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L-functions
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Modular forms
Classical
Maass
Hilbert
Bianchi
Varieties
Elliptic curves over
Q
\Q
Q
Elliptic curves over
Q
(
α
)
\Q(\alpha)
Q
(
α
)
Genus 2 curves over
Q
\Q
Q
Higher genus families
Abelian varieties over
F
q
\F_{q}
F
q
Fields
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p
p
p
-adic fields
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Sato-Tate groups
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Sato-Tate group labels
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Weight
Degree
Include irrational
S
T
0
\mathrm{ST}^0
S
T
0
Maximal
no
yes
SO(1)
SO(2)
SO(3)
SO(4)
SO(5)
SO(6)
U(1)
SU(2)
U(1)_2
SU(2)_2
U(1)xU(1)
U(1)xSU(2)
SU(2)xSU(2)
USp(4)
U(1)_3
SU(2)_3
U(1)xU(1)_2
SU(2)xU(1)_2
U(1)xSU(2)_2
SU(2)xSU(2)_2
U(1)^3
U(1)^2xSU(2)
U(1)xSU(2)^2
SU(2)^3
U(1)xUSp(4)
SU(2)xUSp(4)
U(3)
USp(6)
yes
no
Components
Component group
P
r
[
a
1
=
0
]
\mathrm{Pr}[a_1=0]
P
r
[
a
1
=
0
]
Second trace moment
Fourth trace moment
First
a
2
a_2
a
2
moment
Sort order
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▲ weight
degree
real dimension
component group
trace zero density
character diagonal
columns to display
✓ label
✓ weight
✓ degree
✓ real dimension
✓ identity component
✓ name
✓ components
✓ Pr[t=0]
✓ E[a_1^2]
✓ E[a_1^4]
E[a_1^6]
E[a_1^8]
E[a_1^{10}]
E[a_1^{12}]
✓ E[a_2]
E[a_2^2]
E[a_2^3]
E[a_2^4]
E[a_2^5]
E[a_2^6]
E[a_3^2]
E[a_3^4]
E[a_3^6]
maximal
rational
diagonal
show all
Results (unique match)
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Label
Wt
Deg
d
i
m
R
\mathrm{dim}_{\mathbb{R}}
d
i
m
R
G
0
\mathrm{G}^0
G
0
Name
G
/
G
0
\mathrm{G}/\mathrm{G}^0
G
/
G
0
P
r
[
t
=
0
]
\mathrm{Pr}[t\!=\!0]
P
r
[
t
=
0
]
E
[
a
1
2
]
\mathrm{E}[a_1^2]
E
[
a
1
2
]
E
[
a
1
4
]
\mathrm{E}[a_1^4]
E
[
a
1
4
]
E
[
a
1
6
]
\mathrm{E}[a_1^6]
E
[
a
1
6
]
E
[
a
1
8
]
\mathrm{E}[a_1^8]
E
[
a
1
8
]
E
[
a
1
10
]
\mathrm{E}[a_1^{10}]
E
[
a
1
1
0
]
E
[
a
1
12
]
\mathrm{E}[a_1^{12}]
E
[
a
1
1
2
]
E
[
a
2
]
\mathrm{E}[a_2]
E
[
a
2
]
E
[
a
2
2
]
\mathrm{E}[a_2^2]
E
[
a
2
2
]
E
[
a
2
3
]
\mathrm{E}[a_2^3]
E
[
a
2
3
]
E
[
a
2
4
]
\mathrm{E}[a_2^4]
E
[
a
2
4
]
E
[
a
2
5
]
\mathrm{E}[a_2^5]
E
[
a
2
5
]
E
[
a
2
6
]
\mathrm{E}[a_2^6]
E
[
a
2
6
]
E
[
a
3
2
]
\mathrm{E}[a_3^2]
E
[
a
3
2
]
E
[
a
3
4
]
\mathrm{E}[a_3^4]
E
[
a
3
4
]
E
[
a
3
6
]
\mathrm{E}[a_3^6]
E
[
a
3
6
]
Maximal
Rational
Diagonal
1.6.M.8.3a
1
1
1
6
6
6
3
3
3
S
U
(
2
)
3
\mathrm{SU}(2)_{3}
S
U
(
2
)
3
M
(
D
4
)
M(D_4)
M
(
D
4
)
8
8
8
0
0
0
2
2
2
22
22
2
2
460
460
4
6
0
11494
11494
1
1
4
9
4
310044
310044
3
1
0
0
4
4
310044
310044
3
1
0
0
4
4
2
2
2
9
9
9
59
59
5
9
539
539
5
3
9
5772
5772
5
7
7
2
66783
66783
6
6
7
8
3
9
9
9
1388
1388
1
3
8
8
320178
320178
3
2
0
1
7
8
✓
[
1
,
2
,
6
,
5
,
9
,
40
,
46
,
70
,
103
,
46
,
23
,
195
,
237
,
544
,
1056
,
513
,
539
,
1220
,
1002
,
277
]
[1, 2, 6, 5, 9, 40, 46, 70, 103, 46, 23, 195, 237, 544, 1056, 513, 539, 1220, 1002, 277]
[
1
,
2
,
6
,
5
,
9
,
4
0
,
4
6
,
7
0
,
1
0
3
,
4
6
,
2
3
,
1
9
5
,
2
3
7
,
5
4
4
,
1
0
5
6
,
5
1
3
,
5
3
9
,
1
2
2
0
,
1
0
0
2
,
2
7
7
]
Download
displayed columns
for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV