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

$R= 24.0655991316$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 1.464521427
4 0.5
5 -0.447213595
6 1.035573032
7 -0.656644386
8 0.353553390
9 1.144823012
10 -0.316227766
11 1.249617451
12 0.732260713
13 -1.912152587
14 -0.464317698
15 -0.654953893
16 0.250000000
17 0.0251615880
18 0.809512115
19 -1.317267343
20 -0.223606797
21 -0.961669774
22 0.883612973
23 -0.271129593
24 0.517786516
25 0.200000000
26 -1.352096061
27 0.212096405
28 -0.328322193
29 1.084267560
30 -0.463122339
31 -1.528247544
32 0.176776695
33 1.830091533
34 0.0177919295
35 0.293660297
36 0.572411506
37 1.268273090
38 -0.931448670
39 -2.800388437
40 -0.158113883
41 -1.385924397
42 -0.680003218
43 -0.496194477
44 0.624808725
45 -0.511980415
46 -0.191717574
47 -0.776566707
48 0.366130356
49 -0.568818149
50 0.141421356
51 0.0368496848
52 -0.956076293
53 0.888065518
54 0.149974806
55 -0.558845913
56 -0.232158849
57 -1.929166249
58 0.766692944
59 -0.501648321
60 -0.327476946
61 0.278075634
62 -1.080634202
63 -0.751741604
64 0.125000000
65 0.855140633
66 1.294070133
67 -1.529536093
68 0.0125807940
69 -0.397075099
70 0.207649187
71 -1.156685312
72 0.404756057
73 0.0393283697
74 0.896804502
75 0.292904285
76 -0.658633671
77 -0.820554284
78 -1.980173653
79 0.274828244
80 -0.111803398
81 -0.834203282
82 -0.979996539
83 0.150496737
84 -0.480834887
85 -0.0112526042
86 -0.350862479
87 1.587933076
88 0.441806486
89 0.323040920
90 -0.362024823
91 1.255604262
92 -0.135564796
93 -2.238151276
94 -0.549115584
95 0.589099864
96 0.258893258
97 1.464865037
98 -0.402215170
99 1.430590815
100 0.100000000
101 -0.0438516748
102 0.0260566620
103 1.017633589
104 -0.676048030
105 0.430071797
106 0.627957150
107 -1.392077947
108 0.106048202
109 1.239387240
110 -0.395163734
111 1.857413116
112 -0.164161096
113 -0.304991005
114 -1.364126537
115 0.121252840
116 0.542133780
117 -2.189076285
118 -0.354718930
119 -0.0165222155
120 -0.231561169
121 0.561543774
122 0.196629166
123 -2.029715977
124 -0.764123772
125 -0.0894427190
126 -0.531561586
127 -0.0674083019
128 0.0883883476
129 -0.726687444
130 0.604675740
131 -1.032142992
132 0.915045766
133 0.864976205
134 -1.081545343
135 -0.0948523959
136 0.00889596476
137 -0.416172316
138 -0.280774495
139 -1.752182288
140 0.146830148
141 -1.137298589
142 -0.817900028
143 -2.389459250
144 0.286205753
145 -0.484899194
146 0.0278093569
147 -0.833046385
148 0.634136545
149 0.403984485
150 0.207114606
151 1.637674654
152 -0.465724335
153 0.0288053408
154 -0.580219499
155 0.683453079
156 -1.400194218
157 -0.614705234
158 0.194332915
159 1.300590621
160 -0.0790569415
161 0.178035970
162 -0.589870797
163 -1.370712314
164 -0.692962198
165 -0.818441814
166 0.106417263
167 -0.882705184
168 -0.340001609
169 2.656330793
170 -0.00795679277
171 -1.508035927
172 -0.248097238
173 -0.366609614
174 1.122838246
175 -0.131328877
176 0.312404362
177 -0.734649297
178 0.228424425
179 -1.472237706
180 -0.255990207
181 1.918115290
182 0.887846288
183 0.407433778
184 -0.0958587870
185 -0.567188968
186 -1.582611944
187 0.0313893817
188 -0.388283353
189 -0.138975071
190 0.416556509
191 0.0163769765
192 0.183065178
193 -0.442339096
194 1.035816001
195 1.252371781
196 -0.284409074
197 0.567840640
198 1.011580466
199 -1.000717652
200 0.0707106781
201 -2.241540088
202 -0.0310078166
203 -0.710049899
204 0.0184248424
205 0.619804232
206 0.719575611
207 -0.325635982
208 -0.478038146
209 -1.641624508
210 0.304106684
211 1.655783247
212 0.444032759
213 -1.807402937
214 -0.984347756
215 0.221904916
216 0.0749874031
217 1.123443029
218 0.876379121
219 -0.179533656
220 -0.279422956
221 -0.538237867