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

$R= 25.7533242596$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -0.168725066
4 0.5
5 -0.447213595
6 -0.119306638
7 1.057567966
8 0.353553390
9 -0.971531852
10 -0.316227766
11 0.238378379
12 -0.0843625330
13 -0.938095438
14 0.747813480
15 0.0754561434
16 0.250000000
17 1.571456514
18 -0.686976760
19 0.287880280
20 -0.223606797
21 -0.178438225
22 0.168558968
23 -1.772356603
24 -0.0596533192
25 0.200000000
26 -0.663333646
27 0.332646842
28 0.528783983
29 0.196682006
30 0.0533555507
31 0.168826782
32 0.176776695
33 -0.0402204078
34 1.111187557
35 -0.472958772
36 -0.485765926
37 -1.246648324
38 0.203562098
39 0.158280214
40 -0.158113883
41 -0.0564700098
42 -0.126174878
43 1.038191547
44 0.119189189
45 0.434482252
46 -1.253245373
47 -1.129357882
48 -0.0421812665
49 0.118450003
50 0.141421356
51 -0.265144104
52 -0.469047719
53 0.967221986
54 0.235216837
55 -0.106606052
56 0.373906740
57 -0.0485726194
58 0.139075180
59 1.928571629
60 0.0377280717
61 0.00817734051
62 0.119378562
63 -1.027460965
64 0.125000000
65 0.419529034
66 -0.0284401231
67 -1.859614254
68 0.785728257
69 0.299040985
70 -0.334432355
71 -0.923831901
72 -0.343488380
73 -0.460336396
74 -0.881513483
75 -0.0337450132
76 0.143940140
77 0.252101338
78 0.111921013
79 0.0970755426
80 -0.111803398
81 0.915405991
82 -0.0399303269
83 -0.493418198
84 -0.0892191125
85 -0.702776717
86 0.734112283
87 -0.0331851846
88 0.0842794843
89 -1.744216332
90 0.307225347
91 -0.992099685
92 -0.886178301
93 -0.0284853100
94 -0.798576616
95 -0.128743975
96 -0.0298266596
97 1.023740489
98 0.0837568008
99 -0.231592188
100 0.100000000
101 -1.344695106
102 -0.187485194
103 1.251769300
104 -0.331666823
105 0.0798000002
106 0.683929225
107 -0.940556809
108 0.166323421
109 -0.629479042
110 -0.0753818624
111 0.210340820
112 0.264391991
113 0.522649812
114 -0.0343460285
115 0.792621969
116 0.0983410034
117 0.911389599
118 1.363706077
119 1.661922070
120 0.0266777753
121 -0.943175748
122 0.00578225292
123 0.00952790607
124 0.0844133912
125 -0.0894427190
126 -0.726524615
127 -0.0660677689
128 0.0883883476
129 -0.175168937
130 0.296651824
131 -0.800991319
132 -0.0201102039
133 0.304452962
134 -1.314945850
135 -0.148764190
136 0.555593778
137 -0.444748344
138 0.211453908
139 0.0372489677
140 -0.236479386
141 0.190550983
142 -0.653247802
143 -0.223621673
144 -0.242882963
145 -0.0879588675
146 -0.325506987
147 -0.0199854766
148 -0.623324162
149 -1.628289958
150 -0.0238613276
151 -0.604831926
152 0.101781049
153 -1.526720046
154 0.178262565
155 -0.0755016324
156 0.0791401074
157 -1.728392524
158 0.0686427744
159 -0.163194613
160 -0.0790569415
161 -1.874387490
162 0.647289784
163 0.645122869
164 -0.0282350049
165 0.0179871132
166 -0.348899354
167 -1.054124642
168 -0.0630874394
169 -0.119977033
170 -0.496938182
171 -0.279685070
172 0.519095773
173 0.253865689
174 -0.0234654690
175 0.211513593
176 0.0595945948
177 -0.325399160
178 -1.233347196
179 -0.448490464
180 0.217241126
181 -0.695219757
182 -0.701520415
183 -0.00137365750
184 -0.626622686
185 0.557518079
186 -0.0201421558
187 0.374594936
188 -0.564678941
189 0.351816545
190 -0.0910357380
191 0.323990812
192 -0.0210906332
193 -1.651004900
194 0.723893842
195 -0.0707850640
196 0.0592250018
197 -0.921644348
198 -0.163760406
199 0.916399987
200 0.0707106781
201 0.313216701
202 -0.950843028
203 0.207968203
204 -0.132572052
205 0.0252541561
206 0.885134561
207 1.721987464
208 -0.234523859
209 0.0681355086
210 0.0564271212
211 -1.716139978
212 0.483610993
213 0.151980895
214 -0.665074097
215 -0.464293374
216 0.117608418
217 0.179812048
218 -0.445108899
219 0.0896849531
220 -0.0533030260
221 -1.503564054
222 0.148733420
223 0.0693649504
224 0.186953370
225 -0.194306370
226 0.369569226