Newform orbit 2888.1.f.a

• Label: 2888.1.f.a
• Level: $2888$
• Weight: $1$
• Character orbit: 2888.f
• Self dual: yes
• Analytic conductor: $1.441$
• Analytic rank: $0$
• Dimension: $1$
• Projective image: $D_{3}$
• CM discriminant: -8
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2888 = 2^{3} \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2888.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	\(1.44129975648\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 152)
Projective image:	\(D_{3}\)
Projective field:	Galois closure of 3.1.2888.1
Artin image:	$D_6$
Artin field:	Galois closure of 6.0.158470336.1

$q$-expansion

\(f(q)\)

\(=\)

\( q - q^{2} + q^{3} + q^{4} - q^{6} - q^{8}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2888\mathbb{Z}\right)^\times\).

\(n\)	\(1445\)	\(2167\)	\(2529\)
\(\chi(n)\)	\(-1\)	\(-1\)	\(1\)

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

723.1

0

−1.00000

1.00000

1.00000

0

−1.00000

0

−1.00000

0

0

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2888.1.f.a		1
8.d	odd	2	1	CM	2888.1.f.a		1
19.b	odd	2	1		2888.1.f.b		1
19.c	even	3	2		2888.1.k.a		2
19.d	odd	6	2		152.1.k.a	✓	2
19.e	even	9	6		2888.1.u.d		6
19.f	odd	18	6		2888.1.u.c		6
57.f	even	6	2		1368.1.bz.a		2
76.f	even	6	2		608.1.o.a		2
95.h	odd	6	2		3800.1.bd.c		2
95.l	even	12	4		3800.1.bn.b		4
152.b	even	2	1		2888.1.f.b		1
152.k	odd	6	2		2888.1.k.a		2
152.l	odd	6	2		608.1.o.a		2
152.o	even	6	2		152.1.k.a	✓	2
152.u	odd	18	6		2888.1.u.d		6
152.v	even	18	6		2888.1.u.c		6
456.s	odd	6	2		1368.1.bz.a		2
760.bf	even	6	2		3800.1.bd.c		2
760.bu	odd	12	4		3800.1.bn.b		4

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
152.1.k.a	✓	2	19.d	odd	6	2
152.1.k.a	✓	2	152.o	even	6	2
608.1.o.a		2	76.f	even	6	2
608.1.o.a		2	152.l	odd	6	2
1368.1.bz.a		2	57.f	even	6	2
1368.1.bz.a		2	456.s	odd	6	2
2888.1.f.a		1	1.a	even	1	1	trivial
2888.1.f.a		1	8.d	odd	2	1	CM
2888.1.f.b		1	19.b	odd	2	1
2888.1.f.b		1	152.b	even	2	1
2888.1.k.a		2	19.c	even	3	2
2888.1.k.a		2	152.k	odd	6	2
2888.1.u.c		6	19.f	odd	18	6
2888.1.u.c		6	152.v	even	18	6
2888.1.u.d		6	19.e	even	9	6
2888.1.u.d		6	152.u	odd	18	6
3800.1.bd.c		2	95.h	odd	6	2
3800.1.bd.c		2	760.bf	even	6	2
3800.1.bn.b		4	95.l	even	12	4
3800.1.bn.b		4	760.bu	odd	12	4

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3} - 1 \) acting on \(S_{1}^{\mathrm{new}}(2888, [\chi])\).

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T + 1 \)
$3$	\( T - 1 \)
$5$	\( T \)
$7$	\( T \)
$11$	\( T + 1 \)