Properties

Level 10
Symmetry odd
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

$R= 19.1774440783$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 0.116592990
4 0.5
5 0.447213595
6 -0.0824436945
7 -0.700757475
8 -0.353553390
9 -0.986406074
10 -0.316227766
11 -0.973876495
12 0.0582964954
13 -1.382450421
14 0.495510362
15 0.0521419706
16 0.250000000
17 -1.480998410
18 0.697494424
19 1.571015064
20 0.223606797
21 -0.0817034099
22 0.688634673
23 -1.379682230
24 -0.0412218472
25 0.200000000
26 0.977540067
27 -0.231601025
28 -0.350378737
29 1.482532413
30 -0.0368699410
31 0.356169909
32 -0.176776695
33 -0.113547173
34 1.047224018
35 -0.313388270
36 -0.493203037
37 -0.565077959
38 -1.110875405
39 -0.161184029
40 -0.158113883
41 -1.799966115
42 0.0577730352
43 1.865925392
44 -0.486938247
45 -0.441134207
46 0.975582661
47 0.127437881
48 0.0291482477
49 -0.508938961
50 -0.141421356
51 -0.172674034
52 -0.691225210
53 -0.354232039
54 0.163766655
55 -0.435530809
56 0.247755181
57 0.183169345
58 -1.048308723
59 -0.626632173
60 0.0260709853
61 -0.658907035
62 -0.251850158
63 0.691231430
64 0.125000000
65 -0.618250623
66 0.0802899762
67 -0.284652477
68 -0.740499205
69 -0.160861277
70 0.221598970
71 1.046577885
72 0.348747212
73 0.143337450
74 0.399570456
75 0.0233185981
76 0.785507532
77 0.682451233
78 0.113974320
79 0.261907302
80 0.111803398
81 0.959403018
82 1.272768246
83 1.234788567
84 -0.0408517049
85 -0.662322623
86 -1.319408498
87 0.172852888
88 0.344317336
89 1.536676534
90 0.311928989
91 0.968762466
92 -0.689841115
93 0.0415269149
94 -0.0901121900
95 0.702579295
96 -0.0206109236
97 1.144109062
98 0.359874190
99 0.960637690
100 0.100000000
101 0.411752780
102 0.122098980
103 -0.477559107
104 0.488770033
105 -0.0365388757
106 0.250479877
107 -1.033097256
108 -0.115800512
109 -0.181302224
110 0.307966788
111 -0.0658841363
112 -0.175189368
113 -0.706050447
114 -0.129520286
115 -0.617012650
116 0.741266206
117 1.363657485
118 0.443095858
119 1.037820667
120 -0.0184349705
121 -0.0515645367
122 0.465917632
123 -0.209863358
124 0.178084954
125 0.0894427190
126 -0.488774431
127 -0.153725657
128 -0.0883883476
129 0.217554131
130 0.437169208
131 -1.439548233
132 -0.0567735866
133 -1.100901216
134 0.201279697
135 -0.103575127
136 0.523612009
137 0.599063986
138 0.113746100
139 -0.334013962
140 -0.156694135
141 0.0148593220
142 -0.740042319
143 1.346340022
144 -0.246601518
145 0.663008651
146 -0.101354883
147 -0.0593399827
148 -0.282538979
149 0.0466347085
150 -0.0164887389
151 0.730150570
152 -0.555437702
153 1.460826700
154 -0.482565895
155 0.159284025
156 -0.0805920147
157 -0.724877496
158 -0.185196429
159 -0.0413889092
160 -0.0790569415
161 0.966949573
162 -0.678400380
163 -0.738854408
164 -0.899983057
165 -0.0507798396
166 -0.873127369
167 1.433688586
168 0.0288865176
169 0.912488007
170 0.468332818
171 -1.549187690
172 0.932962696
173 -0.00272025576
174 -0.122225449
175 -0.140151495
176 -0.243469123
177 -0.0740998727
178 -1.086594397
179 0.888306006
180 -0.220567103
181 1.356189175
182 -0.685018509
183 -0.0500635950
184 0.487791330
185 -0.252710545
186 -0.0293639631
187 1.422704091
188 0.0637189406
189 0.144879112
190 -0.496798584