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

$R= 14.20455634$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 0.967336646
4 0.5
5 0.447213595
6 0.684010302
7 1.901307143
8 0.353553390
9 -0.0642598127
10 0.316227766
11 1.085480675
12 0.483668323
13 -0.610875357
14 1.344427174
15 0.432606099
16 0.250000000
17 -0.955875024
18 -0.0454385493
19 1.132614345
20 0.223606797
21 1.839204075
22 0.767550746
23 -0.0738252460
24 0.342005151
25 0.200000000
26 -0.431954107
27 -1.029497518
28 0.950653571
29 -0.294241135
30 0.305898706
31 -1.269636896
32 0.176776695
33 1.050025236
34 -0.675905712
35 0.850290403
36 -0.0321299063
37 -1.070331677
38 0.800879284
39 -0.590922119
40 0.158113883
41 1.677552721
42 1.300513673
43 1.007525484
44 0.542740337
45 -0.0287378618
46 -0.0522023321
47 -0.880984706
48 0.241834161
49 2.614968852
50 0.141421356
51 -0.924652940
52 -0.305437678
53 0.871404122
54 -0.727964676
55 0.485441715
56 0.672213587
57 1.095619362
58 -0.208059902
59 0.215766011
60 0.216303049
61 0.623727769
62 -0.897768858
63 -0.122177640
64 0.125000000
65 -0.273191765
66 0.742479965
67 1.063784821
68 -0.477937512
69 -0.0714138660
70 0.601246110
71 -1.088585105
72 -0.0227192746
73 -1.283538093
74 -0.756838787
75 0.193467329
76 0.566307172
77 2.063832163
78 -0.417845038
79 -0.0629294658
80 0.111803398
81 -0.931610864
82 1.186208904
83 0.118835028
84 0.919602037
85 -0.427480306
86 0.712428102
87 -0.284630233
88 0.383775373
89 -1.440664996
90 -0.0203207370
91 -1.161461683
92 -0.0369126230
93 -1.228166286
94 -0.622950260
95 0.506520533
96 0.171002575
97 0.364997544
98 1.849062208
99 -0.0697527612
100 0.100000000
101 0.176273110
102 -0.653828364
103 0.951286464
104 -0.215977053
105 0.822517067
106 0.616175764
107 -1.134246734
108 -0.514748759
109 0.368189539
110 0.343259129
111 -1.035371503
112 0.475326785
113 -1.090913193
114 0.774719880
115 -0.0330156537
116 -0.147120567
117 0.0392489645
118 0.152569609
119 -1.817414898
120 0.152949353
121 0.178269928
122 0.441042135
123 1.622754665
124 -0.634818448
125 0.0894427190
126 -0.0863926384
127 -1.694927511
128 0.0883883476
129 0.974630729
130 -0.193175749
131 -0.888471302
132 0.525012618
133 2.153392887
134 0.752209460
135 -0.460405286
136 -0.337952856
137 0.794855529
138 -0.0504972289
139 -0.422377368
140 0.425145201
141 -0.852473231
142 -0.769745910
143 -0.664072694
144 -0.0160649531
145 -0.131588636
146 -0.907598489
147 2.527729972
148 -0.535165838
149 -1.228181934
150 0.136802060
151 -0.735058017
152 0.400439642
153 0.0610591416
154 1.459349717
155 -0.567798881
156 -0.295461059
157 -0.555932461
158 -0.0444978520
159 0.834654652
160 0.0790569415
161 -0.0732649213
162 -0.658748359