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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
Number fields
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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degree
real dimension
component group
trace zero density
character diagonal
columns to display
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✓ 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.I.6.2a
1
1
1
6
6
6
6
6
6
S
U
(
2
)
×
S
U
(
2
)
2
\mathrm{SU}(2)\times\mathrm{SU}(2)_2
S
U
(
2
)
×
S
U
(
2
)
2
S
U
(
2
)
×
E
6
\mathrm{SU}(2)\times E_6
S
U
(
2
)
×
E
6
6
6
6
0
0
0
3
3
3
26
26
2
6
345
345
3
4
5
5754
5754
5
7
5
4
110586
110586
1
1
0
5
8
6
110586
110586
1
1
0
5
8
6
2
2
2
9
9
9
51
51
5
1
357
357
3
5
7
2868
2868
2
8
6
8
25403
25403
2
5
4
0
3
12
12
1
2
808
808
8
0
8
101370
101370
1
0
1
3
7
0
✓
[
1
,
3
,
6
,
5
,
7
,
26
,
24
,
28
,
39
,
16
,
13
,
69
,
73
,
135
,
230
,
99
,
101
,
201
,
146
,
43
]
[1, 3, 6, 5, 7, 26, 24, 28, 39, 16, 13, 69, 73, 135, 230, 99, 101, 201, 146, 43]
[
1
,
3
,
6
,
5
,
7
,
2
6
,
2
4
,
2
8
,
3
9
,
1
6
,
1
3
,
6
9
,
7
3
,
1
3
5
,
2
3
0
,
9
9
,
1
0
1
,
2
0
1
,
1
4
6
,
4
3
]
Download
displayed columns
for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV