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

$R= 14.8197544572$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -0.264364223
4 0.5
5 0.447213595
6 -0.186933734
7 -1.315500342
8 0.353553390
9 -0.930111557
10 0.316227766
11 0.671694045
12 -0.132182111
13 1.453023758
14 -0.930199212
15 -0.118227274
16 0.250000000
17 0.241896709
18 -0.657688189
19 -1.362882450
20 0.223606797
21 0.347771225
22 0.474959414
23 1.850622537
24 -0.0934668674
25 0.200000000
26 1.027442952
27 0.510252442
28 -0.657750171
29 -1.331542723
30 -0.0835993076
31 0.812315773
32 0.176776695
33 -0.177571874
34 0.171046803
35 -0.588309637
36 -0.465055778
37 0.733883506
38 -0.963703423
39 -0.384127496
40 0.158113883
41 1.422560660
42 0.245911392
43 0.594910048
44 0.335847022
45 -0.415958533
46 1.308587745
47 0.882991435
48 -0.0660910557
49 0.730541150
50 0.141421356
51 -0.0639488356
52 0.726511879
53 0.626951177
54 0.360802962
55 0.300390709
56 -0.465099606
57 0.360297360
58 -0.941542889
59 1.288902634
60 -0.0591136373
61 0.0119322878
62 0.574393992
63 1.223562072
64 0.125000000
65 0.649811979
66 -0.125562276
67 -0.544010900
68 0.120948354
69 -0.489238389
70 -0.415997734
71 1.510243653
72 -0.328844094
73 -0.805608168
74 0.518934003
75 -0.0528728446
76 -0.681441225
77 -0.883613746
78 -0.271619157
79 1.002893712
80 0.111803398
81 0.795219066
82 1.005902289
83 -0.724513757
84 0.173885612
85 0.108179497
86 0.420664929
87 0.352012256
88 0.237479707
89 0.0206560917
90 -0.294127099
91 -1.911453252
92 0.925311268
93 -0.214747228
94 0.624369231
95 -0.609499561
96 -0.0467334337
97 -1.708935470
98 0.516570601
99 -0.624750392
100 0.100000000
101 0.431092515
102 -0.0452186553
103 1.032661884
104 0.513721476
105 0.155528020
106 0.443321429
107 0.694543545
108 0.255126221
109 -0.659117779
110 0.212408307
111 -0.194012432
112 -0.328875085
113 -0.564049601
114 0.254768706
115 0.827623558
116 -0.665771361
117 -1.351473908
118 0.911391792
119 -0.318215192
120 -0.0417996538
121 -0.548826750
122 0.00843740168
123 -0.376072824
124 0.406157886
125 0.0894427190
126 0.865189038
127 -1.029821465
128 0.0883883476
129 -0.157274194
130 0.459486457
131 -0.329081625
132 -0.0887859372
133 1.792875989
134 -0.384673796
135 0.228191829
136 0.0855234017
137 -0.331141178
138 -0.345943782
139 -0.125311560
140 -0.294154818
141 -0.233446298
142 1.067903528
143 0.975970943
144 -0.232527889
145 -0.595484008
146 -0.569650998
147 -0.193035170
148 0.366941753
149 0.670460532
150 -0.0373867469
151 -0.818349391
152 -0.481851711
153 -0.225349992
154 -0.624809272
155 0.363278657
156 -0.192063748
157 1.037342999
158 0.709152944
159 -0.163476343
160 0.0790569415
161 -2.441397254
162 0.562304794
163 -1.164762208
164 0.711280330
165 -0.0794125564
166 -0.512308591
167 0.841813133
168 0.122955696
169 1.155489468
170 0.0764944559
171 1.295868223
172 0.297455024
173 0.595813091
174 0.248910253