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

$R= 15.1570371874$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -0.0128885988
4 0.5
5 -0.447213595
6 0.00911361567
7 -1.674540940
8 -0.353553390
9 -0.999833884
10 0.316227766
11 -0.278293544
12 -0.00644429944
13 -1.040565369
14 1.184079254
15 0.00576395665
16 0.250000000
17 0.634401937
18 0.706989319
19 -1.330632965
20 -0.223606797
21 0.0215824865
22 0.196783252
23 -0.877053353
24 0.00455680783
25 0.200000000
26 0.735790828
27 0.0257750567
28 -0.837270470
29 -0.154548156
30 -0.00407573283
31 -1.843445794
32 -0.176776695
33 0.00358681386
34 -0.448589912
35 0.748877474
36 -0.499916942
37 -1.263256450
38 0.940899593
39 0.0134114296
40 0.158113883
41 -1.315107147
42 -0.0152611225
43 0.696907031
44 -0.139146772
45 0.447139306
46 0.620170373
47 1.632670328
48 -0.00322214972
49 1.804087361
50 -0.141421356
51 -0.00817655212
52 -0.520282684
53 1.260630194
54 -0.0182257174
55 0.124456656
56 0.592039627
57 0.0171499945
58 0.109282049
59 -1.026719751
60 0.00288197832
61 0.829957327
62 1.303513021
63 1.674262772
64 0.125000000
65 0.465354980
66 -0.00253626040
67 -1.026557871
68 0.317200968
69 0.0113039886
70 -0.529536340
71 -0.214088021
72 0.353494659
73 -0.428230434
74 0.893257202
75 -0.00257771977
76 -0.665316482
77 0.466013933
78 -0.00948331286
79 -0.778025890
80 -0.111803398
81 0.999501675
82 0.929921181
83 0.0988261134
84 0.0107912432
85 -0.283713171
86 -0.492787688
87 0.00199190583
88 0.0983916262
89 0.0647859862
90 -0.316175235
91 1.742469277
92 -0.438526676
93 0.0237594061
94 -1.154472260
95 0.595077152
96 0.00227840391
97 -0.689729316
98 -1.275682407
99 0.278247188
100 0.100000000
101 0.321892521
102 0.00578169545
103 0.783889343
104 0.367895414
105 -0.00965198139
106 -0.891400159
107 -0.253064835
108 0.0128875283
109 0.963740276
110 -0.0880041458
111 0.0162793593
112 -0.418635235
113 0.747933405
114 -0.0121268774
115 0.392230183
116 -0.0772740780
117 1.040394613
118 0.726000498
119 -1.062333712
120 -0.00203786641
121 -0.922566116
122 -0.586868454
123 0.0169313393
124 -0.921722897
125 -0.0894427190
126 -1.183882559
127 1.265051849
128 -0.0883883476
129 -0.00895644708
130 -0.329055662
131 -0.895935443
132 0.00179340693
133 2.228078128
134 0.725886032
135 -0.0115269558
136 -0.224294956
137 -1.167678552
138 -0.00799312700
139 1.615058901
140 0.374438737
141 -0.0208891425
142 0.151383092
143 0.289201012
144 -0.249958471
145 0.0691160365
146 0.302804644
147 -0.0199210922
148 -0.631628225
149 -0.628667623
150 0.00182272313
151 -1.364553804
152 0.470449796
153 -0.633708565
154 -0.329521612
155 0.824414021
156 0.00670571483
157 -1.381386345
158 0.550147383
159 0.0315084526
160 0.0790569415
161 1.528394993
162 -0.706754412
163 0.620558353
164 -0.657553573
165 -0.00160407192
166 -0.0698806149