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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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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.M.1.1a
1
1
1
6
6
6
3
3
3
S
U
(
2
)
3
\mathrm{SU}(2)_{3}
S
U
(
2
)
3
M
(
C
1
)
M(C_1)
M
(
C
1
)
1
1
1
0
0
0
9
9
9
162
162
1
6
2
3645
3645
3
6
4
5
91854
91854
9
1
8
5
4
2480058
2480058
2
4
8
0
0
5
8
2480058
2480058
2
4
8
0
0
5
8
6
6
6
45
45
4
5
405
405
4
0
5
4131
4131
4
1
3
1
45684
45684
4
5
6
8
4
532899
532899
5
3
2
8
9
9
65
65
6
5
11076
11076
1
1
0
7
6
2561186
2561186
2
5
6
1
1
8
6
✓
[
1
,
9
,
34
,
26
,
45
,
320
,
334
,
486
,
810
,
300
,
164
,
1539
,
1836
,
4325
,
8448
,
4023
,
4191
,
9680
,
7920
,
2101
]
[1, 9, 34, 26, 45, 320, 334, 486, 810, 300, 164, 1539, 1836, 4325, 8448, 4023, 4191, 9680, 7920, 2101]
[
1
,
9
,
3
4
,
2
6
,
4
5
,
3
2
0
,
3
3
4
,
4
8
6
,
8
1
0
,
3
0
0
,
1
6
4
,
1
5
3
9
,
1
8
3
6
,
4
3
2
5
,
8
4
4
8
,
4
0
2
3
,
4
1
9
1
,
9
6
8
0
,
7
9
2
0
,
2
1
0
1
]
Download
displayed columns
for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV