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

$R= 28.8123294116$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -1.849724582
4 0.5
5 -0.447213595
6 -1.307952795
7 0.522890791
8 0.353553390
9 2.421481031
10 -0.316227766
11 0.615676263
12 -0.924862291
13 -1.283817031
14 0.369739624
15 0.827221981
16 0.250000000
17 0.232253537
18 1.712245657
19 -1.447766656
20 -0.223606797
21 -0.967203951
22 0.435348860
23 -1.682280331
24 -0.653976397
25 0.200000000
26 -0.907795728
27 -2.629348406
28 0.261445395
29 1.282715878
30 0.584934272
31 0.721077887
32 0.176776695
33 -1.138831519
34 0.164228051
35 -0.233843871
36 1.210740515
37 0.914761971
38 -1.023725620
39 2.374707922
40 -0.158113883
41 0.817789337
42 -0.683916472
43 1.504748078
44 0.307838131
45 -1.082919238
46 -1.189551829
47 0.314282622
48 -0.462431145
49 -0.726585219
50 0.141421356
51 -0.429605077
52 -0.641908515
53 -0.0658919094
54 -1.859230088
55 -0.275338795
56 0.184869812
57 2.677969574
58 0.907017096
59 -1.045149197
60 0.413610990
61 0.933913594
62 0.509879064
63 1.266170133
64 0.125000000
65 0.574140430
66 -0.805275489
67 -0.692089579
68 0.116126768
69 3.111755283
70 -0.165352586
71 1.802353393
72 0.856122828
73 -0.750806036
74 0.646834393
75 -0.369944916
76 -0.723883328
77 0.321931448
78 1.679172075
79 -0.0993212391
80 -0.111803398
81 2.442089352
82 0.578264386
83 -0.163814229
84 -0.483601975
85 -0.103866939
86 1.064017570
87 -2.372671093
88 0.217674430
89 -0.567156160
90 -0.765739536
91 -0.671296104
92 -0.841140165
93 -1.333795494
94 0.222231373
95 0.647460931
96 -0.326988198
97 0.180717360
98 -0.513773336
99 1.490848392
100 0.100000000
101 -0.183292813
102 -0.303776663
103 -1.456345680
104 -0.453897864
105 0.432546756
106 -0.0465926160
107 1.128360460
108 -1.314674203
109 1.953102686
110 -0.194693929
111 -1.692057705
112 0.130722697
113 -0.816406812
114 1.893610445
115 0.752338635
116 0.641357939
117 -3.108738588
118 -0.739032084
119 0.121443236
120 0.292467136
121 -0.620942738
122 0.660376635
123 -1.512685040
124 0.360538943
125 -0.0894427190
126 0.895317487
127 0.672728869
128 0.0883883476
129 -2.783369511
130 0.405978591
131 -0.945964942
132 -0.569415759
133 -0.757023853
134 -0.489381234
135 1.175880354
136 0.0821140256
137 -0.882098781
138 2.200343262
139 1.875351961
140 -0.116921935
141 -0.581336292
142 1.274456306
143 -0.790415672
144 0.605370257
145 -0.573647980
146 -0.530900039
147 1.343982542
148 0.457380985
149 1.479774741
150 -0.261590559
151 -1.146064712
152 -0.511862810
153 0.562397535
154 0.227639910
155 -0.322475834
156 1.187353961
157 -0.266043647
158 -0.0702307216
159 0.121881883
160 -0.0790569415
161 -0.879648905
162 1.726817941
163 0.622702090
164 0.408894668
165 0.509300938
166 -0.115834152
167 -0.929454584
168 -0.341958236
169 0.648186244
170 -0.0734450173
171 -3.505739477
172 0.752374039
173 0.623162747
174 -1.677731819
175 0.104578158
176 0.153919065
177 1.933237854
178 -0.401039967
179 -0.423954544
180 -0.541459619
181 0.218119632
182 -0.474678027
183 -1.727483904
184 -0.594775914
185 -0.409093990
186 -0.943135839
187 0.142994128
188 0.157141311
189 -1.374860004
190 0.457824015
191 -1.648265746
192 -0.231215572
193 -0.618911495
194 0.127786471
195 -1.062001668
196 -0.363292609
197 -0.285799985
198 1.054189008
199 1.047884907
200 0.0707106781
201 1.280152762
202 -0.129607591
203 0.670728808
204 -0.214802538
205 -0.365726510
206 -1.029791906
207 -4.073606653
208 -0.320954257
209 -0.891318601
210 0.305856744
211 0.647052459
212 -0.0329459547
213 -3.333700839
214 0.797871333
215 -0.672943798
216 -0.929615044
217 0.377024064
218 1.381052153
219 1.388257616
220 -0.137669397
221 -0.299670772
222 -1.196465477
223 -1.126690537
224 0.0924349061
225 0.484296206
226 -0.577286793
227 1.553416693
228 1.338984787
229 0.00274601952
230 0.531983750
231 -0.604453699
232 0.453508548
233 0.351882922
234 -2.198210136
235 -0.140551461
236 -0.522574598
237 0.228615332
238 0.0858733357
239 -1.046128732
240 0.206805495