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

$R= 24.5039253761$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 0.556066499
4 0.5
5 0.447213595
6 0.393198392
7 0.0403710325
8 0.353553390
9 -0.690790047
10 0.316227766
11 1.960295116
12 0.278033249
13 1.719668513
14 0.0285466308
15 0.248680498
16 0.250000000
17 0.122717510
18 -0.488462327
19 0.0900990617
20 0.223606797
21 0.0224489787
22 1.386137969
23 -1.458261253
24 0.196599196
25 0.200000000
26 1.215989267
27 -0.940191703
28 0.0201855162
29 1.058560039
30 0.175843667
31 -0.0928470238
32 0.176776695
33 1.090054443
34 0.0867743837
35 0.0180544745
36 -0.345395023
37 -1.755156110
38 0.0637096575
39 0.956250051
40 0.158113883
41 1.384583610
42 0.0158738250
43 1.148642539
44 0.980147558
45 -0.308930700
46 -1.031146421
47 0.960857633
48 0.139016624
49 -0.998370179
50 0.141421356
51 0.0682390964
52 0.859834256
53 -1.353583377
54 -0.664815929
55 0.876670627
56 0.0142733154
57 0.0501010699
58 0.748514982
59 -0.331820039
60 0.124340249
61 1.383192978
62 -0.0656527601
63 -0.0278879074
64 0.125000000
65 0.769059139
66 0.770784889
67 -0.713227636
68 0.0613587552
69 -0.810890231
70 0.0127664414
71 1.677314354
72 -0.244231163
73 0.134547568
74 -1.241082787
75 0.111213299
76 0.0450495308
77 0.0791391378
78 0.676170895
79 1.022245680
80 0.111803398
81 0.167980937
82 0.979048459
83 0.566977829
84 0.0112244893
85 0.0548809390
86 0.812212928
87 0.588629776
88 0.693068984
89 -1.391917217
90 -0.218446993
91 0.0694247934
92 -0.729130626
93 -0.0516291195
94 0.679428948
95 0.0402935253
96 0.0982995982
97 0.672270182
98 -0.705954324
99 -1.354152356
100 0.100000000
101 0.0115465034
102 0.0482523278
103 -0.373623005
104 0.607994633
105 0.0100394884
106 -0.957127985
107 -0.852842945
108 -0.470095851
109 -0.614678224
110 0.619899745
111 -0.975983515
112 0.0100927581
113 0.712213166
114 0.0354268062
115 -0.652154258
116 0.529280019
117 -1.187929894
118 -0.234632200
119 0.00495423262
120 0.0879218335
121 2.842756941
122 0.978065135
123 0.769920561
124 -0.0464235119
125 0.0894427190
126 -0.0197197284
127 -0.425501126
128 0.0883883476
129 0.638721636
130 0.543806932
131 -0.0313769878
132 0.545027221
133 0.00363739272
134 -0.504328098
135 -0.420466512
136 0.0433871918
137 1.364058864
138 -0.573385981
139 0.801604320
140 0.00902723729
141 0.534300744
142 1.186040354
143 3.371057787
144 -0.172697511
145 0.473402441
146 0.0951394982
147 -0.555160218
148 -0.877578055
149 1.135579593
150 0.0786396785
151 0.557432782
152 0.0318548287
153 -0.0847720185
154 0.0559598210
155 -0.0415224513
156 0.478125025
157 0.0637747780
158 0.722836852
159 -0.752682412
160 0.0790569415
161 -0.0588714305
162 0.118780460
163 -0.521544650
164 0.692291805
165 0.487487167
166 0.400913867
167 -0.737955887
168 0.00793691254
169 1.957259086
170 0.0388066841
171 -0.0622393487
172 0.574321269
173 -0.613390690
174 0.416224106
175 0.00807420650
176 0.490073779
177 -0.184511210
178 -0.984234103
179 0.948742002
180 -0.154465350
181 0.0139986698
182 0.0490907422
183 0.769148922
184 -0.515573210
185 -0.784929674
186 -0.0365073005
187 0.240565832
188 0.480428816
189 -0.0379836712
190 0.0284918250
191 -0.431953393
192 0.0695083124
193 0.0578343767
194 0.475366805
195 0.427648023
196 -0.499185089
197 0.00796410763
198 -0.957530314
199 -0.0639071499
200 0.0707106781
201 -0.396884615
202 0.00816461091
203 0.0417637054
204 0.0341195482
205 0.619204614
206 -0.264191360
207 1.007200042
208 0.429917128
209 0.182166369
210 0.00709899039
211 0.688322872
212 -0.676791688
213 0.933423152
214 -0.603051030
215 0.513688560
216 -0.332407964
217 0.00979404889
218 -0.434643140
219 0.0926709343
220 0.438335313
221 0.286683793
222 -0.690124562