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

$R= 15.9393601653$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -1.420989746
4 0.5
5 0.447213595
6 1.004791485
7 -0.394830748
8 -0.353553390
9 1.019211858
10 -0.316227766
11 -1.131834666
12 -0.710494873
13 -0.767647507
14 0.279187499
15 -0.635485933
16 0.250000000
17 1.255856776
18 -0.720691616
19 -0.0262158299
20 0.223606797
21 0.561050445
22 0.800327968
23 1.049709623
24 0.502395742
25 0.200000000
26 0.542808757
27 -0.0272998543
28 -0.197415374
29 -1.226978986
30 0.449356412
31 1.353849161
32 -0.176776695
33 1.608325456
34 -0.888024843
35 -0.176573678
36 0.509605929
37 0.860837401
38 0.0185373910
39 1.090819236
40 -0.158113883
41 -0.284876938
42 -0.396722574
43 1.400908896
44 -0.565917333
45 0.455805399
46 -0.742256793
47 1.666427997
48 -0.355247436
49 -0.844108680
50 -0.141421356
51 -1.784559602
52 -0.383823753
53 -1.927616063
54 0.0193039121
55 -0.506171850
56 0.139593749
57 0.0372524254
58 0.867605161
59 0.416231642
60 -0.317742966
61 -1.010060884
62 -0.957315923
63 -0.402416181
64 0.125000000
65 -0.343302401
66 -1.137257836
67 -1.289641466
68 0.627928388
69 -1.491626611
70 0.124856445
71 1.504573661
72 -0.360345808
73 0.753453894
74 -0.608703964
75 -0.284197949
76 -0.0131079149
77 0.446883128
78 -0.771325679
79 0.0143459461
80 0.111803398
81 -0.980419045
82 0.201438415
83 -0.0767340751
84 0.280525222
85 0.561636224
86 -0.990592180
87 1.743524558
88 0.400163984
89 -1.526831273
90 -0.322303089
91 0.303090840
92 0.524854811
93 -1.923805776
94 -1.178342537
95 -0.0117240755
96 0.251197871
97 1.829016213
98 0.596874971
99 -1.153579310
100 0.100000000
101 0.750378115
102 1.261874196
103 -1.254408075
104 0.271404378
105 0.250909386
106 1.363030390
107 -0.606142502
108 -0.0136499271
109 -0.951870014
110 0.357917548
111 -1.223241220
112 -0.0987076871
113 0.198137200
114 -0.0263414426
115 0.469444415
116 -0.613489493
117 -0.782395446
118 -0.294320217
119 -0.495850893
120 0.224678206
121 0.281049204
122 0.714220900
123 0.404807361
124 0.676924580
125 0.0894427190
126 0.284551210
127 0.734985271
128 -0.0883883476
129 -1.990673673
130 0.242751456
131 0.0573834641
132 0.804162728
133 0.0103615434
134 0.911914226
135 -0.0122088660
136 -0.444012421
137 0.0351996852
138 1.054739292
139 -0.240782217
140 -0.0882868393
141 -2.367994456
142 -1.063894239
143 0.868939280
144 0.254802964
145 -0.548721684
146 -0.532772358
147 1.199402341
148 0.430418700
149 -1.048823013
150 0.200958297
151 -1.149308101
152 0.00926869554
153 1.280640708
154 -0.315994090
155 0.605459751
156 0.545409618
157 -0.930333564
158 -0.0101441158
159 2.737539667
160 -0.0790569415
161 -0.416304763
162 0.693260955
163 -0.792208420
164 -0.142438469
165 0.719265009
166 0.0542591848
167 -0.472878527
168 -0.198361287
169 -0.410877521
170 -0.397136782
171 -0.0603705341
172 0.700454448