Sharedwww / tables / slopes_3-adic.mOpen in CoCalc
Author: William A. Stein
1
/*********************************************************************
2
This is a MAGMA-readable table of the 3-adic slopes of the Hecke
3
operator T_3 acting on Gamma_0(N). The syntax is:
4
<N,
5
[
6
<k, [* slopes of T_3 on S_k(Gamma_0(N)) *]
7
...
8
]>
9
10
William Stein, February 13, 2000
11
***********************************************************************/
12
13
oo := Infinity();
14
15
slopes_3adic :=
16
[*
17
<1,
18
[
19
<2, [**]>,
20
<4, [**]>,
21
<6, [**]>,
22
<8, [**]>,
23
<10, [**]>,
24
<12, [* 2 *]>,
25
<14, [**]>,
26
<16, [* 3 *]>,
27
<18, [* 2 *]>,
28
<20, [* 3 *]>,
29
<22, [* 3 *]>,
30
<24, [* 2, 5 *]>,
31
<26, [* 3 *]>,
32
<28, [* 4, 4 *]>,
33
<30, [* 2, 5 *]>,
34
<32, [* 4, 6 *]>,
35
<34, [* 3, 6 *]>,
36
<36, [* 2, 6, 8 *]>,
37
<38, [* 3, 7 *]>,
38
<40, [* 3, 6, 9 *]>,
39
<42, [* 2, 5, 9 *]>,
40
<44, [* 3, 7, 9 *]>,
41
<46, [* 4, 4, 9 *]>,
42
<48, [* 2, 5, 9, 11 *]>,
43
<50, [* 4, 6, 8 *]>,
44
<52, [* 3, 6, 8, 12 *]>,
45
<54, [* 2, 6, 8, 10 *]>,
46
<56, [* 3, 7, 9, 11 *]>,
47
<58, [* 3, 6, 9, 11 *]>,
48
<60, [* 2, 5, 9, 11, 13 *]>,
49
<62, [* 3, 7, 9, 12 *]>,
50
<64, [* 4, 4, 9, 13, 13 *]>,
51
<66, [* 2, 5, 9, 11, 14 *]>,
52
<68, [* 5, 6, 7, 13, 15 *]>,
53
<70, [* 3, 7, 7, 12, 15 *]>,
54
<72, [* 2, 7, 8, 9, 15, 17 *]>,
55
<74, [* 3, 8, 9, 10, 16 *]>,
56
<76, [* 3, 7, 10, 10, 13, 18 *]>,
57
<78, [* 2, 5, 10, 11, 12, 18 *]>,
58
<80, [* 3, 8, 10, 12, 14, 16 *]>,
59
<82, [* 4, 4, 10, 13, 13, 16 *]>,
60
<84, [* 2, 5, 10, 12, 14, 16, 18 *]>,
61
<86, [* 4, 6, 9, 14, 15, 16 *]>,
62
<88, [* 3, 6, 9, 13, 16, 16, 19 *]>,
63
<90, [* 2, 6, 8, 11, 16, 17, 18 *]>,
64
<92, [* 3, 7, 10, 12, 17, 18, 19 *]>,
65
<94, [* 3, 6, 9, 12, 15, 19, 19 *]>,
66
<96, [* 2, 5, 9, 12, 14, 19, 20, 21 *]>,
67
<98, [* 3, 7, 9, 13, 16, 18, 21 *]>,
68
<100, [* 4, 4, 9, 14, 14, 18, 22, 22 *]>,
69
<102, [* 2, 5, 9, 11, 15, 18, 20, 23 *]>,
70
<104, [* 4, 6, 8, 14, 16, 18, 22, 24 *]>,
71
<106, [* 3, 6, 8, 12, 16, 18, 21, 24 *]>,
72
<108, [* 2, 6, 8, 10, 16, 18, 20, 24, 26 *]>,
73
<110, [* 3, 7, 9, 11, 17, 19, 21, 25 *]>,
74
<112, [* 3, 6, 9, 11, 15, 19, 21, 24, 27 *]>,
75
<114, [* 2, 5, 9, 11, 13, 19, 21, 23, 27 *]>,
76
<116, [* 3, 7, 9, 12, 16, 18, 22, 25, 27 *]>,
77
<118, [* 4, 4, 9, 13, 13, 18, 23, 23, 27 *]>,
78
<120, [* 2, 5, 9, 11, 14, 18, 20, 24, 27, 29 *]>,
79
<122, [* 5, 6, 7, 13, 15, 18, 22, 25, 27 *]>,
80
