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

$R= 13.3121869995$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 1.314971969
4 0.5
5 0.447213595
6 -0.929825596
7 0.917647866
8 -0.353553390
9 0.729151279
10 -0.316227766
11 -1.929780429
12 0.657485984
13 -1.856797388
14 -0.648875028
15 0.588073342
16 0.250000000
17 -0.535991941
18 -0.515587814
19 -0.998533767
20 0.223606797
21 1.206681221
22 1.364560827
23 0.201042261
24 -0.464912798
25 0.200000000
26 1.312954024
27 -0.356158475
28 0.458823933
29 0.0715020116
30 -0.415830648
31 0.759722033
32 -0.176776695
33 -2.537607171
34 0.379003536
35 0.410384601
36 0.364575639
37 -0.825097385
38 0.706069997
39 -2.441636517
40 -0.158113883
41 -0.0959027925
42 -0.853252474
43 -1.161112361
44 -0.964890214
45 0.326086365
46 -0.142158346
47 1.425181083
48 0.328742992
49 -0.157922393
50 -0.141421356
51 -0.704814379
52 -0.928398694
53 0.198475581
54 0.251842072
55 -0.863024044
56 -0.324437514
57 -1.313043913
58 -0.0505595573
59 0.404895279
60 0.294036671
61 1.020324162
62 -0.537204601
63 0.669104115
64 0.125000000
65 -0.830385036
66 1.794359238
67 -0.885586572
68 -0.267995970
69 0.264364938
70 -0.290185734
71 -0.134808088
72 -0.257793907
73 -0.726051015
74 0.583431956
75 0.262994393
76 -0.499266883
77 -1.770858893
78 1.726497738
79 0.404975315
80 0.111803398
81 -1.197489688
82 0.0678135149
83 -0.188060935
84 0.603340610
85 -0.239702883
86 0.821030424
87 0.0940231352
88 0.682280413
89 1.404477437
90 -0.230577880
91 -1.703886153
92 0.100521130
93 0.999013203
94 -1.007755208
95 -0.446557876
96 -0.232456399
97 0.0724270828
98 0.111667995
99 -1.407101824
100 0.100000000
101 -0.251067421
102 0.498379027
103 0.845212829
104 0.656477012
105 0.539644247
106 -0.140343429
107 -1.498057523
108 -0.178079237
109 0.288565481
110 0.610250154
111 -1.084980150
112 0.229411966
113 1.093371232
114 0.928462255
115 0.0899088324
116 0.0357510058
117 -1.353886290
118 -0.286304197
119 -0.491855220
120 -0.207915324
121 2.724064661
122 -0.721478134
123 -0.126091503
124 0.379861016
125 0.0894427190
126 -0.473128057
127 0.738729060
128 -0.0883883476
129 -1.526710421
130 0.587170889
131 -1.061539245
132 -1.268803585
133 -0.916423498
134 0.626204270
135 -0.159278912
136 0.189501768
137 0.267936555
138 -0.186934240
139 -1.057507301
140 0.205192300
141 1.875598994
142 0.0953237134
143 3.583692208
144 0.182287819
145 0.0319766717
146 0.513395596
147 -0.212181000
148 -0.412548692
149 -1.334828448
150 -0.185965119
151 -1.750665903
152 0.353034998
153 -0.362050091
154 1.252186332
155 0.339758022
156 -1.220818258