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

$R= 19.9058807142$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 1.461198431
4 0.5
5 0.447213595
6 -1.033223319
7 0.299236994
8 -0.353553390
9 1.135100854
10 -0.316227766
11 -1.599091316
12 0.730599215
13 0.572306904
14 -0.211592507
15 0.653467804
16 0.250000000
17 0.180151533
18 -0.802637511
19 -0.162652296
20 0.223606797
21 0.437244626
22 1.130728313
23 -1.517038596
24 -0.516611659
25 0.200000000
26 -0.404682093
27 0.197409157
28 0.149618497
29 -0.907412759
30 -0.462071515
31 -1.844354156
32 -0.176776695
33 -2.336589722
34 -0.127386371
35 0.133822852
36 0.567550427
37 -1.443154931
38 0.115012541
39 0.836253950
40 -0.158113883
41 1.871848907
42 -0.309178640
43 0.150646865
44 -0.799545658
45 0.507632534
46 1.072708278
47 -0.0312624437
48 0.365299607
49 -0.910457221
50 -0.141421356
51 0.263237138
52 0.286153452
53 0.247275574
54 -0.139589353
55 -0.715135377
56 -0.105796253
57 -0.237667279
58 0.641637715
59 0.121263381
60 0.326733902
61 0.104192581
62 1.304155330
63 0.339664168
64 0.125000000
65 0.255943428
66 1.652218437
67 0.289109663
68 0.0900757668
69 -2.216694416
70 -0.0946270462
71 1.464967674
72 -0.401318755
73 -0.927011395
74 1.020464638
75 0.292239686
76 -0.0813261480
77 -0.478507279
78 -0.591320839
79 -0.0699483241
80 0.111803398
81 -0.846646904
82 -1.323597055
83 0.347467382
84 0.218622313
85 0.0805662151
86 -0.106523419
87 -1.325910100
88 0.565364156
89 -0.983830243
90 -0.358950407
91 0.171255397
92 -0.758519298
93 -2.694967399
94 0.0221058859
95 -0.0727403181
96 -0.258305829
97 -0.296286056
98 0.643790475
99 -1.815129920
100 0.100000000
101 1.417417647
102 -0.186136765
103 -0.224465548
104 -0.202341046
105 0.195541741
106 -0.174850235
107 1.468932601
108 0.0987045785
109 -1.884898351
110 0.505677074
111 -2.108735721
112 0.0748092485
113 -1.789964155
114 0.168056145
115 -0.678440285
116 -0.453706379
117 0.649626056
118 -0.0857461590
119 0.0539080157
120 -0.231035757
121 1.557093032
122 -0.0736752809
123 2.735142702
124 -0.922177078
125 0.0894427190
126 -0.240178836
127 -0.967643131
128 -0.0883883476
129 0.220124964
130 -0.180979333
131 -0.367063030
132 -1.168294861
133 -0.0486716315
134 -0.204431403
135 0.0882840589
136 -0.0636931855
137 -0.583466868
138 1.567439653
139 0.929401317
140 0.0669114260
141 -0.0456803406
142 -1.035888576
143 -0.915172042
144 0.283775213
145 -0.405807322
146 0.655496044
147 -1.330358186
148 -0.721577465
149 1.633823892
150 -0.206644663
151 1.253083161
152 0.0575062707
153 0.204495074
154 0.338355742
155 -0.824820253
156 0.418126975
157 -0.986139509
158 0.0494609343
159 0.361332299
160 -0.0790569415
161 -0.453955586
162 0.598669767
163 1.901068941
164 0.935924453
165 -1.044954691
166 -0.245696542
167 -1.441821624
168 -0.154589320
169 -0.672633008
170 -0.0569689170
171 -0.184418338
172 0.0753234326
173 -1.237230244
174 0.937560023
175 0.0598473988
176 -0.399772829
177 0.176480888
178 0.695673036
179 0.450875899
180 0.253816267
181 -1.080429742
182 -0.121095853
183 0.153452663
184 0.536354139
185 -0.645398505
186 1.905629722
187 -0.293385973
188 -0.0156312218
189 0.0907169981
190 0.0514351722