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

$R= 19.32164295$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -1.506964206
4 0.5
5 -0.447213595
6 1.065584609
7 1.930047321
8 -0.353553390
9 1.270941121
10 0.316227766
11 -1.410153783
12 -0.753482103
13 -1.560944216
14 -1.364749549
15 0.673934881
16 0.250000000
17 0.530188113
18 -0.898691085
19 -0.341761822
20 -0.223606797
21 -2.908512231
22 0.997129302
23 0.804289575
24 0.532792304
25 0.200000000
26 1.103754240
27 -0.408298571
28 0.965023660
29 0.294872404
30 -0.476543924
31 0.0334853600
32 -0.176776695
33 2.125051277
34 -0.374899610
35 -0.863143402
36 0.635470560
37 0.00695390836
38 0.241662102
39 2.352287063
40 0.158113883
41 0.535008349
42 2.056628721
43 -1.288619749
44 -0.705076891
45 -0.568382148
46 -0.568718612
47 -0.298751568
48 -0.376741051
49 2.725082663
50 -0.141421356
51 -0.798974510
52 -0.780472108
53 1.266966394
54 0.288710688
55 0.630639943
56 -0.682374774
57 0.515022834
58 -0.208506276
59 0.614795901
60 0.336967440
61 -0.145222761
62 -0.0236777251
63 2.452976506
64 0.125000000
65 0.698075475
66 -1.502638168
67 -1.096359254
68 0.265094056
69 -1.212035601
70 0.610334552
71 1.798019011
72 -0.449345542
73 0.704756092
74 -0.00491715575
75 -0.301392841
76 -0.170880911
77 -2.721663531
78 -1.663318133
79 0.281497940
80 -0.111803398
81 -0.655649787
82 -0.378308031
83 0.597255953
84 -1.454256115
85 -0.237107332
86 0.911191763
87 -0.444362158
88 0.498564651
89 -0.187771698
90 0.401906871
91 -3.012696204
92 0.402144787
93 -0.0504612389
94 0.211249259
95 0.152840533
96 0.266396152
97 -1.044445456
98 -1.926924430
99 -1.792222429
100 0.100000000
101 0.962174308
102 0.564960294
103 -1.336057096
104 0.551877120
105 1.300726212
106 -0.895880529
107 0.700134165
108 -0.204149285
109 -0.375449658
110 -0.445929780
111 -0.0104792862
112 0.482511830
113 1.023360547
114 -0.364176138
115 -0.359689232
116 0.147436202
117 -1.983868196
118 -0.434726350
119 1.023288143
120 -0.238271962
121 0.988533698
122 0.102687999
123 -0.806238433
124 0.0167426800
125 -0.0894427190
126 -1.734516321