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

$R= 23.6305864$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 1.530160501
4 0.5
5 -0.447213595
6 -1.081986866
7 -1.582482224
8 -0.353553390
9 1.345919643
10 0.316227766
11 -1.748189414
12 0.765080250
13 0.399246205
14 1.118983912
15 -0.684308579
16 0.250000000
17 0.592811371
18 -0.951708906
19 -0.600173137
20 -0.223606797
21 -2.440227963
22 1.236156589
23 -1.891898128
24 -0.540993433
25 0.200000000
26 -0.282309699
27 0.540064964
28 -0.791241112
29 -1.029095062
30 0.483879236
31 1.770181288
32 -0.176776695
33 -2.695149738
34 -0.419180940
35 0.707707565
36 0.672959821
37 0.461539581
38 0.424386495
39 0.606962471
40 0.158113883
41 0.234179857
42 1.725501740
43 0.990567979
44 -0.874094707
45 -0.601913562
46 1.337773995
47 0.627037435
48 0.382540125
49 1.581482729
50 -0.141421356
51 0.905265394
52 0.199623102
53 -0.151153233
54 -0.381883598
55 0.781814073
56 0.559491956
57 -0.927184821
58 0.727680096
59 -0.752179739
60 -0.342154289
61 0.770923935
62 -1.251707193
63 -2.176225382
64 0.125000000
65 -0.178548331
66 1.905758656
67 -1.084046841
68 0.296405685
69 -2.912176985
70 -0.500424818
71 0.647888389
72 -0.475854453
73 0.974856206
74 -0.326357768
75 0.306032100
76 -0.300086568
77 2.850268511
78 -0.429187279
79 0.456811726
80 -0.111803398
81 -0.505709614
82 -0.165590165
83 0.742919013
84 -1.220113981
85 -0.265113304
86 -0.700437335
87 -1.583723330
88 0.618078294
89 0.215354317
90 0.425617161
91 -0.616442765
92 -0.945949064
93 2.723053132
94 -0.443382422
95 0.268405586
96 -0.270496716
97 -0.512533731
98 -1.118277162
99 -2.403457834
100 0.100000000
101 -0.403061984
102 -0.640119298
103 0.181967678
104 -0.141154849
105 1.091303121
106 0.106881476
107 0.374216070
108 0.270032482
109 0.334468390
110 -0.552826032
111 0.691804654
112 -0.395620556
113 0.362085635
114 0.655618674
115 0.846082564
116 -0.514547531
117 0.538589608
118 0.531871394
119 -0.948756835
120 0.241939618
121 2.129400620
122 -0.545125542
123 0.331567500
124 0.885090644
125 -0.0894427190
126 1.538823725