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

$R= 28.7563609961$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -1.125563500
4 0.5
5 0.447213595
6 -0.795893584
7 -0.508985761
8 0.353553390
9 0.266893194
10 0.316227766
11 -1.786276090
12 -0.562781750
13 0.552266682
14 -0.359907283
15 -0.503367300
16 0.250000000
17 -1.834573995
18 0.188721987
19 -1.108175146
20 0.223606797
21 0.572895796
22 -1.263087936
23 1.521188422
24 -0.397946792
25 0.200000000
26 0.390511516
27 0.825158262
28 -0.254492880
29 -1.740575448
30 -0.355934431
31 -1.351490084
32 0.176776695
33 2.010567169
34 -1.297239713
35 -0.227625352
36 0.133446597
37 0.376446822
38 -0.783598160
39 -0.621611220
40 0.158113883
41 -0.342442417
42 0.405098502
43 0.901175207
44 -0.893138045
45 0.119358265
46 1.075642649
47 1.113115433
48 -0.281390875
49 -0.740933494
50 0.141421356
51 2.064929529
52 0.276133341
53 -0.131345329
54 0.583475003
55 -0.798846952
56 -0.179953641
57 1.247321497
58 -1.230772702
59 -1.315391129
60 -0.251683650
61 0.384719664
62 -0.955647803
63 -0.135844835
64 0.125000000
65 0.246981168
66 1.421685679
67 -0.880147305
68 -0.917286997
69 -1.712194166
70 -0.160955430
71 -0.185623447
72 0.0943609937
73 -0.711030254
74 0.266188101
75 -0.225112700
76 -0.554087573
77 0.909189096
78 -0.439545509
79 -1.648904369
80 0.111803398
81 -1.195661217
82 -0.242143355
83 -0.0485571828
84 0.286447898
85 -0.820446432
86 0.637227100
87 1.959128194
88 -0.631543968
89 1.695392696
90 0.0843990385
91 -0.281095878
92 0.760594211
93 1.521187910
94 0.787091471
95 -0.495590991
96 -0.198973396
97 0.162234299
98 -0.523919098
99 -0.476744931
100 0.100000000
101 -1.068946303
102 1.460125672
103 0.103255951
104 0.195255758
105 0.256206788
106 -0.0928751734
107 -0.0444723749
108 0.412579131
109 0.180731985
110 -0.564870097
111 -0.423714803
112 -0.127246440
113 0.184975270
114 0.881989488
115 0.680296143
116 -0.870287724
117 0.147396219
118 -0.930121987
119 0.933772043
120 -0.177967215
121 2.190782270
122 0.272037883
123 0.385440686
124 -0.675745042
125 0.0894427190
126 -0.0960568046
127 0.721712995
128 0.0883883476
129 -1.014329921
130 0.174642059
131 1.623807206
132 1.005283584
133 0.564045371
134 -0.622358128
135 0.369021993
136 -0.648619856
137 -0.981347180
138 -1.210704105
139 1.053020160
140 -0.113812676
141 -1.252882104
142 -0.131255598
143 -0.986500770
144 0.0667232985
145 -0.778409004
146 -0.502774314
147 0.833967697
148 0.188223411
149 -0.427717914
150 -0.159178716
151 0.554855934
152 -0.391799080
153 -0.489635315
154 0.642893775
155 -0.604404739
156 -0.310805610
157 0.411673817
158 -1.165951461
159 0.147837509
160 0.0790569415
161 -0.774263250
162 -0.845460154
163 0.730203098
164 -0.171221208
165 0.899152972
166 -0.0343351132
167 1.072047136
168 0.202549251
169 -0.695001457
170 -0.580143236
171 -0.295764376
172 0.450587603
173 -0.0354396518
174 1.385312831
175 -0.101797152
176 -0.446569022
177 1.480556254
178 1.198823672
179 -0.130299377
180 0.0596791325
181 -0.0238962625
182 -0.198764801
183 -0.433026253
184 0.537821324
185 0.168352137
186 1.075642287
187 3.277056244
188 0.556557716
189 -0.419993819
190 -0.350435750
191 0.611987650
192 -0.140695437
193 1.330828883
194 0.114716973
195 -0.277992989
196 -0.370466747
197 -1.030249084
198 -0.337109574
199 0.377957139
200 0.0707106781
201 0.990652863
202 -0.755859180
203 0.885935998
204 1.032464764
205 -0.153144904
206 0.0730129837
207 0.405946475
208 0.138066670
209 1.979558966
210 0.181165557
211 1.471109340
212 -0.0656726649
213 0.209172243
214 -0.0314467178
215 0.403017804
216 0.291737501
217 0.687728902
218 0.127796812
219 0.800190608
220 -0.399423476
221 -1.012101444
222 -0.299611610
223 -0.625136401
224 -0.0899768209
225 0.0533786388
226 0.130797267
227 0.356956853
228 0.623660748
229 -0.656191613
230 0.481042016
231 -1.026659941
232 -0.615386351
233 0.101634215
234 0.104224866
235 0.497800355
236 -0.657695564
237 1.816706670
238 0.660276543
239 0.364426982
240 -0.125841825