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

$R= 22.5940390606$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -1.108560537
4 0.5
5 0.447213595
6 -0.783870673
7 0.146344007
8 0.353553390
9 0.228906466
10 0.316227766
11 -1.163325354
12 -0.554280268
13 1.460541175
14 0.103480840
15 -0.495763344
16 0.250000000
17 0.412258101
18 0.161861314
19 -0.867925669
20 0.223606797
21 -0.162231191
22 -0.822595247
23 0.0678769167
24 -0.391935336
25 0.200000000
26 1.032758569
27 0.854803862
28 0.0731720037
29 -0.226359994
30 -0.350557622
31 0.354441808
32 0.176776695
33 1.289616581
34 0.291510498
35 0.0654470297
36 0.114453233
37 -0.934614162
38 -0.613716126
39 -1.619098310
40 0.158113883
41 -0.777528833
42 -0.114714775
43 -1.098872264
44 -0.581662677
45 0.102370083
46 0.0479962281
47 1.279926779
48 -0.277140134
49 -0.978583431
50 0.141421356
51 -0.457013062
52 0.730270587
53 -0.0855838414
54 0.604437607
55 -0.520254914
56 0.0517404200
57 0.962148146
58 -0.160060687
59 0.914746393
60 -0.247881672
61 -1.495643380
62 0.250628206
63 0.0334990896
64 0.125000000
65 0.653173870
66 0.911896629
67 1.370838336
68 0.206129050
69 -0.0752456713
70 0.0462780385
71 1.566947160
72 0.0809306572
73 0.620681931
74 -0.660872012
75 -0.221712107
76 -0.433962834
77 -0.170245694
78 -1.144875395
79 1.403788310
80 0.111803398
81 -1.176508295
82 -0.549795911
83 0.778414700
84 -0.0811155958
85 0.184367427
86 -0.777020030
87 0.250933757
88 -0.411297623
89 -1.851460791
90 0.0723865804
91 0.213741448
92 0.0339384583
93 -0.392920201
94 0.905044904
95 -0.388148159
96 -0.195967668
97 1.429835411
98 -0.691962980
99 -0.266292696
100 0.100000000
101 -1.059294942
102 -0.323157035
103 1.190431975
104 0.516379284
105 -0.0725519945
106 -0.0605169146
107 1.737645736
108 0.427401931
109 0.845670498
110 -0.367875778
111 1.036076378
112 0.0365860018
113 1.025645628
114 0.680341479
115 0.0303554799
116 -0.113179997
117 0.334327319
118 0.646823377
119 0.0603315036
120 -0.175278811
121 0.353325879
122 -1.057579576
123 0.861937782
124 0.177220904
125 0.0894427190
126 0.0236874334
127 0.575995344
128 0.0883883476
129 1.218166431
130 0.461863672
131 1.020956639
132 0.644808290
133 -0.127015719
134 0.969329083
135 0.382279908
136 0.145755249
137 0.985526057
138 -0.0532067244
139 -1.092468500
140 0.0327235148
141 -1.418876275
142 1.107998962
143 -1.699084398
144 0.0572266165
145 -0.101231267
146 0.438888402
147 1.084819227
148 -0.467307081
149 0.877400760
150 -0.156774134
151 0.753759289
152 -0.306858063
153 0.0943683847
154 -0.120381885
155 0.158511195
156 -0.809549155
157 0.850151986
158 0.992628233
159 0.0948734036
160 0.0790569415
161 0.00993691485
162 -0.831916994
163 0.607427708
164 -0.388764416
165 0.576734068
166 0.550422313
167 -0.972496660
168 -0.0573573878
169 1.133197015
170 0.130367458
171 -0.198622022
172 -0.549436132
173 -0.704120009
174 0.177436961
175 0.0292688015
176 -0.290831338
177 -1.014149509
178 -1.309180480
179 1.081541161
180 0.0511850419
181 -0.0618085144
182 0.151138027
183 1.658359075
184 0.0239981140
185 -0.417972160
186 -0.277836539
187 -0.478602848
188 0.639963389
189 0.126247356
190 -0.274462195
191 1.345507716
192 -0.138570067
193 1.083203198
194 1.011046315
195 -0.724082777
196 -0.489291715
197 -1.007082749
198 -0.188297371