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

$R= 20.6936600416$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -1.339850215
4 0.5
5 0.447213595
6 -0.947417173
7 0.758059368
8 0.353553390
9 0.795198601
10 0.316227766
11 1.718011073
12 -0.669925107
13 1.578773939
14 0.536028919
15 -0.599199232
16 0.250000000
17 -1.033399283
18 0.562290323
19 -0.363469585
20 0.223606797
21 -1.015686008
22 1.214817280
23 1.122444299
24 -0.473708586
25 0.200000000
26 1.116361758
27 0.274403198
28 0.379029684
29 0.0316289221
30 -0.423697840
31 -1.807098425
32 0.176776695
33 -2.301877507
34 -0.730723640
35 0.339014455
36 0.397599300
37 0.875977124
38 -0.257011809
39 -2.115320604
40 0.158113883
41 0.699021964
42 -0.718198463
43 -1.017312019
44 0.859005536
45 0.355623625
46 0.793687975
47 -0.148493919
48 -0.334962553
49 -0.425345994
50 0.141421356
51 1.384600252
52 0.789386969
53 -0.664374795
54 0.194032362
55 0.768317909
56 0.268014459
57 0.486994803
58 0.0223650253
59 1.077380029
60 -0.299599616
61 1.358705432
62 -1.277811551
63 0.602807749
64 0.125000000
65 0.706049170
66 -1.627673195
67 -0.373081907
68 -0.516699641
69 -1.503907237
70 0.239719420
71 -1.061083835
72 0.281145161
73 0.621044584
74 0.619409364
75 -0.267970043
76 -0.181734792
77 1.302354388
78 -1.495757543
79 0.392714543
80 0.111803398
81 -1.162857785
82 0.494283171
83 1.382984188
84 -0.507843004
85 -0.462150209
86 -0.719348227
87 -0.0423780181
88 0.607408640
89 1.162666628
90 0.251463877
91 1.196804375
92 0.561222149
93 2.421241215
94 -0.105001057
95 -0.162548540
96 -0.236854293
97 -0.874630992
98 -0.300765036
99 1.366160002
100 0.100000000
101 1.107954311
102 0.979060227
103 -0.0361129266
104 0.558180879
105 -0.454228591
106 -0.469783923
107 1.614137822
108 0.137201599
109 0.568858492
110 0.543282803
111 -1.173678138
112 0.189514842
113 -0.815124792
114 0.344357327
115 0.501972351
116 0.0158144610
117 1.255438829
118 0.761822724
119 -0.783378010
120 -0.211848920
121 1.951562047
122 0.960749824
123 -0.936584732
124 -0.903549212
125 0.0894427190
126 0.426249447
127 0.292579312
128 0.0883883476
129 1.363045710
130 0.499252156
131 -1.339076652
132 -1.150938753
133 -0.275531507
134 -0.263808746
135 0.122716841
136 -0.365361820
137 -0.917630472
138 -1.063423005
139 1.842840588
140 0.169507227
141 0.198959584
142 -0.750299575
143 2.712351260
144 0.198799650
145 0.0141448839
146 0.439144837
147 0.569898602
148 0.437988562
149 -0.278368673
150 -0.189483434
151 -0.754035650
152 -0.128505904
153 -0.821758858
154 0.920903619
155 -0.808158984
156 -1.057660302
157 -0.818644165
158 0.277691117
159 0.890157180
160 0.0790569415
161 0.850880984
162 -0.822264625
163 -0.250481219
164 0.349510982
165 -1.029430916
166 0.977917497
167 -0.580625255
168 -0.359099231
169 1.492500168
170 -0.326789546
171 -0.289132116
172 -0.508656009
173 1.097511743
174 -0.0299657839
175 0.151611873
176 0.429502768
177 -1.443200305
178 0.822129456
179 0.962038043
180 0.177811812
181 -0.265609299
182 0.846268489
183 -1.818225808
184 0.396843987
185 0.391748879
186 1.712076082
187 -1.776618964
188 -0.0742469599
189 0.210823711
190 -0.114939175
191 0.307604958
192 -0.167481276
193 -0.929184552
194 -0.618457506
195 -0.946000133
196 -0.212672997