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

$R= 20.9322050353$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 1.840643955
4 0.5
5 -0.447213595
6 -1.301531822
7 0.344453269
8 -0.353553390
9 2.387970171
10 0.316227766
11 1.238751878
12 0.920321977
13 1.801287181
14 -0.243565242
15 -0.823161001
16 0.250000000
17 -0.478918028
18 -1.688549901
19 0.753451359
20 -0.223606797
21 0.634015827
22 -0.875929853
23 -0.817737089
24 -0.650765911
25 0.200000000
26 -1.273702380
27 2.554758907
28 0.172226634
29 -1.115834508
30 0.582062726
31 0.827433949
32 -0.176776695
33 2.280101158
34 0.338646185
35 -0.154044184
36 1.193985085
37 1.395706290
38 -0.532770565
39 3.315528362
40 0.158113883
41 -0.816935093
42 -0.448316891
43 -0.565934166
44 0.619375939
45 -1.067932726
46 0.578227441
47 -1.126530865
48 0.460160988
49 -0.881351945
50 -0.141421356
51 -0.881517573
52 0.900643590
53 0.651189766
54 -1.806487347
55 -0.553986681
56 -0.121782621
57 1.386835691
58 0.789014147
59 -0.615505007
60 -0.411580500
61 1.324923418
62 -0.585084156
63 0.822544132
64 0.125000000
65 -0.805560116
66 -1.612274990
67 0.526721245
68 -0.239459014
69 -1.505162832
70 0.108925687
71 0.352190719
72 -0.844274950
73 0.571037656
74 -0.986913382
75 0.368128791
76 0.376725679
77 0.426692134
78 -2.344432588
79 -1.341448685
80 -0.111803398
81 2.314431369
82 0.577660344
83 0.754385453
84 0.317007913
85 0.214178653
86 0.400175886
87 -2.053854044
88 -0.437964926
89 0.0412674664
90 0.755142472
91 0.620459258
92 -0.408868544
93 1.523011297
94 0.796577614
95 -0.336953691
96 -0.325382955
97 0.665369101
98 0.623209937
99 2.958102536
100 0.100000000
101 1.908678667
102 0.623327054
103 -0.740548347
104 -0.636851190
105 -0.283540498
106 -0.460460699
107 -1.680537685
108 1.277379453
109 -1.184975462
110 0.391727739
111 2.568998350
112 0.0861133172
113 0.309471832
114 -0.980640921
115 0.365703144
116 -0.557917254
117 4.301420055
118 0.435227764
119 -0.164964879
120 0.291031363
121 0.534506203
122 -0.936862333
123 -1.503686689
124 0.413716974
125 -0.0894427190
126 -0.581626533
127 0.480383874
128 -0.0883883476
129 -1.041683217
130 0.569617021
131 1.238304157
132 1.140050579
133 0.259529002
134 -0.372448164
135 -1.142522916
136 0.169323092
137 -0.221743707
138 1.064310845
139 -0.325477491
140 -0.0770220924
141 -2.073541516
142 -0.249036445
143 2.231348793
144 0.596992542
145 0.499016362
146 -0.403784599
147 -1.622250338
148 0.697853145
149 1.222118826
150 -0.260306364
151 1.078700019
152 -0.266385282
153 -1.143660397
154 -0.301716901
155 -0.370039711
156 1.657764181
157 -1.031077772
158 0.948547462
159 1.198607077
160 0.0790569415
161 -0.281581973
162 -1.636550115
163 -0.323464131
164 -0.408467546
165 -1.019692236
166 -0.533431069
167 -1.614696863
168 -0.224158445
169 2.244639135
170 -0.151447178
171 1.798885011
172 -0.282967083
173 0.182093559
174 1.452294122
175 0.0688906538
176 0.309687969
177 -1.129499922
178 -0.0291805053
179 -0.296233352
180 -0.533966363
181 0.0675790448
182 -0.438730949
183 2.437711287
184 0.289113720
185 -0.624178828
186 -1.076931616
187 -0.616910993
188 -0.563265432
189 0.855175850
190 0.238262240
191 0.0436279726
192 0.230080494
193 0.636167344
194 -0.470487003
195 -1.482749360
196 -0.440675972