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

$R= 13.5633748047$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -1.354821340
4 0.5
5 0.447213595
6 -0.958003356
7 -1.011631704
8 0.353553390
9 0.835540863
10 0.316227766
11 0.400329452
12 -0.677410670
13 -1.225484391
14 -0.715331638
15 -0.605894522
16 0.250000000
17 -1.065984088
18 0.590816610
19 1.061320882
20 0.223606797
21 1.370580221
22 0.283075670
23 -1.208403211
24 -0.479001678
25 0.200000000
26 -0.866548323
27 0.222812747
28 -0.505815852
29 1.400672868
30 -0.428432125
31 0.804696799
32 0.176776695
33 -0.542374885
34 -0.753764577
35 -0.452415451
36 0.417770431
37 1.735929519
38 0.750467193
39 1.660312405
40 0.158113883
41 -0.297426119
42 0.969146568
43 -0.0433900781
44 0.200164726
45 0.373665233
46 -0.854470105
47 1.637120390
48 -0.338705335
49 0.0233987054
50 0.141421356
51 1.444217990
52 -0.612742195
53 0.299257152
54 0.157552404
55 0.179032773
56 -0.357665819
57 -1.437900180
58 0.990425283
59 1.950149426
60 -0.302947261
61 0.687672910
62 0.569006563
63 -0.845259627
64 0.125000000
65 -0.548053281
66 -0.383516959
67 -1.491570415
68 -0.532992044
69 1.637170457
70 -0.319906033
71 0.0262759134
72 0.295408305
73 -0.308705045
74 1.227487534
75 -0.270964268
76 0.530660441
77 -0.404985966
78 1.174018161
79 -0.802123748
80 0.111803398
81 -1.137412328
82 -0.210312025
83 1.653854955
84 0.685290110
85 -0.476722576
86 -0.0306814185
87 -1.897661488
88 0.141537835
89 -0.800028866
90 0.264221220
91 1.239738863
92 -0.604201605
93 -1.090220404
94 1.157618929
95 0.474637127
96 -0.239500839
97 -0.966729956
98 0.0165453832
99 0.334491618
100 0.100000000
101 -0.127206000
102 1.021216334
103 1.736046218
104 -0.433274161
105 0.612942108
106 0.211606761
107 -0.622460264
108 0.111406373
109 -0.135230615
110 0.126595288
111 -2.351874044
112 -0.252907926
113 0.0737114003
114 -1.016748968
115 -0.540414344
116 0.700336434
117 -1.023943699
118 1.378963884
119 1.078382782
120 -0.214216062
121 -0.839738189
122 0.486258178
123 0.402960277
124 0.402348399
125 0.0894427190
126 -0.597688814
127 1.748319287
128 0.0883883476
129 0.0587989205
130 -0.387532191
131 0.671639446
132 -0.271187442
133 -1.073617432
134 -1.054699555
135 0.0996448899
136 -0.376882288
137 0.429936437
138 1.157654332
139 1.232045027
140 -0.226207725
141 -2.217997927
142 0.0185798766
143 -0.490429064
144 0.208885215
145 0.626399949
146 -0.218287430
147 -0.0315204204
148 0.867964759
149 0.616869887
150 -0.191600671
151 -1.374163558
152 0.375233596
153 -0.890115413
154 -0.286368323
155 0.359871348
156 0.830156202
157 -0.573157675
158 -0.567187141
159 -0.385573611
160 0.0790569415
161 1.249624368
162 -0.804271970
163 1.092928164
164 -0.148713059
165 -0.242557422
166 1.169452053