<124, [* 3, 7, 7, 12, 15, 18, 21, 24, 27, 30 *]>,
81
<126, [* 2, 7, 8, 9, 15, 17, 20, 24, 27, 29 *]>,
82
<128, [* 3, 8, 9, 10, 16, 19, 21, 25, 27, 30 *]>,
83
<130, [* 3, 7, 10, 10, 13, 18, 21, 24, 27, 30 *]>,
84
<132, [* 2, 5, 10, 11, 12, 18, 21, 23, 27, 29, 32 *]>,
85
<134, [* 3, 8, 10, 12, 14, 16, 22, 25, 27, 30 *]>,
86
<136, [* 4, 4, 10, 13, 13, 16, 23, 23, 27, 31, 31 *]>,
87
<138, [* 2, 5, 10, 12, 14, 16, 18, 24, 27, 29, 32 *]>,
88
<140, [* 4, 6, 9, 14, 15, 16, 21, 25, 27, 31, 33 *]>,
89
<142, [* 3, 6, 9, 13, 16, 16, 19, 23, 27, 30, 33 *]>,
90
<144, [* 2, 6, 8, 11, 16, 17, 18, 23, 27, 29, 33, 35 *]>,
91
<146, [* 3, 7, 10, 12, 17, 18, 19, 24, 26, 30, 34 *]>,
92
<148, [* 3, 6, 9, 12, 15, 19, 19, 23, 26, 30, 33, 36 *]>,
93
<150, [* 2, 5, 9, 12, 14, 19, 20, 21, 26, 28, 32, 36 *]>
94
]>,
95
96
<2,[
97
<2, [**]>,
98
<4, [**]>,
99
<6, [**]>,
100
<8, [* 1 *]>,
101
<10, [* 1 *]>,
102
<12, [* 2, 2 *]>,
103
<14, [* 1, 3 *]>,
104
<16, [* 1, 3, 3 *]>,
105
<18, [* 2, 2, 2 *]>,
106
<20, [* 1, 3, 3, 3 *]>,
107
<22, [* 1, 3, 3, 4 *]>,
108
<24, [* 2, 2, 2, 5, 5 *]>,
109
<26, [* 1, 3, 3, 3, 6 *]>,
110
<28, [* 1, 4, 4, 4, 4, 4 *]>,
111
<30, [* 2, 2, 3, 5, 5, 5 *]>,
112
<32, [* 1, 3, 4, 4, 6, 6, 6 *]>,
113
<34, [* 1, 3, 3, 5, 6, 6, 7 *]>,
114
<36, [* 2, 2, 2, 6, 6, 6, 8, 8 *]>,
115
<38, [* 1, 3, 3, 3, 7, 7, 7, 9 *]>,
116
<40, [* 1, 3, 3, 4, 6, 6, 8, 9, 9 *]>,
117
<42, [* 2, 2, 2, 5, 5, 6, 8, 9, 9 *]>,
118
<44, [* 1, 3, 3, 3, 6, 7, 7, 9, 9, 10 *]>,
119
<46, [* 1, 4, 4, 4, 4, 4, 8, 9, 9, 10 *]>,
120
<48, [* 2, 2, 3, 5, 5, 5, 7, 9, 9, 11, 11 *]>,
121
<50, [* 1, 3, 4, 4, 6, 6, 6, 8, 8, 10, 12 *]>
122
]>,
123
124
<3,[
125
<2, [**]>,
126
<4, [**]>,
127
<6, [* 2 *]>,
128
<8, [* 3 *]>,
129
<10, [* 4, 4 *]>,
130
<12, [* 2, 5, 9 *]>,
131
<14, [* 6, 6, 6 *]>,
132
<16, [* 3, 7, 7, 12 *]>,
133
<18, [* 2, 8, 8, 8, 15 *]>,
134
<20, [* 3, 9, 9, 9, 16 *]>,
135
<22, [* 3, 10, 10, 10, 10, 18 *]>,
136
<24, [* 2, 5, 11, 11, 11, 18, 21 *]>,
137
<26, [* 3, 12, 12, 12, 12, 12, 22 *]>,
138
<28, [* 4, 4, 13, 13, 13, 13, 23, 23 *]>,
139
<30, [* 2, 5, 14, 14, 14, 14, 14, 24, 27 *]>,
140
<32, [* 4, 6, 15, 15, 15, 15, 15, 25, 27 *]>,
141
<34, [* 3, 6, 16, 16, 16, 16, 16, 16, 27, 30 *]>,
142
<36, [* 2, 6, 8, 17, 17, 17, 17, 17, 27, 29, 33 *]>,
143
<38, [* 3, 7, 18, 18, 18, 18, 18, 18, 18, 30, 34 *]>,
144
<40, [* 3, 6, 9, 19, 19, 19, 19, 19, 19, 30, 33, 36 *]>,
145
<42, [* 2, 5, 9, 20, 20, 20, 20, 20, 20, 20, 32, 36, 39 *]>,
146
