Newform orbit 1452.3.e.b

• Label: 1452.3.e.b
• Level: $1452$
• Weight: $3$
• Character orbit: 1452.e
• Self dual: yes
• Analytic conductor: $39.564$
• Analytic rank: $0$
• Dimension: $1$
• CM discriminant: -3
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1452 = 2^{2} \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1452.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	\(39.5641343851\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 12)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

$q$-expansion

\(f(q)\)

\(=\)

\( q - 3 q^{3} - 2 q^{7} + 9 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1452\mathbb{Z}\right)^\times\).

\(n\)	\(485\)	\(727\)	\(1333\)
\(\chi(n)\)	\(-1\)	\(1\)	\(1\)

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

Label  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

485.1

0

0

−3.00000

0

0

0

−2.00000

0

9.00000

0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	CM by \(\Q(\sqrt{-3}) \)

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1452.3.e.b		1
3.b	odd	2	1	CM	1452.3.e.b		1
11.b	odd	2	1		12.3.c.a	✓	1
33.d	even	2	1		12.3.c.a	✓	1
44.c	even	2	1		48.3.e.a		1
55.d	odd	2	1		300.3.g.b		1
55.e	even	4	2		300.3.b.a		2
77.b	even	2	1		588.3.c.c		1
77.h	odd	6	2		588.3.p.c		2
77.i	even	6	2		588.3.p.b		2
88.b	odd	2	1		192.3.e.b		1
88.g	even	2	1		192.3.e.a		1
99.g	even	6	2		324.3.g.b		2
99.h	odd	6	2		324.3.g.b		2
132.d	odd	2	1		48.3.e.a		1
165.d	even	2	1		300.3.g.b		1
165.l	odd	4	2		300.3.b.a		2
176.i	even	4	2		768.3.h.b		2
176.l	odd	4	2		768.3.h.a		2
220.g	even	2	1		1200.3.l.b		1
220.i	odd	4	2		1200.3.c.c		2
231.h	odd	2	1		588.3.c.c		1
231.k	odd	6	2		588.3.p.b		2
231.l	even	6	2		588.3.p.c		2
264.m	even	2	1		192.3.e.b		1
264.p	odd	2	1		192.3.e.a		1
396.k	even	6	2		1296.3.q.b		2
396.o	odd	6	2		1296.3.q.b		2
528.s	odd	4	2		768.3.h.b		2
528.x	even	4	2		768.3.h.a		2
660.g	odd	2	1		1200.3.l.b		1
660.q	even	4	2		1200.3.c.c		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
12.3.c.a	✓	1	11.b	odd	2	1
12.3.c.a	✓	1	33.d	even	2	1
48.3.e.a		1	44.c	even	2	1
48.3.e.a		1	132.d	odd	2	1
192.3.e.a		1	88.g	even	2	1
192.3.e.a		1	264.p	odd	2	1
192.3.e.b		1	88.b	odd	2	1
192.3.e.b		1	264.m	even	2	1
300.3.b.a		2	55.e	even	4	2
300.3.b.a		2	165.l	odd	4	2
300.3.g.b		1	55.d	odd	2	1
300.3.g.b		1	165.d	even	2	1
324.3.g.b		2	99.g	even	6	2
324.3.g.b		2	99.h	odd	6	2
588.3.c.c		1	77.b	even	2	1
588.3.c.c		1	231.h	odd	2	1
588.3.p.b		2	77.i	even	6	2
588.3.p.b		2	231.k	odd	6	2
588.3.p.c		2	77.h	odd	6	2
588.3.p.c		2	231.l	even	6	2
768.3.h.a		2	176.l	odd	4	2
768.3.h.a		2	528.x	even	4	2
768.3.h.b		2	176.i	even	4	2
768.3.h.b		2	528.s	odd	4	2
1200.3.c.c		2	220.i	odd	4	2
1200.3.c.c		2	660.q	even	4	2
1200.3.l.b		1	220.g	even	2	1
1200.3.l.b		1	660.g	odd	2	1
1296.3.q.b		2	396.k	even	6	2
1296.3.q.b		2	396.o	odd	6	2
1452.3.e.b		1	1.a	even	1	1	trivial
1452.3.e.b		1	3.b	odd	2	1	CM

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{3}^{\mathrm{new}}(1452, [\chi])\):

\( T_{5} \)

\( T_{7} + 2 \)

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T \)
$3$	\( T + 3 \)
$5$	\( T \)
$7$	\( T + 2 \)
$11$	\( T \)