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

$R= 22.3710520524$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 1.056908496
4 0.5
5 -0.447213595
6 -0.747347164
7 -0.824789287
8 -0.353553390
9 0.117055569
10 0.316227766
11 1.193090884
12 0.528454248
13 -0.400043352
14 0.583214097
15 -0.472663848
16 0.250000000
17 -1.023229091
18 -0.0827707866
19 -0.706763069
20 -0.223606797
21 -0.871726804
22 -0.843642655
23 0.656435248
24 -0.373673582
25 0.200000000
26 0.282873367
27 -0.933191470
28 -0.412394643
29 0.516988135
30 0.334223812
31 -0.929411531
32 -0.176776695
33 1.260987892
34 0.723532228
35 0.368856982
36 0.0585277845
37 -0.0821905380
38 0.499756958
39 -0.422809217
40 0.158113883
41 1.348400693
42 0.616403935
43 0.839240082
44 0.596545442
45 -0.0523488419
46 -0.464169815
47 1.736519781
48 0.264227124
49 -0.319722632
50 -0.141421356
51 -1.081459519
52 -0.200021676
53 -0.824536047
54 0.659866017
55 -0.533566464
56 0.291607048
57 -0.746983892
58 -0.365565816
59 -1.476514741
60 -0.236331924
61 -0.447356795
62 0.657193196
63 -0.0965461793
64 0.125000000
65 0.178904825
66 -0.891653089
67 1.582426112
68 -0.511614545
69 0.693791991
70 -0.260821273
71 0.288301194
72 -0.0413853933
73 0.337920675
74 0.0581174868
75 0.211381699
76 -0.353381534
77 -0.984048580
78 0.298971264
79 -1.352877379
80 -0.111803398
81 -1.103353562
82 -0.953463273
83 1.157695968
84 -0.435863402
85 0.457601960
86 -0.593432353
87 0.546409152
88 -0.421821327
89 0.173056129
90 0.0370162211
91 0.329951471
92 0.328217624
93 -0.982302943
94 -1.227904913
95 0.316074053
96 -0.186836791
97 -1.582576924
98 0.226078041
99 0.139657932
100 0.100000000
101 1.712787664
102 0.764707359
103 1.805490375
104 0.141436683
105 0.389848078
106 0.583035030
107 -0.193649056
108 -0.466595735
109 1.631465898
110 0.377288465
111 -0.0868678780
112 -0.206197321
113 -0.0982335924
114 0.528197375
115 -0.293566767
116 0.258494067
117 -0.0468273021
118 1.044053586
119 0.843948391
120 0.167111906
121 0.423465857
122 0.316329023
123 1.425136148
124 -0.464705765
125 -0.0894427190
126 0.0682684581
127 0.363244063
128 -0.0883883476
129 0.886999976
130 -0.126504815
131 0.591477491
132 0.630493946
133 0.582930597
134 -1.118944234
135 0.417335912
136 0.361766114
137 1.731308856
138 -0.490585021
139 -1.699371531
140 0.184428491
141 1.835342507
142 -0.203859729
143 -0.477288065
144 0.0292638922
145 -0.231204122
146 -0.238946001
147 -0.337917435
148 -0.0410952690
149 0.219422028
150 -0.149469432
151 0.189419817
152 0.249878479
153 -0.119774472
154 0.695827423
155 0.415645472
156 -0.211404608
157 0.186500778
158 0.956628769
159 -0.871457691
160 0.0790569415
161 -0.541417206
162 0.780188786
163 1.603818100
164 0.674200346
165 -0.563930929
166 -0.818614669
167 -0.753975397
168 0.308201967
169 -0.839979843
170 -0.323573449
171 -0.0827098937
172 0.419620041
173 0.384119713
174 -0.386369617
175 -0.164957857
176 0.298272721
177 -1.560460868
178 -0.122369162
179 1.667675279
180 -0.0261744209
181 0.287014536
182 -0.233310922
183 -0.472929955
184 -0.232084907
185 0.0367567260
186 0.694593072
187 -1.221634541
188 0.868259890
189 0.769608901
190 -0.223498106
191 0.0314902287
192 0.132113562
193 0.431073730
194 1.119050875
195 0.189086030
196 -0.159861316
197 -1.436030675
198 -0.0987530710
199 1.038181195
200 -0.0707106781
201 1.665354056
202 -1.211123772
203 -0.426600423
204 -0.540729759
205 -0.603023122
206 -1.276674488
207 0.112321846
208 -0.100010838
209 -0.867471153
210 -0.275664220