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

$R= 15.7523478762$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -1.853799564
4 0.5
5 -0.447213595
6 -1.310834243
7 -1.382138576
8 0.353553390
9 2.436572825
10 -0.316227766
11 1.620315235
12 -0.926899782
13 -0.356393013
14 -0.977319559
15 0.829044368
16 0.250000000
17 0.709251549
18 1.722917167
19 -0.513428980
20 -0.223606797
21 2.562207891
22 1.145735890
23 0.322160787
24 -0.655417121
25 0.200000000
26 -0.252007916
27 -2.663118078
28 -0.691069288
29 0.998406872
30 0.586222894
31 0.364561368
32 0.176776695
33 -3.003739678
34 0.501516580
35 0.618111162
36 1.218286412
37 0.395243843
38 -0.363049113
39 0.660681213
40 -0.158113883
41 -1.122515461
42 1.811754574
43 -0.780673148
44 0.810157617
45 -1.089668494
46 0.227802077
47 -0.954314677
48 -0.463449891
49 0.910307044
50 0.141421356
51 -1.314810214
52 -0.178196506
53 -1.227478343
54 -1.883108852
55 -0.724627002
56 -0.488659779
57 0.951794420
58 0.705980270
59 -0.312811234
60 0.414522184
61 0.508481380
62 0.257783815
63 -3.367681296
64 0.125000000
65 0.159383801
66 -2.123964695
67 0.505983331
68 0.354625774
69 -0.597221528
70 0.437070594
71 -1.480698610
72 0.861458583
73 0.975227008
74 0.279479601
75 -0.370759912
76 -0.256714490
77 -2.239500193
78 0.467172166
79 0.880709667
80 -0.111803398
81 2.500314308
82 -0.793738294
83 -1.447444399
84 1.281103945
85 -0.317186935
86 -0.552019277
87 -1.850846225
88 0.572867945
89 0.586115788
90 -0.770511981
91 0.492584531
92 0.161080393
93 -0.675823707
94 -0.674802379
95 0.229612420
96 -0.327708560
97 -1.584076851
98 0.643684283
99 3.948016069
100 0.100000000
101 0.707773843
102 -0.929711218
103 1.357047910
104 -0.126003958
105 -1.145854203
106 -0.867958260
107 0.184679195
108 -1.331559039
109 0.219088716
110 -0.512388667
111 -0.732702803
112 -0.345534644
113 0.842881707
114 0.673020289
115 -0.144074684
116 0.499203436
117 -0.868377359
118 -0.221190945
119 -0.980283265
120 0.293111447
121 1.625422410
122 0.359550632
123 2.080919098
124 0.182280684
125 -0.0894427190
126 -2.381310281
127 -0.694448544
128 0.0883883476
129 1.447212350
130 0.112701366
131 -1.177710052
132 -1.501869839
133 0.709628157
134 0.357784244
135 1.190982611
136 0.250758290
137 0.615369892
138 -0.422299392
139 -1.427439823
140 0.309055581
141 1.769092525
142 -1.047012028
143 -0.577490851
144 0.609143206
145 -0.446501127
146 0.689589630
147 -1.687528403
148 0.197621921
149 -0.154950090
150 -0.262166848
151 -1.109362475
152 -0.181524556
153 1.728443932
154 -1.583565773
155 -0.163036800
156 0.330340606
157 0.563593404
158 0.622755778
159 2.279134639
160 -0.0790569415
161 -0.444042628
162 1.767989202
163 -0.0456298237
164 -0.561257730
165 1.343313221
166 -1.023497750
167 -1.218115148
168 0.905877287
169 -0.826990120
170 -0.224285033
171 -1.149146726
172 -0.390336574