 0.533583013
146 -0.796135436
147 -0.515997529
148 -0.182540460
149 -1.711188632
150 0.161333747
151 1.180555210
152 -0.176763682
153 0.115345304
154 -0.268003079
155 0.527502261
156 0.573603426
157 -0.958884210
158 -0.628386558
159 0.326195691
160 0.0790569415
161 0.0151171657
162 -0.856001917
163 1.036933525
164 0.879482105
165 -0.261284169
166 0.577661791
167 -0.558997803
168 0.298491616
169 0.0112604628
170 0.121008261
171 -0.150703363
172 -0.290008588
173 0.480003832
174 0.962458969
175 0.148011991
176 -0.128034757
177 1.553775466
178 1.197360720
179 -0.141834325
180 0.0674015524
181 1.375345970
182 0.526239468
183 1.481500255
184 0.00722201325
185 -0.163269151
186 0.951490714
187 -0.195976556
188 -0.354413651
189 -0.589774100
190 -0.158102244
191 1.491580214
192 0.142600233
193 -1.318449828
194 -0.827564876
195 0.513046501
196 -0.226155628
197 1.663506924
198 -0.109158554
199 1.517067803
200 0.0707106781
201 1.004029692
202 -0.0164405936
203 0.883024411
204 0.218270604
205 0.786632709
206 -0.344958866
207 0.00617094817
208 0.251403614
209 0.256282394
210 0.266979018
211 -0.256115175
212 0.142967723
213 0.592112366
214 1.094795086
215 -0.259391567
216 -0.281757731
217 0.872738753
218 0.580410832
219 -1.283546146
220 -0.114517768
221 0.387216844
222 -0.294499366
223 -0.221824818
224 0.130825353
225 0.0602857812
226 -0.747687957
227 -0.315581318
228 -0.285179473
229 1.568912214
230 0.00645956502
231 -0.404387823
232 0.421834411
233 0.125493212
234 0.214339102
235 -0.316997207
236 0.681001338
237 -0.866493588
238 0.200247421