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

$R= 14.3176285454$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -1.160633473
4 0.5
5 -0.447213595
6 -0.820691799
7 0.665508122
8 0.353553390
9 0.347070059
10 -0.316227766
11 -0.573124021
12 -0.580316736
13 0.976349294
14 0.470585306
15 0.519051068
16 0.250000000
17 1.379250791
18 0.245415592
19 0.136126989
20 -0.223606797
21 -0.772411003
22 -0.405259881
23 -1.614962374
24 -0.410345899
25 0.200000000
26 0.690383206
27 0.757812345
28 0.332754061
29 -0.137627386
30 0.367024530
31 -1.808827956
32 0.176776695
33 0.665186923
34 0.975277587
35 -0.297624280
36 0.173535029
37 -0.107111548
38 0.0962563175
39 -1.133183672
40 -0.158113883
41 -0.887345999
42 -0.546177058
43 -0.699649966
44 -0.286562010
45 -0.155214448
46 -1.141950846
47 0.499697815
48 -0.290158368
49 -0.557098938
50 0.141421356
51 -1.600804636
52 0.488174647
53 -1.123531123
54 0.535854248
55 0.256308854
56 0.235292653
57 -0.157993540
58 -0.0973172579
59 -0.847668357
60 0.259525534
61 -0.779804393
62 -1.279034514
63 0.230977943
64 0.125000000
65 -0.436636678
66 0.470358184
67 -1.243203858
68 0.689625395
69 1.874379389
70 -0.210452146
71 1.056044752
72 0.122707796
73 -1.654937232
74 -0.0757393022
75 -0.232126694
76 0.0680634948
77 -0.381418691
78 -0.801281858
79 1.824881354
80 -0.111803398
81 -1.226612433
82 -0.627448373
83 1.373406276
84 -0.386205501
85 -0.616819705
86 -0.494727235
87 0.159734949
88 -0.202629940
89 0.551377838
90 -0.109753189
91 0.649768382
92 -0.807481187
93 2.099386266
94 0.353339713
95 -0.0608778405
96 -0.205172949
97 0.0256349652
98 -0.393928437
99 -0.198914198
100 0.100000000
101 0.765876551
102 -1.131939813
103 -1.022846873
104 0.345191603
105 0.345432702
106 -0.794456476
107 -1.358498152
108 0.378906172
109 -0.495803850
110 0.181237728
111 0.124317112
112 0.166377030
113 1.949174581
114 -0.111718304
115 0.722233130
116 -0.0688136930
117 0.338861267
118 -0.599392043
119 0.917903644
120 0.183512265
121 -0.671527939
122 -0.551404974
123 1.029885020
124 -0.904413978
125 -0.0894427190
126 0.163326070
127 -1.149999314
128 0.0883883476
129 0.812039690
130 -0.308748756
131 -0.734884508
132 0.332593461
133 0.0905694871
134 -0.879077878
135 -0.338903983
136 0.487638793
137 0.290468588
138 1.325386377
139 -0.317170473
140 -0.148812140
141 -0.580044351
142 0.746736405
143 -0.559777336
144 0.0867675147
145 0.0615488381
146 -1.170217339
147 0.647248981
148 -0.0535557741
149 1.205255652
150 -0.164138359
151 -1.295975002
152 0.0481281587
153 0.477284341
154 -0.269703743
155 0.808932454
156 -0.566591836
157 1.533923680
158 1.290385980
159 1.311649521
160 -0.0790569415
161 -1.076311316
162 -0.867345969
163 -1.598717892
164 -0.443672999
165 -0.297480635
166 0.971144891