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

$R= 29.6437951433$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 0.657146895
4 0.5
5 0.447213595
6 -0.464673025
7 1.800812017
8 -0.353553390
9 -0.568157958
10 -0.316227766
11 -0.865075459
12 0.328573447
13 0.916463374
14 -1.273366389
15 0.293885025
16 0.250000000
17 0.0521462953
18 0.401748345
19 -1.499519830
20 0.223606797
21 1.183398025
22 0.611700723
23 1.755351544
24 -0.232336512
25 0.200000000
26 -0.648037466
27 -1.030510133
28 0.900406008
29 -0.814177902
30 -0.207808094
31 -0.681620456
32 -0.176776695
33 -0.568481651
34 -0.0368729990
35 0.805347617
36 -0.284078979
37 -1.397204568
38 1.060320640
39 0.602251060
40 -0.158113883
41 0.780351431
42 -0.836788768
43 -0.250176497
44 -0.432537729
45 -0.254087963
46 -1.241220980
47 -1.141599517
48 0.164286723
49 2.242923921
50 -0.141421356
51 0.0342677760
52 0.458231687
53 -1.432091487
54 0.728680703
55 -0.386873506
56 -0.636683194
57 -0.985404800
58 0.575710716
59 -0.272141011
60 0.146942512
61 -0.681036399
62 0.481978446
63 -1.023145679
64 0.125000000
65 0.409854880
66 0.401977231
67 -0.403813068
68 0.0260731476
69 1.153523817
70 -0.569466761
71 -1.522017727
72 0.200874172
73 -1.507214442
74 0.987972824
75 0.131429379
76 -0.749759915
77 -1.557838282
78 -0.425855809
79 0.159297658
80 0.111803398
81 -0.109038576
82 -0.551791788
83 0.0552044603
84 0.591699012
85 0.0233205322
86 0.176901497
87 -0.535034480
88 0.305850361
89 -0.599872669
90 0.179667321
91 1.650378257
92 0.877675772
93 -0.447924766
94 0.807232760
95 -0.670605654
96 -0.116168256
97 -1.355580690
98 -1.585986714
99 0.491499506
100 0.100000000
101 1.088483087
102 -0.0242309768
103 1.669399273
104 -0.324018733
105 0.529231686
106 1.012641601
107 0.0853548352
108 -0.515255066
109 1.015201283
110 0.273560879
111 -0.918168643
112 0.450203004
113 1.289472903
114 0.696786416
115 0.785017075
116 -0.407088951
117 -0.520695959
118 0.192432754
119 0.0939056753
120 -0.103904047
121 -0.251644449
122 0.481565456
123 0.512805520
124 -0.340810228
125 0.0894427190
126 0.723473247
127 0.108834933
128 -0.0883883476
129 -0.164402708
130 -0.289811165
131 0.360189291
132 -0.284240825
133 -2.700353330
134 0.285538959
135 -0.460858141
136 -0.0184364995
137 0.320319102
138 -0.815664513
139 -0.0259983876
140 0.402673808
141 -0.750198577
142 1.076229056
143 -0.792809974
144 -0.142039489
145 -0.364111427
146 1.065761552
147 1.473930490
148 -0.698602284
149 0.440320834
150 -0.0929346051
151 1.377679955
152 0.530160320
153 -0.0296273340
154 1.101558013
155 -0.304829935
156 0.301125530
157 -1.675673169
158 -0.112640454
159 -0.941094487
160 -0.0790569415
161 3.161058168
162 0.0771019165
163 -0.954353956
164 0.390175715
165 -0.254232723
166 -0.0390354482
167 1.900199181
168 -0.418394384
169 -0.160094934
170 -0.0164901064
171 0.851964206
172 -0.125088248
173 -0.184208929
174 0.378326509
175 0.360162403
176 -0.216268864
177 -0.178836579
178 0.424174032
179 0.462176231
180 -0.127043981
181 -0.571192130
182 -1.166993657
183 -0.447541350
184 -0.620610490
185 -0.624848878
186 0.316730639
187 -0.0451073844
188 -0.570799758
189 -1.855755905
190 0.474189806
191 -1.281622855
192 0.0821433618
193 -0.782010898
194 0.958540298
195 0.269334862
196 1.121461960
197 0.127879551
198 -0.347542634
199 -1.786793796
200 -0.0707106781
201 -0.265336989
202 -0.769673772
203 -1.466156614
204 0.0171338880
205 0.348983769
206 -1.180443546
207 -0.997140650
208 0.229115843
209 1.297219661
210 -0.374223313
211 0.139700315
212 -0.716045743
213 -0.999579655
214 -0.0603549828
215 -0.111882330
216 0.364340351
217 -1.226598406
218 -0.717855711
219 -0.988990710
220 -0.193436753
221 0.0510569977
222 0.649243274
223 0.144095316
224 -0.318341597
225 -0.113631591
226 -0.911795034
227 -0.525332431
228 -0.492702400
229 -0.390392807
230 -0.555090897
231 -0.996347007
232 0.287855358
233 1.189114175
234 0.368187643
235 -0.510538824
236 -0.136070505
237 0.166843464
238 -0.0664013398