<44, [* 3, 7, 9, 21, 21, 21, 21, 21, 21, 21, 34, 36, 40 *]>,
147
<46, [* 4, 4, 9, 22, 22, 22, 22, 22, 22, 22, 22, 36, 41, 41 *]>,
148
<48, [* 2, 5, 9, 11, 23, 23, 23, 23, 23, 23, 23, 36, 38, 42, 45 *]>,
149
<50, [* 4, 6, 8, 24, 24, 24, 24, 24, 24, 24, 24, 24, 41, 43, 45 *]>
150
]>,
151
152
<6,[
153
<2, [**]>,
154
<4, [* 1 *]>,
155
<6, [* 2, 2, 2 *]>,
156
<8, [* 1, 3, 3, 3, 6 *]>,
157
<10, [* 1, 4, 4, 4, 4, 4, 8 *]>,
158
<12, [* 2, 2, 5, 5, 5, 5, 5, 9, 9 *]>,
159
<14, [* 1, 3, 6, 6, 6, 6, 6, 6, 6, 10, 12 *]>,
160
<16, [* 1, 3, 3, 7, 7, 7, 7, 7, 7, 7, 12, 12, 14 *]>,
161
<18, [* 2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 15, 15, 15 *]>,
162
<20, [* 1, 3, 3, 3, 9, 9, 9, 9, 9, 9, 9, 9, 9, 16, 16, 16, 18 *]>,
163
<22, [* 1, 3, 3, 4, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 17, 18, 18, 20 *]>,
164
<24, [* 2, 2, 2, 5, 5, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 18, 18, 21, 21, 21 *]>,
165
<26, [* 1, 3, 3, 3, 6, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 19, 22, 22, 22, 24 *]>,
166
<28, [* 1, 4, 4, 4, 4, 4, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 23, 23, 23, 23, 23, 26 *]>,
167
<30, [* 2, 2, 3, 5, 5, 5, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 24, 24, 24, 26, 27, 27 *]>,
168
<32, [* 1, 3, 4, 4, 6, 6, 6, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 25, 25, 25, 27, 27, 28, 30 *]>,
169
<34, [* 1, 3, 3, 5, 6, 6, 7, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 26, 27, 27, 28, 30, 30, 32 *]>,
170
<36, [* 2, 2, 2, 6, 6, 6, 8, 8, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 27, 27, 29, 29, 29, 33, 33, 33 *]>,
171
<38, [* 1, 3, 3, 3, 7, 7, 7, 9, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 28, 30, 30, 30, 34, 34, 34, 36 *]>,
172
<40, [* 1, 3, 3, 4, 6, 6, 8, 9, 9, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 30, 30, 31, 33, 33, 35, 36, 36, 38 *]>,
173
<42, [* 2, 2, 2, 5, 5, 6, 8, 9, 9, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 32, 32, 33, 35, 36,
174
36, 39, 39, 39 *]>,
175
<44, [* 1, 3, 3, 3, 6, 7, 7, 9, 9, 10, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21,
176
21, 33, 34, 34, 36, 36, 37, 40, 40, 40, 42 *]>,
177
<46, [* 1, 4, 4, 4, 4, 4, 8, 9, 9, 10, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 35, 36, 36, 37, 41, 41, 41, 41, 41, 44 *]>,
178
<48, [* 2, 2, 3, 5, 5, 5, 7, 9, 9, 11, 11, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 36, 36, 38, 38, 40, 42, 42, 42, 44, 45, 45 *]>,
179
<50, [* 1, 3, 4, 4, 6, 6, 6, 8, 8, 10, 12, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 37, 39, 41,
180
41, 43, 43, 43, 45, 45, 46, 48 *]>
181
]>,
182
183
<9,[
184
<2, [**]>,
185
<4, [* oo *]>,
186
<6, [* 2, oo, oo *]>,
187
<8, [* 3, oo, oo, oo, oo *]>,
188
<10, [* 4, 4, oo, oo, oo, oo, oo *]>,
189
<12, [* 2, 5, 9, oo, oo, oo, oo, oo, oo *]>,
190
<14, [* 6, 6, 6, oo, oo, oo, oo, oo, oo, oo, oo *]>,
191
<16, [* 3, 7, 7, 12, oo, oo, oo, oo, oo, oo, oo, oo, oo *]>,
192
<18, [* 2, 8, 8, 8, 15, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo *]>,
193
<20, [* 3, 9, 9, 9, 16, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo *]>,
194
<22, [* 3, 10, 10, 10, 10, 18, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo *]>,
195
<24, [* 2, 5, 11, 11, 11, 18, 21, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo *]>,
196
<26, [* 3, 12, 12, 12, 12, 12, 22, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo *]>,
197
<28, [* 4, 4, 13, 13, 13, 13, 23, 23, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo *]>,
198
<30, [* 2, 5, 14, 14, 14, 14, 14, 24, 27, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo *]>,
199
<32, [* 4, 6, 15, 15, 15, 15, 15, 25, 27, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo *]>,
200
<34, [* 3, 6, 16, 16, 16, 16, 16, 16, 27, 30, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo *]>,
201
<36, [* 2, 6, 8, 17, 17, 17, 17, 17, 27, 29, 33, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo *]>,
202
<38, [* 3, 7, 18, 18, 18, 18, 18, 18, 18, 30, 34, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo *]>,
203
<40, [* 3, 6, 9, 19, 19, 19, 19, 19, 19, 30, 33, 36, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo *]>,
204
<42, [* 2, 5, 9, 20, 20, 20, 20, 20, 20, 20, 32, 36, 39, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo *]>,
205
<44, [* 3, 7, 9, 21, 21, 21, 21, 21, 21, 21, 34, 36, 40, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo,
206
oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo *]>,
207
<46, [* 4, 4, 9, 22, 22, 22, 22, 22, 22, 22, 22, 36, 41, 41, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo *]>,
208
<48, [* 2, 5, 9, 11, 23, 23, 23, 23, 23, 23, 23, 36, 38, 42, 45, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo *]>,
209
<50, [* 4, 6, 8, 24, 24, 24, 24, 24, 24, 24, 24, 24, 41, 43, 45, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo *]>
210
]>
211
212
213
*];
214
215
216
217
218