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

$R= 28.522720264$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 0.0822174030
4 0.5
5 0.447213595
6 0.0581364832
7 -1.668828224
8 0.353553390
9 -0.993240298
10 0.316227766
11 1.805805903
12 0.0411087015
13 -1.640470665
14 -1.180039754
15 0.0367687404
16 0.250000000
17 0.582021674
18 -0.702326950
19 0.885891672
20 0.223606797
21 -0.137206722
22 1.276897599
23 -1.281479222
24 0.0290682416
25 0.200000000
26 -1.159987931
27 -0.163879040
28 -0.834414112
29 -1.161080578
30 0.0259994256
31 -0.0831270403
32 0.176776695
33 0.148468671
34 0.411551472
35 -0.746322670
36 -0.496620149
37 -0.126890462
38 0.626420008
39 -0.134875237
40 0.158113883
41 0.0481459917
42 -0.0970198040
43 1.466989981
44 0.902902951
45 -0.444190565
46 -0.906142647
47 -0.395132448
48 0.0205543507
49 1.784987643
50 0.141421356
51 0.0478523105
52 -0.820235332
53 0.623188239
54 -0.115879981
55 0.807580950
56 -0.590019877
57 0.0728357126
58 -0.821007950
59 0.273766806
60 0.0183843702
61 0.606240665
62 -0.0587796939
63 1.657547444
64 0.125000000
65 -0.733640784
66 0.104983204
67 0.0305521425
68 0.291010837
69 -0.105359893
70 -0.527729821
71 -0.913872338
72 -0.351163475
73 1.512899691
74 -0.0897251066
75 0.0164434806
76 0.442945836
77 -3.013579860
78 -0.0953711952
79 0.0591215104
80 0.111803398
81 0.979766589
82 0.0340443572
83 -0.952023001
84 -0.0686033613
85 0.260288005
86 1.037318563
87 -0.0954610298
88 0.638448799
89 1.615623900
90 -0.314090160
91 2.737663747
92 -0.640739611
93 -0.00683448938
94 -0.279400833
95 0.396182799
96 0.0145341208
97 -0.897136316
98 1.262176867
99 -1.793599194
100 0.100000000
101 -0.290457546
102 0.0338366933
103 1.770111310
104 -0.579993965
105 -0.0613607117
106 0.440660630
107 -0.121773824
108 -0.0819395204
109 0.389509249
110 0.571045966
111 -0.0104326043
112 -0.417207056
113 0.214789360
114 0.0515026263
115 -0.573094930
116 -0.580540289
117 1.629381573
118 0.193582365
119 -0.971294198
120 0.0129997128
121 2.260934961
122 0.428676885
123 0.00395843840
124 -0.0415635201
125 0.0894427190
126 1.172063037
127 0.130275210
128 0.0883883476
129 0.120612106
130 -0.518762373
131 0.0499595229
132 0.0742343358
133 -1.478401026
134 0.0216036271
135 -0.0732889351
136 0.205775736
137 1.198188501
138 -0.0745006952
139 -0.719120460
140 -0.373161335
141 -0.0324867635
142 -0.646205327
143 -2.962371611
144 -0.248310074
145 -0.519251020
146 1.069781631
147 0.146757049
148 -0.0634452313
149 1.631866164
150 0.0116272966
151 -0.380356872
152 0.313210004
153 -0.578087382
154 -2.130922754
155 -0.0371755425
156 -0.0674376189
157 -0.540089359
158 0.0418052209
159 0.0512369190
160 0.0790569415
161 2.138568706
162 0.692799599
163 -1.108069561
164 0.0240729958
165 0.0663972085
166 -0.673181920
167 -1.002035623
168 -0.0485099020
169 1.691144072
170 0.184051413
171 -0.879903396
172 0.733494990
173 1.326879997
174 -0.0675011415
175 -0.333765644
176 0.451451475
177 0.0225086170
178 1.142418615
179 0.299763540
180 -0.222095282
181 1.634814949
182 1.935820600
183 0.0498430989
184 -0.453071323
185 -0.0567471400
186 -0.00483271379
187 1.051020014
188 -0.197566224
189 0.273486241
190 0.280143544
191 0.850325527
192 0.0102771753
193 0.874450265
194 -0.634371172
195 -0.0603180400
196 0.892493821
197 -0.984783684
198 -1.268266153
199 1.448322770
200 0.0707106781
201 0.00248890990
202 -0.205384501
203 1.937594148
204 0.0239261552
205 0.0215315420
206 1.251657710
207 1.272884233
208 -0.410117666
209 1.599964671
210 -0.0433885754
211 -0.331194813
212 0.311594119
213 -0.0753565383
214 -0.0861070968
215 0.656057864
216 -0.0579399905
217 0.141031023
218 0.275424631
219 0.124372740
220 0.403790475
221 -0.956092135
222 -0.00737696525
223 0.230877960
224 -0.295009938
225 -0.198648059
226 0.151879013
227 0.399281510
228 0.0364178563
229 -0.584284013
230 -0.405239311
231 -0.233225002
232 -0.410503975
233 0.748665898
234 1.152146759
235 -0.176708603
236 0.136883403
237 0.00839608143
238 -0.686808713