Properties

Level 10
Symmetry odd
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

$R= 11.9357108569$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -0.150663366
4 0.5
5 -0.447213595
6 -0.106535088
7 0.822857299
8 0.353553390
9 -0.977300549
10 -0.316227766
11 0.0183129191
12 -0.0753316833
13 1.203617376
14 0.581847976
15 0.0673787058
16 0.250000000
17 -0.292599073
18 -0.691055846
19 1.138542757
20 -0.223606797
21 -0.123974450
22 0.0129491892
23 -0.623686591
24 -0.0532675441
25 0.200000000
26 0.851086008
27 0.297906757
28 0.411428649
29 1.533414038
30 0.0476439398
31 1.307613389
32 0.176776695
33 -0.00275908604
34 -0.206898788
35 -0.367992971
36 -0.488650274
37 1.534036927
38 0.805071304
39 -0.181341046
40 -0.158113883
41 1.312425911
42 -0.0876631749
43 0.857752894
44 0.00915645955
45 0.437062092
46 -0.441013018
47 -1.099101488
48 -0.0376658416
49 -0.322905865
50 0.141421356
51 0.0440839614
52 0.601808688
53 -0.126435883
54 0.210651888
55 -0.00818978639
56 0.290923988
57 -0.171536684
58 1.084287465
59 -0.911429582
60 0.0336893529
61 0.0733270291
62 0.924622294
63 -0.804178891
64 0.125000000
65 -0.538274054
66 -0.00195096845
67 0.763819968
68 -0.146299536
69 0.0939667217
70 -0.260210325
71 -0.918583441
72 -0.345527923
73 -0.839009043
74 1.084727914
75 -0.0301326733
76 0.569271378
77 0.0150689190
78 -0.128227483
79 0.226776898
80 -0.111803398
81 0.932416916
82 0.928025261
83 -1.241491155
84 -0.0619872254
85 0.130854283
86 0.606522888
87 -0.231029323
88 0.00647459464
89 -1.131743914
90 0.309049569
91 0.990405360
92 -0.311843295
93 -0.197009415
94 -0.777182115
95 -0.509171800
96 -0.0266337720
97 -1.239511813
98 -0.228328926
99 -0.0178970989
100 0.100000000
101 1.757075603
102 0.0311720680
103 0.492598901
104 0.425543004
105 0.0554430599
106 -0.0894036702
107 0.471650675
108 0.148953378
109 0.599319588
110 -0.00579105349
111 -0.231121522
112 0.205714324
113 -1.180432653
114 -0.121294753
115 0.278921123
116 0.766707019
117 -1.176291766
118 -0.644478038
119 -0.240755963
120 0.0238219699
121 -0.999653844
122 0.0518500395
123 -0.197738842
124 0.653806694
125 -0.0894427190
126 -0.568640347
127 1.927665900
128 0.0883883476
129 -0.129210603
130 -0.380617234
131 -0.928733389
132 -0.00137954302
133 0.936821773
134 0.540102279
135 -0.133227952
136 -0.103449394
137 1.748990874
138 0.0664445061
139 -0.400299536
140 -0.183996485
141 0.166838052
142 -0.649536580
143 0.0230858494
144 -0.244325137
145 -0.685763605
146 -0.593268983
147 0.0486037582
148 0.767018463
149 0.771179430
150 -0.0213070176
151 -1.548186843
152 0.402535652
153 0.294177182
154 0.0106553348
155 -0.584782485
156 -0.0906705230
157 0.349612628
158 0.160355482
159 0.124894997
160 -0.0790569415
161 -0.403721928
162 0.659318324