Newform orbit 27.3.b.a

• Label: 27.3.b.a
• Level: $27$
• Weight: $3$
• Character orbit: 27.b
• Self dual: yes
• Analytic conductor: $0.736$
• Analytic rank: $0$
• Dimension: $1$
• CM discriminant: -3
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	27.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	\(0.735696713773\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

$q$-expansion

\(f(q)\)

\(=\)

\( q + 4 q^{4} - 13 q^{7}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/27\mathbb{Z}\right)^\times\).

\(n\)	\(2\)
\(\chi(n)\)	\(-1\)

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

26.1

0

0

0

4.00000

0

0

−13.0000

0

0

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	27.3.b.a	✓	1
3.b	odd	2	1	CM	27.3.b.a	✓	1
4.b	odd	2	1		432.3.e.b		1
5.b	even	2	1		675.3.c.c		1
5.c	odd	4	2		675.3.d.c		2
8.b	even	2	1		1728.3.e.a		1
8.d	odd	2	1		1728.3.e.d		1
9.c	even	3	2		81.3.d.a		2
9.d	odd	6	2		81.3.d.a		2
12.b	even	2	1		432.3.e.b		1
15.d	odd	2	1		675.3.c.c		1
15.e	even	4	2		675.3.d.c		2
24.f	even	2	1		1728.3.e.d		1
24.h	odd	2	1		1728.3.e.a		1
36.f	odd	6	2		1296.3.q.a		2
36.h	even	6	2		1296.3.q.a		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
27.3.b.a	✓	1	1.a	even	1	1	trivial
27.3.b.a	✓	1	3.b	odd	2	1	CM
81.3.d.a		2	9.c	even	3	2
81.3.d.a		2	9.d	odd	6	2
432.3.e.b		1	4.b	odd	2	1
432.3.e.b		1	12.b	even	2	1
675.3.c.c		1	5.b	even	2	1
675.3.c.c		1	15.d	odd	2	1
675.3.d.c		2	5.c	odd	4	2
675.3.d.c		2	15.e	even	4	2
1296.3.q.a		2	36.f	odd	6	2
1296.3.q.a		2	36.h	even	6	2
1728.3.e.a		1	8.b	even	2	1
1728.3.e.a		1	24.h	odd	2	1
1728.3.e.d		1	8.d	odd	2	1
1728.3.e.d		1	24.f	even	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2} \) acting on \(S_{3}^{\mathrm{new}}(27, [\chi])\).

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T \)
$3$	\( T \)
$5$	\( T \)
$7$	\( T + 13 \)
$11$	\( T \)