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

$R= 27.0839397618$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 0.931785802
4 0.5
5 -0.447213595
6 -0.658872059
7 -0.767954458
8 -0.353553390
9 -0.131775217
10 0.316227766
11 -0.420698044
12 0.465892901
13 -1.600299419
14 0.543025805
15 -0.416707279
16 0.250000000
17 -0.843049615
18 0.0931791498
19 1.188317395
20 -0.223606797
21 -0.715569061
22 0.297478440
23 -1.417689107
24 -0.329436029
25 0.200000000
26 1.131582571
27 -1.054572079
28 -0.383977229
29 -0.884869555
30 0.294656542
31 -1.816611984
32 -0.176776695
33 -0.392000465
34 0.596126099
35 0.343439674
36 -0.0658876087
37 0.756304293
38 -0.840267288
39 -1.491136279
40 0.158113883
41 -0.0446178231
42 0.505983735
43 0.509000348
44 -0.210349022
45 0.0589316687
46 1.002457581
47 -0.167604654
48 0.232946450
49 -0.410245949
50 -0.141421356
51 -0.785541662
52 -0.800149709
53 1.829110787
54 0.745695068
55 0.188141885
56 0.271512902
57 1.107257278
58 0.625697263
59 -0.821179338
60 -0.208353639
61 0.365725396
62 1.284538653
63 0.101197365
64 0.125000000
65 0.715675657
66 0.277186187
67 1.384731333
68 -0.421524807
69 -1.320982583
70 -0.242848522
71 0.479873525
72 0.0465895749
73 -0.276131705
74 -0.534787894
75 0.186357160
76 0.594158697
77 0.323076938
78 1.054392574
79 0.464399491
80 -0.111803398
81 -0.850860074
82 0.0315495653
83 -1.826755557
84 -0.357784530
85 0.377023249
86 -0.359917598
87 -0.824508889
88 0.148739220
89 -1.579492017
90 -0.0416709826
91 1.228957073
92 -0.708844553
93 -1.692693256
94 0.118514387
95 -0.531431694
96 -0.164718014
97 -0.0700152537
98 0.290087693
99 0.0554375762
100 0.100000000
101 -0.142502472
102 0.555461836
103 0.453328481
104 0.565791285
105 0.320012212
106 -1.293376641
107 1.208705064
108 -0.527286039
109 -0.206048116
110 -0.133036402
111 0.704713603
112 -0.191988614
113 0.632132136
114 -0.782949129
115 0.634009842
116 -0.442434777
117 0.210879803
118 0.580661478
119 0.647423710
120 0.147328271
121 -0.823013155
122 -0.258606908
123 -0.0415742542
124 -0.908305992
125 -0.0894427190
126 -0.0715573435
127 -1.775439762
128 -0.0883883476
129 0.474279298
130 -0.506059110
131 -0.567118086
132 -0.196000232
133 -0.912573641
134 -0.979152916
135 0.471618971
136 0.298063049
137 0.164156104
138 0.934075742
139 -0.567934529
140 0.171719837
141 -0.156171636
142 -0.339321824
143 0.673242836
144 -0.0329438043
145 0.395725695
146 0.195254601
147 -0.382261353
148 0.378152146
149 -0.680688228
150 -0.131774411
151 1.279985509
152 -0.420133644
153 0.111093052
154 -0.228449894
155 0.812413577
156 -0.745568139
157 0.396033059
158 -0.328380029
159 1.704339466
160 0.0790569415
161 1.088720681
162 0.601648928
163 -0.760376531
164 -0.0223089115
165 0.175307937
166 1.291711242
167 1.432401239
168 0.252991867
169 1.560958305
170 -0.266595696
171 -0.156590345
172 0.254500174
173 1.313978625
174 0.583015826
175 -0.153590891
176 -0.105174511
177 -0.765163071
178 1.116869516
179 -0.548370704
180 0.0294658343
181 0.0516435025
182 -0.869003880
183 0.340779149
184 0.501228790
185 -0.338229562
186 1.196914880
187 0.354672456
188 -0.0838023273
189 0.809868566
190 0.375778955
191 0.637303322
192 0.116473225
193 0.859228720
194 0.0495082607
195 0.666856416
196 -0.205122974
197 0.467593062
198 -0.0392002861
199 -0.459920721
200 -0.0707106781
201 1.290209642
202 0.100764464
203 0.679441672
204 -0.392770831
205 0.0199536971
206 -0.320551643
207 0.186793210
208 -0.400074854
209 -0.500809292
210 -0.226282805
211 -1.477415481
212 0.914555393
213 0.445092296
214 -0.854683547
215 -0.227631876
216 0.372847534
217 1.391470924
218 0.145698020
219 -0.265691493
220 0.0940709425
221 1.335942160
222 -0.498307767
223 0.433458653
224 0.135756451
225 -0.0263550434
226 -0.446984920
227 0.856404209
228 0.553628639
229 -0.889623599
230 -0.448312659
231 0.120927822
232 0.312848631