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

$R= 11.9521606244$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 0.715894435
4 0.5
5 0.447213595
6 0.506213809
7 -1.595477208
8 0.353553390
9 -0.487495157
10 0.316227766
11 -0.526632824
12 0.357947217
13 -1.884529007
14 -1.128172753
15 0.320157724
16 0.250000000
17 -0.303654676
18 -0.344711131
19 0.557365630
20 0.223606797
21 -1.142193255
22 -0.372385641
23 1.723437249
24 0.253106904
25 0.200000000
26 -1.332563240
27 -1.064889505
28 -0.797738604
29 -0.908136166
30 0.226385698
31 -0.819765595
32 0.176776695
33 -0.377013508
34 -0.214716281
35 -0.713519098
36 -0.243747578
37 0.541787938
38 0.394117016
39 -1.349123829
40 0.158113883
41 -1.215776642
42 -0.807652596
43 0.250088142
44 -0.263316412
45 -0.218014462
46 1.218654165
47 -1.246080009
48 0.178973608
49 1.545547522
50 0.141421356
51 -0.217384693
52 -0.942264503
53 1.037155965
54 -0.752990590
55 -0.235517358
56 -0.564086376
57 0.399014953
58 -0.642149241
59 -0.265014525
60 0.160078862
61 0.529957613
62 -0.579661811
63 0.777787412
64 0.125000000
65 -0.842786993
66 -0.266588808
67 0.877698249
68 -0.151827338
69 1.233799136
70 -0.504534193
71 0.217560642
72 -0.172355565
73 -1.098619636
74 0.383101925
75 0.143178887
76 0.278682815
77 0.840230668
78 -0.953974608
79 0.382836584
80 0.111803398
81 -0.274853314
82 -0.859683908
83 0.0420046066
84 -0.571096627
85 -0.135798499
86 0.176839021
87 -0.650129627
88 -0.186192820
89 -0.140389229
90 -0.154159504
91 3.006723084
92 0.861718624
93 -0.586865625
94 -0.881111624
95 0.249261487
96 0.126553452
97 -0.268518737
98 1.092867133
99 0.256730937
100 0.100000000
101 -0.119222238
102 -0.153714190
103 -1.549026394
104 -0.666281620
105 -0.510804352
106 0.733380016
107 -1.474086291
108 -0.532444752
109 0.770697745
110 -0.166535921
111 0.387862802
112 -0.398869302
113 1.046880579
114 0.282146179
115 0.770744568
116 -0.454068083
117 0.918698704
118 -0.187393567
119 0.484471023
120 0.113192849
121 -0.722658988
122 0.374736622
123 -0.870370012
124 -0.409882797
125 0.0894427190
126 0.549978753
127 1.622022064
128 0.0883883476
129 0.179018274
130 -0.595940397
131 -1.298387391
132 -0.188506754
133 -0.889332911
134 0.620626384
135 -0.476233064
136 -0.107358140
137 -0.0506346838
138 0.872427736
139 -0.335271469
140 -0.356759549
141 -0.892295976
142 0.153838605
143 0.991815838
144 -0.121873789
145 -0.406130840
146 -0.776841395
147 1.107811037
148 0.270893969
149 -0.209171724
150 0.101242761
151 0.841017466
152 0.197058508
153 0.155079950
154 0.594132803
155 -0.366610319
156 -0.674561914
157 1.124407957
158 0.270706345
159 0.785423300
160 0.0790569415
161 -2.739270468
162 -0.194350642
163 0.173310482
164 -0.607888321
165 -0.168605566
166 0.0297017421