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

$R= 8.953063681$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -0.932667354
4 0.5
5 0.447213595
6 -0.659495411
7 0.176261254
8 0.353553390
9 -0.130131605
10 0.316227766
11 -0.167368102
12 -0.466333677
13 -0.758909315
14 0.124635528
15 -0.417101521
16 0.250000000
17 -1.572128645
18 -0.0920169404
19 -1.564365529
20 0.223606797
21 -0.164393117
22 -0.118347120
23 -0.260928017
24 -0.329747705
25 0.200000000
26 -0.536629923
27 1.054036854
28 0.0881306270
29 -0.888899023
30 -0.294935314
31 -0.323058358
32 0.176776695
33 0.156098765
34 -1.111662826
35 0.0788264292
36 -0.0650658025
37 1.484102368
38 -1.106173474
39 0.707809943
40 0.158113883
41 1.801012749
42 -0.116243488
43 -1.408299749
44 -0.0836840511
45 -0.0581966230
46 -0.184503970
47 -1.133688313
48 -0.233166838
49 -0.968931970
50 0.141421356
51 1.466273065
52 -0.379454657
53 0.783747286
54 0.745316607
55 -0.0748492908
56 0.0623177640
57 1.459032660
58 -0.628546527
59 -1.107437377
60 -0.208550760
61 -0.0781485310
62 -0.228436756
63 -0.0229371599
64 0.125000000
65 -0.339394563
66 0.110378495
67 0.944980759
68 -0.786064322
69 0.243359044
70 0.0557387026
71 -1.219797277
72 -0.0460084702
73 -0.0906830151
74 1.049418848
75 -0.186533470
76 -0.782182764
77 -0.0295005116
78 0.500497211
79 1.469824250
80 0.111803398
81 -0.852934160
82 1.273508328
83 0.235716918
84 -0.0821965588
85 -0.703077304
86 -0.995818302
87 0.829047101
88 -0.0591735600
89 -0.360919025
90 -0.0411512267
91 -0.133766307
92 -0.130464008
93 0.301305984
94 -0.801638694
95 -0.699605533
96 -0.164873852
97 1.166966189
98 -0.685138366
99 0.0217798798
100 0.100000000
101 -0.755015899
102 1.036811627
103 0.390196299
104 -0.268314961
105 -0.0735188372
106 0.554193020
107 -0.272324100
108 0.527018427
109 1.010770799
110 -0.0529264411
111 -1.384173830
112 0.0440653135
113 1.454895999
114 1.031691888
115 -0.116690557
116 -0.444449511
117 0.0987580873
118 -0.783076479
119 -0.277105366
120 -0.147467657
121 -0.971987918
122 -0.0552593562
123 -1.679745797
124 -0.161529179
125 0.0894427190
126 -0.0162190213
127 -0.381759999
128 0.0883883476
129 1.313475202
130 -0.239988197
131 0.583300000
132 0.0780493826
133 -0.275737030
134 0.668202303
135 0.471379611
136 -0.555831413
137 1.943000000
138 0.172080830
139 -1.131999999
140 0.0394132146
141 1.057354080
142 -0.862526926
143 0.127017212
144 -0.0325329012
145 -0.397527728
146 -0.0641225749
147 0.903691217
148 0.742051184
149 -1.100000000
150 -0.131899082
151 -1.580000000
152 -0.553086737
153 0.204583624
154 -0.0208600118
155 -0.144476090
156 0.353904971