Properties

Level 10
Symmetry odd
Weight 0
Character \( \chi_{10}(1,\cdot) \)
Multiplicity 1
Precision 0
Fricke Eigenvalue 1
Atkin-Lehner Eigenvalues n/a

Related objects

Downloads

Learn more about

Spectral parameter

$R= 14.712382788$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 1.027229132
4 0.5
5 -0.447213595
6 -0.726360685
7 0.711730781
8 -0.353553390
9 0.0551996915
10 0.316227766
11 1.372980515
12 0.513614566
13 -1.869077700
14 -0.503269662
15 -0.459390833
16 0.250000000
17 -1.581135045
18 -0.0390320761
19 0.344200819
20 -0.223606797
21 0.731110593
22 -0.970843832
23 0.269596353
24 -0.363180342
25 0.200000000
26 1.321637516
27 -0.970526401
28 0.355865390
29 0.956618098
30 0.324838373
31 -0.228936717
32 -0.176776695
33 1.410365584
34 1.118031312
35 -0.318295681
36 0.0275998457
37 1.070843377
38 -0.243386733
39 -1.919971065
40 0.158113883
41 -1.522617020
42 -0.516973258
43 0.119772102
44 0.686490257
45 -0.0246860525
46 -0.190633409
47 -0.796719155
48 0.256807283
49 -0.493439294
50 -0.141421356
51 -1.624187981
52 -0.934538850
53 -1.063261890
54 0.686265799
55 -0.614015552
56 -0.251634831
57 0.353573109
58 -0.676431144
59 -0.163568747
60 -0.229695416
61 0.494094954
62 0.161882705
63 0.0392873196
64 0.125000000
65 0.835876958
66 -0.997279068
67 -0.877421973
68 -0.790567522
69 0.276937228
70 0.225069035
71 0.333325624
72 -0.0195160380
73 -1.195995495
74 -0.757200613
75 0.205445826
76 0.172100409
77 0.977192495
78 1.357624560
79 -1.422799374
80 -0.111803398
81 -1.052152686
82 1.076652820
83 0.0899792682
84 0.365555296
85 0.707105088
86 -0.0846916660
87 0.982665978
88 -0.485421916
89 -0.989122190
90 0.0174556751
91 -1.330280137
92 0.134798176
93 -0.235170467
94 0.563365517
95 -0.153931286
96 -0.181590171
97 -0.327359973
98 0.348914271
99 0.0757880820
100 0.100000000
101 0.510476436
102 1.148474335
103 -1.921493869
104 0.660818758
105 -0.326962597
106 0.751839693
107 0.171340498
108 -0.485263200
109 -1.179487587
110 0.434174561
111 1.100001393
112 0.177932695
113 0.500667888
114 -0.250013943
115 -0.120567154
116 0.478309049
117 -0.103172464
118 0.115660570
119 -1.125343082
120 0.162419186
121 0.885073954
122 -0.349377892
123 -1.564079992
124 -0.114468358
125 -0.0894427190
126 -0.0277803301
127 -1.015791940
128 -0.0883883476
129 0.123026951
130 -0.591054265
131 0.721261074
132 0.705182792
133 0.244962309
134 0.620431027
135 0.434032601
136 0.559015656
137 1.660772134
138 -0.195824192
139 1.340696729
140 -0.159147840
141 -0.818575247
142 -0.235696809
143 -2.566272154
144 0.0137999228
145 -0.427812619
146 0.845696525
147 -0.506810539
148 0.535421688
149 0.481376998
150 -0.145272137
151 -1.479654485
152 -0.121693366
153 -0.0892687377
154 -0.690979439
155 0.102383612
156 -0.959985532
157 1.793921247
158 1.006071086
159 -1.091118055
160 0.0790569415
161 0.185035367
162 0.743984299
163 0.973090253
164 -0.761308510
165 -0.630734663
166 -0.0636249507
167 0.378228334
168 -0.258486629
169 2.491514208
170 -0.499998803
171 -0.115197697
172 0.0598860513