Newform orbit 2232.1.i.a

• Label: 2232.1.i.a
• Level: $2232$
• Weight: $1$
• Character orbit: 2232.i
• Self dual: yes
• Analytic conductor: $1.114$
• Analytic rank: $0$
• Dimension: $1$
• Projective image: $D_{2}$
• CM/RM discs: -31, -248, 8
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2232 = 2^{3} \cdot 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2232.i (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	\(1.11391310820\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 248)
Projective image:	\(D_{2}\)
Projective field:	Galois closure of \(\Q(\sqrt{2}, \sqrt{-31})\)
Artin image:	$D_4$
Artin field:	Galois closure of 4.2.17856.3

$q$-expansion

\(f(q)\)

\(=\)

\( q - q^{2} + q^{4} - 2 q^{7} - q^{8}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2232\mathbb{Z}\right)^\times\).

\(n\)	\(497\)	\(559\)	\(1117\)	\(1801\)
\(\chi(n)\)	\(1\)	\(1\)	\(-1\)	\(-1\)

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

1549.1

0

−1.00000

0

1.00000

0

0

−2.00000

−1.00000

0

0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
8.b	even	2	1	RM by \(\Q(\sqrt{2}) \)
31.b	odd	2	1	CM by \(\Q(\sqrt{-31}) \)
248.g	odd	2	1	CM by \(\Q(\sqrt{-62}) \)

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2232.1.i.a		1
3.b	odd	2	1		248.1.g.a	✓	1
8.b	even	2	1	RM	2232.1.i.a		1
12.b	even	2	1		992.1.g.a		1
24.f	even	2	1		992.1.g.a		1
24.h	odd	2	1		248.1.g.a	✓	1
31.b	odd	2	1	CM	2232.1.i.a		1
93.c	even	2	1		248.1.g.a	✓	1
248.g	odd	2	1	CM	2232.1.i.a		1
372.b	odd	2	1		992.1.g.a		1
744.m	odd	2	1		992.1.g.a		1
744.o	even	2	1		248.1.g.a	✓	1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
248.1.g.a	✓	1	3.b	odd	2	1
248.1.g.a	✓	1	24.h	odd	2	1
248.1.g.a	✓	1	93.c	even	2	1
248.1.g.a	✓	1	744.o	even	2	1
992.1.g.a		1	12.b	even	2	1
992.1.g.a		1	24.f	even	2	1
992.1.g.a		1	372.b	odd	2	1
992.1.g.a		1	744.m	odd	2	1
2232.1.i.a		1	1.a	even	1	1	trivial
2232.1.i.a		1	8.b	even	2	1	RM
2232.1.i.a		1	31.b	odd	2	1	CM
2232.1.i.a		1	248.g	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 \(S_{1}^{\mathrm{new}}(2232, [\chi])\):

\( T_{5} \)

\( T_{7} + 2 \)

Hecke characteristic polynomials

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