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

$R= 26.1494656272$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 0.800155619
4 0.5
5 -0.447213595
6 -0.565795464
7 -1.070586959
8 -0.353553390
9 -0.359750984
10 0.316227766
11 0.517556796
12 0.400077809
13 1.403364846
14 0.757019298
15 -0.357840471
16 0.250000000
17 1.261921101
18 0.254382360
19 -0.895843244
20 -0.223606797
21 -0.856636171
22 -0.365967920
23 0.277894786
24 -0.282897732
25 0.200000000
26 -0.992328799
27 -1.088012391
28 -0.535293479
29 -0.326531156
30 0.253031424
31 -0.248891675
32 -0.176776695
33 0.414125979
34 -0.892312967
35 0.478781043
36 -0.179875492
37 -1.849475939
38 0.633456833
39 1.122910268
40 0.158113883
41 0.844380266
42 0.605733245
43 -1.899640658
44 0.258778398
45 0.160885531
46 -0.196501288
47 0.202097796
48 0.200038904
49 0.146156437
50 -0.141421356
51 1.009733260
52 0.701682423
53 0.398297646
54 0.769340939
55 -0.231458435
56 0.378509649
57 -0.716814006
58 0.230892394
59 0.559686028
60 -0.178920235
61 1.519755107
62 0.175992991
63 0.385144712
64 0.125000000
65 -0.627603838
66 -0.292831288
67 -0.294072652
68 0.630960550
69 0.222359075
70 -0.338549322
71 -0.508633555
72 0.127191180
73 0.497761334
74 1.307776978
75 0.160031123
76 -0.447921622
77 -0.554089557
78 -0.794017465
79 -1.440143254
80 -0.111803398
81 -0.510828244
82 -0.597067012
83 -1.551257986
84 -0.428318085
85 -0.564348272
86 1.343248791
87 -0.261275739
88 -0.182983960
89 1.174556654
90 -0.113763250
91 -1.502424103
92 0.138947393
93 -0.199152072
94 -0.142904722
95 0.400633278
96 -0.141448866
97 1.661223776
98 -0.103348207
99 -0.186191567
100 0.100000000
101 0.177133804
102 -0.713989235
103 1.158619796
104 -0.496164399
105 0.383099342
106 -0.281638966
107 0.224103943
108 -0.544006195
109 0.479045975
110 0.163665829
111 -1.479868565
112 -0.267646739
113 0.784201183
114 0.506864044
115 -0.124278326
116 -0.163265578
117 -0.504861885
118 -0.395757785
119 -1.350996274
120 0.126515712
121 -0.732134962
122 -1.074629142
123 0.675635615
124 -0.124445837
125 -0.0894427190
126 -0.272338438
127 -0.700876287
128 -0.0883883476
129 -1.520008147
130 0.443782930
131 1.288628334
132 0.207062989
133 0.959078095
134 0.207940767
135 0.486573933
136 -0.446156483
137 -0.282663846
138 -0.157231609
139 0.434419391
140 0.239390521
141 0.161709689
142 0.359658236
143 0.726321013
144 -0.0899377461
145 0.146029172
146 -0.351970414
147 0.116947883
148 -0.924737969
149 1.386775918
150 -0.113159092
151 1.591619905
152 0.316728416
153 -0.453977379
154 0.391800483
155 0.111307741
156 0.561455134
157 1.481099201
158 1.018335061
159 0.318700095
160 0.0790569415
161 -0.297510618
162 0.361210115
163 1.680068583
164 0.422190133
165 -0.185202768
166 1.096905041
167 -1.590931918
168 0.302866622
169 0.969433486
170 0.399054490
171 0.322280830
172 -0.949820329
173 0.687759188
174 0.184749847
175 -0.214117391
176 0.129389199
177 0.447839103
178 -0.830536975
179 -0.757891277
180 0.0804427656
181 0.327646642
182 1.062374272
183 1.216052542
184 -0.0982506440
185 0.827110784
186 0.140821781
187 0.653101806
188 0.101048898
189 1.164815049
190 -0.283290507
191 0.397695280
192 0.100019452
193 0.188936989
194 -1.174662597
195 -0.502180738
196 0.0730782186
197 1.813714508
198 0.131657319
199 -1.649621712
200 -0.0707106781
201 -0.235630966
202 -0.125252514
203 0.350404573
204 0.504866630
205 -0.377618334
206 -0.819267914
207 -0.101344515
208 0.350841211
209 -0.464902790
210 -0.270892142
211 1.017296719
212 0.199148823
213 -0.405126132
214 -0.158465418
215 0.849545128
216 0.384670469
217 0.279793035
218 -0.338736657
219 0.384355065
220 -0.115729217
221 1.738964479
222 1.046425098