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

$R= 14.6481407612$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 1.385435318
4 0.5
5 -0.447213595
6 0.979650708
7 1.361667025
8 0.353553390
9 0.919431021
10 -0.316227766
11 -1.377100082
12 0.692717659
13 1.645930560
14 0.962843987
15 -0.619585510
16 0.250000000
17 0.0847043257
18 0.650135910
19 0.664141306
20 -0.223606797
21 1.886501589
22 -0.973756806
23 1.298466047
24 0.489825354
25 0.200000000
26 1.163848660
27 -0.111623108
28 0.680833512
29 -1.340710730
30 -0.438113115
31 1.002714302
32 0.176776695
33 -1.907883091
34 0.0598950031
35 -0.608956006
36 0.459715510
37 -0.166118532
38 0.469618821
39 2.280330330
40 -0.158113883
41 -0.859026794
42 1.333958066
43 0.192022552
44 -0.688550041
45 -0.411182052
46 0.918154147
47 1.101821121
48 0.346358829
49 0.854137089
50 0.141421356
51 0.117352364
52 0.822965280
53 0.602475365
54 -0.0789294568
55 0.615857879
56 0.481421993
57 0.920124822
58 -0.948025649
59 -1.139019949
60 -0.309792755
61 1.514585919
62 0.709026083
63 1.251958904
64 0.125000000
65 -0.736082524
66 -1.349077071
67 -1.062076541
68 0.0423521628
69 1.798940722
70 -0.430596921
71 0.269208852
72 0.325067955
73 1.303681388
74 -0.117463541
75 0.277087063
76 0.332070653
77 -1.875151773
78 1.612437040
79 0.269640122
80 -0.111803398
81 -1.074077618
82 -0.607423671
83 -0.831560340
84 0.943250794
85 -0.0378809260
86 0.135780448
87 -1.857467998
88 -0.486878403
89 0.340920579
90 -0.290749617
91 2.241209369
92 0.649233023
93 1.389195803
94 0.779105186
95 -0.297013021
96 0.244912677
97 -1.338109948
98 0.603966127
99 -1.266148559
100 0.100000000
101 -0.925180253
102 0.0829806527
103 -0.562850008
104 0.581924330
105 -0.843669158
106 0.426014416
107 -0.420163014
108 -0.0558115541
109 0.999460652
110 0.435477282
111 -0.230146436
112 0.340416756
113 -1.004287227
114 0.650626501
115 -0.580691669
116 -0.670355365
117 1.513318767
118 -0.805408730
119 0.115337216
120 -0.219056557
121 0.896402430
122 1.070973974
123 -1.190130152
124 0.501357151
125 -0.0894427190
126 0.885268631
127 -0.0333520846
128 0.0883883476
129 0.266034415
130 -0.520488944
131 -0.976120459
132 -0.953941545
133 0.904313852
134 -0.751001524
135 0.0499193716
136 0.0299475015
137 -1.498364172
138 1.272043183
139 -0.518660114
140 -0.304478003
141 1.526400973
142 0.190359405
143 -2.266869701
144 0.229857755
145 0.599584066
146 0.921841950
147 1.183353642
148 -0.0830592664
149 0.158177139
150 0.195930141
151 -0.534374897
152 0.234809410
153 0.0786608253
154 -1.325932535
155 -0.448427468
156 1.140165165
157 -0.446195304
158 0.190664359
159 0.832170500
160 -0.0790569415
161 1.762583460
162 -0.759487567