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

$R= 18.6547712142$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 1.960694744
4 0.5
5 -0.447213595
6 -1.386420549
7 0.0615814938
8 -0.353553390
9 2.844323879
10 0.316227766
11 -0.790624144
12 0.980347372
13 -1.500931252
14 -0.0435446918
15 -0.876849346
16 0.250000000
17 0.351555565
18 -2.011240703
19 0.219278474
20 -0.223606797
21 0.120742511
22 0.559055693
23 0.894961957
24 -0.693210274
25 0.200000000
26 1.061318666
27 3.616156138
28 0.0307907469
29 1.500591460
30 0.620026118
31 0.147463261
32 -0.176776695
33 -1.550172604
34 -0.248587324
35 -0.0275400812
36 1.422161939
37 0.464326348
38 -0.155053296
39 -2.942868017
40 0.158113883
41 0.845928262
42 -0.0853778485
43 1.679428038
44 -0.395312072
45 -1.272020309
46 -0.632833669
47 0.975578671
48 0.490173686
49 -0.996207719
50 -0.141421356
51 0.689293149
52 -0.750465626
53 0.564682168
54 -2.557008527
55 0.353577866
56 -0.0217723459
57 0.429938152
58 -1.061078397
59 -1.260939708
60 -0.438424673
61 0.892276419
62 -0.104272271
63 0.175157713
64 0.125000000
65 0.671236861
66 1.096137560
67 -1.111122503
68 0.175777782
69 1.754747206
70 0.0194737782
71 0.248854043
72 -1.005620351
73 0.636239658
74 -0.328328309
75 0.392138948
76 0.109639237
77 -0.0486878158
78 2.080921931
79 0.225037941
80 -0.111803398
81 4.245854454
82 -0.598161610
83 -1.917671675
84 0.0603712556
85 -0.157220428
86 -1.187534954
87 2.942201790
88 0.279527846
89 0.0867452800
90 0.899454186
91 -0.0924295886
92 0.447480978
93 0.289130441
94 -0.689838293
95 -0.0980643149
96 -0.346605137
97 1.213275214
98 0.704425234
99 -2.248791134
100 0.100000000
101 0.901361342
102 -0.487403860
103 0.194407087
104 0.530659333
105 -0.0539976926
106 -0.399290590
107 0.735066899
108 1.808078069
109 1.302645887
110 -0.250017306
111 0.910402229
112 0.0153953734
113 -1.387723902
114 -0.304012183
115 -0.400239154
116 0.750295730
117 -4.269134608
118 0.891619018
119 0.0216492865
120 0.310013059
121 -0.374913481
122 -0.630934706
123 1.658607122
124 0.0737316306
125 -0.0894427190
126 -0.123855207
127 0.845819094
128 -0.0883883476
129 3.292845668
130 -0.474636136
131 0.0940373494
132 -0.775086302
133 0.0135034799
134 0.785682256
135 -1.617194188
136 -0.124293662
137 -1.208178237
138 -1.240793648
139 -0.162647690
140 -0.0137700406
141 1.912811243
142 -0.175966381
143 1.186673510
144 0.711080969
145 -0.671084902
146 -0.449889376
147 -1.953265039
148 0.232163174
149 0.509403122
150 -0.277284109
151 0.176677961
152 -0.0775266481
153 0.999926954
154 0.0344274847
155 -0.0659475752
156 -1.471434008
157 1.361729035
158 -0.159125854
159 1.107174441
160 0.0790569415
161 0.0550944419
162 -3.002272476
163 0.165907794
164 0.422964131
165 0.693258264
166 1.355998646
167 -0.106194238
168 -0.0426889242
169 1.253667992
170 0.111171631
171 0.623992382
172 0.839714019
173 -0.681160526
174 -2.080450837
175 0.0123162987
176 -0.197656036
177 -2.472558790
178 -0.0613381757
179 0.735657878
180 -0.636010154
181 -0.0353716041
182 0.0653575888
183 1.728616385
184 -0.316416834
185 -0.207653055
186 -0.204446095
187 -0.324697325
188 0.487789335
189 0.336644486
190 0.0693419421
191 0.0305727615
192 0.245086843