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

$R= 19.3345983161$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -1.567876662
4 0.5
5 0.447213595
6 -1.108656220
7 -1.779966850
8 0.353553390
9 1.458237229
10 0.316227766
11 0.191442020
12 -0.783938331
13 -0.442808244
14 -1.258626629
15 -0.701175759
16 0.250000000
17 -1.460146644
18 1.031129433
19 -0.475906164
20 0.223606797
21 2.790768484
22 0.135369950
23 -0.541289448
24 -0.554328110
25 0.200000000
26 -0.313112712
27 -0.718459458
28 -0.889983425
29 -1.975061720
30 -0.495806134
31 1.033149673
32 0.176776695
33 -0.300157476
34 -1.032479593
35 -0.796025374
36 0.729118614
37 -1.413586841
38 -0.336516476
39 0.694268711
40 0.158113883
41 -0.476999756
42 1.973371320
43 0.645526772
44 0.0957210103
45 0.652143514
46 -0.382749439
47 -1.048096000
48 -0.391969165
49 2.168281987
50 0.141421356
51 2.289329847
52 -0.221404122
53 -0.860976048
54 -0.508027554
55 0.0856154743
56 -0.629313314
57 0.746162168
58 -1.396579535
59 0.169572527
60 -0.350587879
61 -0.0733736938
62 0.730547139
63 -2.595613928
64 0.125000000
65 -0.198029866
66 -0.212243386
67 1.588870248
68 -0.730073322
69 0.848675093
70 -0.562874940
71 1.001943627
72 0.515564716
73 1.277939321
74 -0.999556841
75 -0.313575332
76 -0.237953082
77 -0.340760450
78 0.490922114
79 1.691028363
80 0.111803398
81 -0.331781411
82 -0.337289762
83 0.736645004
84 1.395384242
85 -0.652997430
86 0.456456358
87 3.096653178
88 0.0676849754
89 0.814658253
90 0.461135101
91 0.788183995
92 -0.270644724
93 -1.619851261
94 -0.741115789
95 -0.212831706
96 -0.277164055
97 0.669044477
98 1.533206896
99 0.279167881
100 0.100000000
101 0.0858963579
102 1.618800659
103 -0.794145828
104 -0.156556356
105 1.248069608
106 -0.608802002
107 0.313675347
108 -0.359229729
109 -0.749634740
110 0.0605392824
111 2.216329819
112 -0.444991712
113 -0.180565659
114 0.527616329
115 -0.242072000
116 -0.987530860
117 -0.645719465
118 0.119905883
119 2.599012627
120 -0.247903067
121 -0.963349923
122 -0.0518830365
123 0.747876792
124 0.516574836
125 0.0894427190
126 -1.835376209
127 -0.751470060
128 0.0883883476
129 -1.012106416
130 -0.140028261
131 1.413678345
132 -0.150078738
133 0.847097070
134 1.123500927
135 -0.321304837
136 -0.516239796
137 -1.150099317
138 0.600103913
139 1.110290991
140 -0.398012687
141 1.643286187
142 0.708481133
143 -0.0847717606
144 0.364559307
145 -0.883274453
146 0.903639560
147 -3.399599860
148 -0.706793420
149 1.894685045
150 -0.221731244
151 -0.646495920
152 -0.168258238
153 -2.129234120
154 -0.240954025
155 0.462038579
156 0.347134355
157 -0.709903172
158 1.195737623
159 1.349895798
160 0.0790569415
161 0.963282635
162 -0.234604886
163 0.923072752
164 -0.238499878
165 -0.134234504
166 0.520886677
167 -1.125465772
168 0.986685660
169 -0.804113282
170 -0.461738911
171 -0.696123646
172 0.322763386
173 -0.760585465
174 2.189664461
175 -0.355993370
176 0.0478605051
177 -0.265450773
178 0.576050375
179 -1.636088620
180 0.326071757
181 0.116508176
182 0.557330247
183 0.113138373
184 -0.191374719
185 -0.632175254
186 -1.145407811
187 -0.288815204
188 -0.524048000
189 1.278587145
190 -0.150494743