Properties

Level 10
Symmetry even
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

$R= 29.1157220269$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 0.726479496
4 0.5
5 -0.447213595
6 -0.513698578
7 0.0991319332
8 -0.353553390
9 -0.472227541
10 0.316227766
11 1.141330545
12 0.363239748
13 0.278639654
14 -0.0700968622
15 -0.324891507
16 0.250000000
17 1.137880861
18 0.333915296
19 1.142092964
20 -0.223606797
21 0.0720173169
22 -0.807042568
23 0.850235771
24 -0.256849289
25 0.200000000
26 -0.197027989
27 -1.069543122
28 0.0495659666
29 0.518345431
30 0.229732988
31 -0.220978290
32 -0.176776695
33 0.829153239
34 -0.804603273
35 -0.0443331483
36 -0.236113770
37 -1.275310456
38 -0.807581680
39 0.202425995
40 0.158113883
41 -0.827598811
42 -0.0509239331
43 1.603028889
44 0.570665272
45 0.211186576
46 -0.601207479
47 -1.304594171
48 0.181619874
49 -0.990172859
50 -0.141421356
51 0.826647115
52 0.139319827
53 0.947197707
54 0.756281194
55 -0.510418536
56 -0.0350484311
57 0.829707121
58 -0.366525569
59 -0.527460481
60 -0.162445753
61 1.056836243
62 0.156255247
63 -0.0468128291
64 0.125000000
65 -0.124611441
66 -0.586299878
67 0.00534569850
68 0.568940430
69 0.617678855
70 0.0313482698
71 1.632290006
72 0.166957648
73 -0.126702647
74 0.901780672
75 0.145295899
76 0.571046482
77 0.113142303
78 -0.143136794
79 -0.293691635
80 -0.111803398
81 -0.304773607
82 0.585200731
83 0.464127331
84 0.0360086584
85 -0.508875791
86 -1.133512598
87 0.376567328
88 -0.403521284
89 0.153753041
90 -0.149331460
91 0.0276220876
92 0.425117885
93 -0.160536197
94 0.922487385
95 -0.510759501
96 -0.128424644
97 -0.0802321048
98 0.700157943
99 -0.538967717
100 0.100000000
101 -1.071033978
102 -0.584527780
103 -1.841330750
104 -0.0985139945
105 -0.0322071232
106 -0.669769922
107 0.0679730767
108 -0.534771561
109 0.286821535
110 0.360920408
111 -0.926486898
112 0.0247829833
113 0.0484618886
114 -0.586691532
115 -0.380236996
116 0.259172715
117 -0.131581318
118 0.372970883
119 0.112800329
120 0.114866494
121 0.302635413
122 -0.747296074
123 -0.601233567
124 -0.110489145
125 -0.0894427190
126 0.0331016689
127 1.848028078
128 -0.0883883476
129 1.164567620
130 0.0881135954
131 -0.241151341
132 0.414576619
133 0.113217883
134 -0.00377997966
135 0.478314225
136 -0.402301636
137 1.137850601
138 -0.436764907
139 -0.246625202
140 -0.0221665741
141 -0.947760916
142 -1.154203332
143 0.318019948
144 -0.118056885
145 -0.231811124
146 0.0895923014
147 -0.719340280
148 -0.637655228
149 -1.417753808
150 -0.102739715
151 1.398229936
152 -0.403790840
153 -0.537338681
154 -0.0800036900
155 0.0988244958
156 0.101212997
157 -0.736942191
158 0.207671346
159 0.688119711
160 0.0790569415
161 0.0842855245
162 0.215507484
163 -1.063032073
164 -0.413799405
165 -0.370808601
166 -0.328187583
167 -0.491110054
168 -0.0254619665
169 -0.922359955
170 0.359829522
171 -0.539327776
172 0.801514444
173 1.473523269
174 -0.266273311
175 0.0198263866
176 0.285332636
177 -0.383189317
178 -0.108719818
179 1.614143293
180 0.105593288
181 1.403924999
182 -0.0195317654
183 0.767769468
184 -0.300603739
185 0.570336174
186 0.113516233
187 1.298698466
188 -0.652297085
189 -0.106025798
190 0.361161506
191 1.646861462
192 0.0908099370
193 -0.0914429879
194 0.0567326653
195 -0.0905276573
196 -0.495086429
197 -0.334779648
198 0.381107727
199 1.692211708
200 -0.0707106781
201 0.00390699008
202 0.757335389
203 0.0513870749
204 0.413323557
205 0.370113439
206 1.302017460
207 -0.401431872
208 0.0696599135
209 1.303738266
210 0.0227738752
211 0.0845932158
212 0.473598853
213 1.186045361
214 -0.0480642235
215 -0.716896313
216 0.378140597
217 -0.0217513026
218 -0.202813452
219 -0.0913950427
220 -0.255209268
221 0.318806632
222 0.655125168
223 1.685930353
224 -0.0175242155
225 -0.0944455083
226 -0.0342677300
227 0.440446291
228 0.414853560
229 -0.0511241272
230 0.268868158
231 0.0795330115
232 -0.183262784
233 -0.420544545
234 0.0930420429
235 0.583432250
236 -0.263730240
237 -0.254598506
238 -0.0797618780