Properties

Level 10
Symmetry odd
Weight 0
Character \( \chi_{10}(1,\cdot) \)
Multiplicity 1
Precision 0
Fricke Eigenvalue -1
Atkin-Lehner Eigenvalues n/a

Related objects

Downloads

Learn more about

Spectral parameter

$R= 7.788215329$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -1.270888494
4 0.499999999
5 -0.447213595
6 -0.898653872
7 0.240524903
8 0.353553390
9 0.615157564
10 -0.316227766
11 1.647485159
12 -0.635444247
13 1.008112193
14 0.170076790
15 0.568358612
16 0.249999999
17 1.401907303
18 0.434982085
19 -1.012060647
20 -0.223606797
21 -0.305680332
22 1.164947928
23 -0.483614624
24 -0.449326936
25 0.200000000
26 0.712842968
27 0.489091823
28 0.120262451
29 -1.079357638
30 0.401890229
31 1.001147235
32 0.176776695
33 -2.093769933
34 0.991298160
35 -0.107566007
36 0.307578782
37 -0.0281677104
38 -0.715634946
39 -1.281198187
40 -0.158113883
41 1.203215897
42 -0.216148636
43 1.744735422
44 0.823742579
45 -0.275106826
46 -0.341967180
47 0.781514493
48 -0.317722123
49 -0.942147770
50 0.141421356
51 -1.781667861
52 0.504056096
53 -0.811119205
54 0.345840144
55 -0.736777761
56 0.0850383953
57 1.286216232
58 -0.763221105
59 1.598250112
60 0.284179306
61 -0.241689769
62 0.707917998
63 0.147960714
64 0.124999999
65 -0.450841478
66 -1.480518918
67 -0.263064039
68 0.700953651
69 0.614620261
70 -0.0760606530
71 -0.610464250
72 0.217491042
73 0.652651752
74 -0.0199175790
75 -0.254177698
76 -0.506030323
77 0.396261209
78 -0.905943926
79 -0.584606913
80 -0.111803398
81 -1.236738735
82 0.850802120
83 1.050817600
84 -0.152840166
85 -0.626952005
86 1.233714248
87 1.371743204
88 0.582473964
89 -0.640455899
90 -0.194529902
91 0.242476088
92 -0.241807312
93 -1.272346502
94 0.552614197
95 0.452607281
96 -0.224663468
97 0.451948000
98 -0.666199077
99 1.013462958
100 0.100000000
101 -1.708709999
102 -1.259829426
103 0.957289999
104 0.356421484
105 0.136704400
106 -0.573547890
107 -0.0473599999
108 0.244545911
109 -0.240100000
110 -0.520980551
111 0.0357980191
112 0.0601312259
113 -0.743399999
114 0.909492220
115 0.216279034
116 -0.539678819
117 0.620147841
118 1.130133492
119 0.337193619
120 0.200945114
121 1.714207351
122 -0.170900475
123 -1.529153240
124 0.500573617
125 -0.0894427190
126 0.104624024
127 1.510000000
128 0.0883883476
129 -2.217364174
130 -0.318793066
131 -0.660000000
132 -1.046884966
133 -0.243425790
134 -0.186014366
135 -0.218728512
136 0.495649080