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

$R= 12.4596489912$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -0.853825301
4 0.5
5 0.447213595
6 -0.603745660
7 1.789748957
8 0.353553390
9 -0.270982353
10 0.316227766
11 -1.409375906
12 -0.426912650
13 -0.452488940
14 1.265543624
15 -0.381842283
16 0.250000000
17 1.430488888
18 -0.191613460
19 0.0535442925
20 0.223606797
21 -1.528132943
22 -0.996579260
23 1.534605561
24 -0.301872830
25 0.200000000
26 -0.319957998
27 1.085196891
28 0.894874478
29 0.127322680
30 -0.270003267
31 -0.798448014
32 0.176776695
33 1.203360808
34 1.011508393
35 0.800400066
36 -0.135491176
37 1.839660897
38 0.0378615323
39 0.386346506
40 0.158113883
41 0.230714310
42 -1.080553167
43 0.421643250
44 -0.704687953
45 -0.121186992
46 1.085129999
47 0.289060842
48 -0.213456325
49 2.203201330
50 0.141421356
51 -1.221387606
52 -0.226244470
53 -0.279495565
54 0.767350081
55 -0.630292066
56 0.632771812
57 -0.0457174717
58 0.0900307310
59 0.740305329
60 -0.190921141
61 -0.605669183
62 -0.564588005
63 -0.484990385
64 0.125000000
65 -0.202359205
66 0.850904588
67 -0.273875602
68 0.715244444
69 -1.310285057
70 0.565968314
71 0.0322399637
72 -0.0958067300
73 1.403221796
74 1.300836695
75 -0.170765060
76 0.0267721462
77 -2.522429060
78 0.273188234
79 0.585724300
80 0.111803398
81 -0.655586209
82 0.163139653
83 -0.291751204
84 -0.764066471
85 0.639734079
86 0.298146801
87 -0.108711320
88 -0.498289630
89 0.0767044714
90 -0.0856921444
91 -0.809841600
92 0.767302780
93 0.681735143
94 0.204396882
95 0.0239457355
96 -0.150936415
97 0.322174839
98 1.557898601
99 0.381916030
100 0.100000000
101 -1.411189006
102 -0.863651459
103 0.864938041
104 -0.159978999
105 -0.683401828
106 -0.197633209
107 0.772039570
108 0.542598445
109 -0.981173393
110 -0.445683794
111 -1.570747641
112 0.447437239
113 -1.282381179
114 -0.0323271342
115 0.686296471
116 0.0636613404
117 0.122619905
118 0.523474918
119 2.560216458
120 -0.135001633
121 0.986343539
122 -0.428272786
123 -0.196971802
124 -0.399224007
125 0.0894427190
126 -0.342939990
127 0.118923786
128 0.0883883476
129 -0.359974121
130 -0.143089566
131 -1.010615403
132 0.601680404
133 0.0956748983
134 -0.193659295
135 0.485314803
136 0.505754196
137 -0.602623972
138 -0.926511449
139 -0.964242226
140 0.400200033
141 -0.246530333
142 0.0227970969
143 0.636674518
144 -0.0677455884
145 0.0569404338
146 0.992227647
147 -1.874049292
148 0.919830448
149 0.806723236
150 -0.120749132
151 1.484932438
152 0.0189307661
153 -0.376936901
154 -1.783626693
155 -0.357076807
156 0.193173253
157 -0.906814481
158 0.414169625
159 0.242233969
160 0.0790569415
161 2.654105115
162 -0.463569454