Properties

Level 10
Symmetry odd
Weight 0
Character \( \chi_{10}(1,\cdot) \)
Multiplicity 1
Precision 0
Fricke Eigenvalue 1
Atkin-Lehner Eigenvalues n/a

Related objects

Downloads

Learn more about

Spectral parameter

$R= 20.5489421376$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 0.800324233
4 0.5
5 0.447213595
6 0.565914692
7 0.541120349
8 0.353553390
9 -0.359481121
10 0.316227766
11 0.191877682
12 0.400162116
13 -1.855769790
14 0.382629868
15 0.357915878
16 0.250000000
17 -1.483355168
18 -0.254191538
19 -1.091077625
20 0.223606797
21 0.433071729
22 0.135678010
23 -0.529937681
24 0.282957346
25 0.200000000
26 -1.312227402
27 -1.088025686
28 0.270560174
29 0.0945939948
30 0.253084744
31 -1.178538063
32 0.176776695
33 0.153564359
34 -1.048890498
35 0.241996377
36 -0.179740560
37 1.091991106
38 -0.771508387
39 -1.485217534
40 0.158113883
41 -0.0471331813
42 0.306227956
43 -0.531263016
44 0.0959388414
45 -0.160764844
46 -0.374722528
47 1.049220409
48 0.200081058
49 -0.707188767
50 0.141421356
51 -1.187165088
52 -0.927884895
53 -1.394808089
54 -0.769350340
55 0.0858103084
56 0.191314934
57 -0.873215864
58 0.0668880552
59 1.251477919
60 0.178957939
61 0.232043451
62 -0.833352256
63 -0.194522550
64 0.125000000
65 -0.829925480
66 0.108586399
67 1.917259235
68 -0.741677584
69 -0.424121969
70 0.171117279
71 1.045273264
72 -0.127095769
73 1.616461313
74 0.772154316
75 0.160064846
76 -0.545538812
77 0.103828918
78 -1.050207390
79 0.205760527
80 0.111803398
81 -0.511292202
82 -0.0333281921
83 -0.826556686
84 0.216535864
85 -0.663376598
86 -0.375659681
87 0.0757058664
88 0.0678390053
89 -0.865985828
90 -0.113677911
91 -1.004194797
92 -0.264968840
93 -0.943212572
94 0.741910866
95 -0.487944747
96 0.141478673
97 -0.560749668
98 -0.500057972
99 -0.0689764046
100 0.100000000
101 -0.841637068
102 -0.839452484
103 0.0673929887
104 -0.656113701
105 0.193675565
106 -0.986278258
107 -0.324714646
108 -0.544012843
109 -1.475383363
110 0.0606770510
111 0.873946945
112 0.135280087
113 -0.0841403169
114 -0.617456858
115 -0.236995336
116 0.0472969974
117 0.667114207
118 0.884928523
119 -0.802673667
120 0.126542372
121 -0.963182953
122 0.164079498
123 -0.0377218310
124 -0.589269031
125 0.0894427190
126 -0.137548214
127 0.329380437
128 0.0883883476
129 -0.425182665
130 -0.586845934
131 -0.0224612214
132 0.0767821797
133 -0.590404296
134 1.355707007
135 -0.486579879
136 -0.524445249
137 -1.013231444
138 -0.299899520
139 -0.232192026
140 0.120998188
141 0.839716422
142 0.739119813
143 -0.356080896
144 -0.0898702802
145 0.0423037205
146 1.143010756
147 -0.565979759
148 0.545995553
149 0.127224292
150 0.113182938
151 0.947266048
152 -0.385754193
153 0.533237575
154 0.0734181326
155 -0.527058244
156 -0.742608767
157 -1.793318160
158 0.145494663
159 -1.116287208
160 0.0790569415
161 -0.286769199
162 -0.361538183
163 1.405547553
164 -0.0235665906
165 0.0686760693
166 -0.584463838
167 -0.784996405
168 0.153113978
169 2.443866438
170 -0.469078091
171 0.392106491
172 -0.265631508
173 0.377879357
174 0.0535321315
175 0.108224069
176 0.0479694207
177 1.001092891
178 -0.612344451
179 1.036621246
180 -0.0803824223
181 -0.919123635
182 -0.710072951
183 0.185836207
184 -0.187361264
185 0.488353269
186 -0.666952006
187 -0.286071404
188 0.524610204
189 -0.590378721
190 -0.345029039
191 -0.978033897
192 0.100040529
193 0.819762298
194 -0.396509893
195 -0.664209473
196 -0.353594383