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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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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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results
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CSV
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.G.2.1b
1
1
1
6
6
6
5
5
5
U
(
1
)
2
×
S
U
(
2
)
\mathrm{U}(1)^2\times\mathrm{SU}(2)
U
(
1
)
2
×
S
U
(
2
)
F
a
×
S
U
(
2
)
F_{a}\times \mathrm{SU}(2)
F
a
×
S
U
(
2
)
2
2
2
0
0
0
4
4
4
41
41
4
1
620
620
6
2
0
11739
11739
1
1
7
3
9
255885
255885
2
5
5
8
8
5
255885
255885
2
5
5
8
8
5
3
3
3
14
14
1
4
84
84
8
4
627
627
6
2
7
5493
5493
5
4
9
3
53714
53714
5
3
7
1
4
18
18
1
8
1460
1460
1
4
6
0
228960
228960
2
2
8
9
6
0
✓
[
1
,
4
,
9
,
6
,
11
,
47
,
42
,
53
,
76
,
28
,
26
,
164
,
170
,
349
,
620
,
273
,
278
,
592
,
456
,
115
]
[1, 4, 9, 6, 11, 47, 42, 53, 76, 28, 26, 164, 170, 349, 620, 273, 278, 592, 456, 115]
[
1
,
4
,
9
,
6
,
1
1
,
4
7
,
4
2
,
5
3
,
7
6
,
2
8
,
2
6
,
1
6
4
,
1
7
0
,
3
4
9
,
6
2
0
,
2
7
3
,
2
7
8
,
5
9
2
,
4
5
6
,
1
1
5
]
Download
displayed columns
for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV