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

$R= 30.7377364898$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 1.090857685
4 0.5
5 0.447213595
6 0.771352867
7 -0.249888696
8 0.353553390
9 0.189970490
10 0.316227766
11 -0.370451128
12 0.545428842
13 -1.666927687
14 -0.176697991
15 0.487846387
16 0.250000000
17 -0.0285743847
18 0.134329422
19 0.963102401
20 0.223606797
21 -0.272593004
22 -0.261948505
23 0.000386586500
24 0.385676433
25 0.200000000
26 -1.178695871
27 -0.883626915
28 -0.124944348
29 1.566458955
30 0.344959489
31 -0.685375923
32 0.176776695
33 -0.404109461
34 -0.0202051412
35 -0.111753622
36 0.0949852454
37 -0.808207076
38 0.681016239
39 -1.818380880
40 0.158113883
41 0.409648553
42 -0.192752362
43 0.250830200
44 -0.185225564
45 0.0849573862
46 0.000273357936
47 -1.018319725
48 0.272714421
49 -0.937555639
50 0.141421356
51 -0.0311705872
52 -0.833463843
53 -0.328182633
54 -0.624818584
55 -0.165670781
56 -0.0883489958
57 1.050607656
58 1.107653749
59 -0.776819237
60 0.243923193
61 0.997908311
62 -0.484633962
63 -0.0474714782
64 0.125000000
65 -0.745472724
66 -0.285748540
67 -1.528174049
68 -0.0142871923
69 0.000421710855
70 -0.0790217441
71 -1.700950551
72 0.0671647111
73 0.151556584
74 -0.571488704
75 0.218171537
76 0.481551200
77 0.0925715495
78 -1.285789451
79 -1.586425277
80 0.111803398
81 -1.153881703
82 0.289665269
83 -0.412027651
84 -0.136296502
85 -0.0127788533
86 0.177363736
87 1.708783791
88 -0.130974252
89 0.0589003948
90 0.0600739439
91 0.416546386
92 0.000193293250
93 -0.747647593
94 -0.720060783
95 0.430712487
96 0.192838216
97 0.546166550
98 -0.662951950
99 -0.0703747827
100 0.100000000
101 0.363860302
102 -0.0220409336
103 -0.334327890
104 -0.589347935
105 -0.121907297
106 -0.232060165
107 -1.064690110
108 -0.441813457
109 -1.862812791
110 -0.117146932
111 -0.881638901
112 -0.0624721740
113 -0.475966678
114 0.742891798
115 0.000172886738
116 0.783229477
117 -0.316667071
118 -0.549294150
119 0.00714041575
120 0.172479744
121 -0.862765961
122 0.705627734
123 0.446868272
124 -0.342687961
125 0.0894427190
126 -0.0335674042
127 0.597281597
128 0.0883883476
129 0.273620052
130 -0.527128818
131 1.147647369
132 -0.202054730
133 -0.240668403
134 -1.080582233
135 -0.395169970
136 -0.0101025706
137 -1.333509524
138 0.000298194605
139 1.017629407
140 -0.0558768111
141 -1.110841898
142 -1.202753669
143 0.617515243
144 0.0474926227
145 0.700541741
146 0.107166688
147 -1.022739775
148 -0.404103538
149 -1.162903105
150 0.154270573
151 1.090513808
152 0.340508119
153 -0.00542828976
154 0.0654579704
155 -0.306509430
156 -0.909190440
157 0.995471773
158 -1.121772071
159 -0.358000549
160 0.0790569415
161 -9.660407799e-5
162 -0.815917577
163 1.208151153
164 0.204824276
165 -0.180723245
166 -0.291347546
167 1.880839320
168 -0.0963761811
169 1.778647911
170 -0.00903601386
171 0.182961025
172 0.125415100
173 1.536314861
174 1.208292606
175 -0.0499777392
176 -0.0926127821
177 -0.847399255
178 0.0416488686
179 -1.222945396
180 0.0424786931
181 -0.191932997
182 0.294542774
183 1.088575814
184 0.000136678968
185 -0.361441192
186 -0.528666683
187 0.0105856095
188 -0.509159862
189 0.220808496
190 0.304559720
191 0.445064167
192 0.136357210
193 0.131384121
194 0.386198071
195 -0.813204651
196 -0.468777819
197 0.953865590
198 -0.0497624861
199 -0.530984262
200 0.0707106781
201 -1.667016636
202 0.257288087
203 -0.391440353
204 -0.0155852936
205 0.183200402
206 -0.236405518
207 8.519179169e-5
208 -0.416731921
209 -0.356793183
210 -0.0862014769
211 -1.390125213
212 -0.164091316
213 -1.855460540
214 -0.752849596
215 0.112174676
216 -0.312409292
217 0.171200360
218 -1.317207556
219 0.165495789
220 -0.0828353906
221 0.0478839922
222 -0.623412845
223 -0.324032530
224 -0.0441744979
225 0.0379940981
226 -0.336559265
227 -1.293572334
228 0.525303828
229 -0.563232074
230 0.000122249385
231 0.100078086
232 0.553826874
233 1.060703557
234 -0.223917433
235 -0.455406425
236 -0.388409618
237 -1.735605331
238 0.00504903640
239 -0.337649024
240 0.121961596
241 -1.213578653
242 -0.610067661
243 -0.401024106
244 0.498954155
245 -0.419287628
246 0.315983586
247 -1.625731113
248 -0.242316981
249 -0.591329584
250 0.0632455532