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

$R= 28.8519682703$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -0.942469602
4 0.5
5 -0.447213595
6 0.666426646
7 1.191277825
8 -0.353553390
9 -0.111751048
10 0.316227766
11 -1.452646586
12 -0.471234801
13 1.411580201
14 -0.842360628
15 0.421485219
16 0.250000000
17 -1.268924551
18 0.0790199241
19 0.264181875
20 -0.223606797
21 -1.122743138
22 1.027176252
23 -1.512614823
24 0.333213323
25 0.200000000
26 -0.998137932
27 1.047791568
28 0.595638912
29 0.881835843
30 -0.298035056
31 0.791215638
32 -0.176776695
33 1.369075251
34 0.897265154
35 -0.532755639
36 -0.0558755242
37 -0.252755345
38 -0.186804795
39 -1.330371431
40 0.158113883
41 1.385808546
42 0.793899286
43 -1.730033953
44 -0.726323293
45 0.0499765881
46 1.069580199
47 -0.288157175
48 -0.235617400
49 0.419142856
50 -0.141421356
51 1.195922817
52 0.705790100
53 1.911019714
54 -0.740900523
55 0.649643303
56 -0.421180314
57 -0.248983386
58 -0.623552104
59 -1.102891976
60 0.210742609
61 -0.780806491
62 -0.559473943
63 -0.133126545
64 0.125000000
65 -0.631277857
66 -0.968082393
67 -0.434541375
68 -0.634462275
69 1.425593491
70 0.376715125
71 -0.846754329
72 0.0395099620
73 0.612598805
74 0.178725019
75 -0.188493920
76 0.132090937
77 -1.730505666
78 0.940714660
79 1.159092514
80 -0.111803398
81 -0.875760654
82 -0.979914620
83 -0.953807286
84 -0.561371569
85 0.567480310
86 1.223318739
87 -0.831103476
88 0.513588126
89 -0.619859156
90 -0.0353387843
91 1.681584192
92 -0.756307411
93 -0.745696687
94 0.203757892
95 -0.118145726
96 0.166606661
97 -1.100287590
98 -0.296378756
99 0.162334779
100 0.100000000
101 -1.412806163
102 -0.845645133
103 0.196518594
104 -0.499068966
105 0.502105995
106 -1.351294999
107 -0.621034557
108 0.523895784
109 -0.785794953
110 -0.459367184
111 0.238214230
112 0.297819456
113 -0.851171361
114 0.176057841
115 0.676461914
116 0.440917921
117 -0.157745567
118 0.779862395
119 -1.511641679
120 -0.149017528
121 1.110182105
122 0.552113565
123 -1.306082429
124 0.395607819
125 -0.0894427190
126 0.0941346833
127 -0.0751428612
128 -0.0883883476
129 1.630504412
130 0.446380853
131 0.346059743
132 0.684537625
133 0.314714009
134 0.307267153
135 -0.468586634
136 0.448632577
137 -0.497968445
138 -1.008046825
139 -1.216556734
140 -0.266377819
141 0.271579378
142 0.598745728
143 -2.050527161
144 -0.0279377621
145 -0.394368978
146 -0.433172769
147 -0.395029401
148 -0.126377672
149 -1.190861941
150 0.133285329
151 1.245536100
152 -0.0934023976
153 0.141803649
154 1.223652291
155 -0.353842390
156 -0.665185715
157 1.791858295
158 -0.819602176
159 -1.801077988
160 0.0790569415
161 -1.801944501
162 0.619256297
163 -1.393363569
164 0.692904273
165 -0.612269065
166 0.674443600
167 0.0992979783
168 0.396949643
169 0.992558646
170 -0.401269176
171 -0.0295225599
172 -0.865016976
173 1.663674150
174 0.587678904
175 0.238255565
176 -0.363161646
177 1.039442106
178 0.438306612
179 0.204954006
180 0.0249882940
181 1.002625769
182 -1.189059585
183 0.735885679
184 0.534790099
185 0.113035627
186 0.527287184
187 1.843299022
188 -0.144078587
189 1.248209484
190 0.0835416442
191 -0.0136531594
192 -0.117808700
193 -1.588410618
194 0.778020816
195 0.594960191
196 0.209571428
197 1.212915626
198 -0.114788023
199 -0.266133811
200 -0.0707106781
201 0.409539244
202 0.999004818
203 1.050498251
204 0.597961408
205 -0.619752422
206 -0.138959630
207 0.169029312
208 0.352895050
209 -0.383799436
210 -0.355042554
211 1.588681280
212 0.955509857
213 0.798147003
214 0.439137746
215 0.773694704
216 -0.370450261
217 0.943105645
218 0.555640940
219 -0.577226676
220 0.324821651
221 -1.792302843
222 -0.168442897
223 0.453383469
224 -0.210590157
225 -0.0223502096
226 0.601869041
227 0.266882212
228 -0.124491693
229 -0.0148863251
230 -0.478330806
231 1.637992890
232 -0.311776052
233 0.263805039
234 0.111542960
235 0.128867806
236 -0.551445988
237 -1.100224180
238 1.068892082
239 0.521105818
240 0.105371304