Newform orbit 2280.1.t.a

• Label: 2280.1.t.a
• Level: $2280$
• Weight: $1$
• Character orbit: 2280.t
• Self dual: yes
• Analytic conductor: $1.138$
• Analytic rank: $0$
• Dimension: $1$
• Projective image: $D_{2}$
• CM/RM discs: -95, -2280, 24
• Inner twists: $4$

Newspace parameters

Level:	$N$	$=$	$2280 = 2^{3} \cdot 3 \cdot 5 \cdot 19$
Weight:	$k$	$=$	$1$
Character orbit:	$[\chi]$	$=$	2280.t (of order $2$, degree $1$, minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	$1.13786822880$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	yes
Projective image:	$D_{2}$
Projective field:	Galois closure of $\Q(\sqrt{6}, \sqrt{-95})$
Artin image:	$D_4$
Artin field:	Galois closure of 4.2.54720.2
Stark unit:	Root of $x^{4} - 26x^{3} - 45x^{2} - 26x + 1$

$q$-expansion

$f(q)$

$=$

q - q^2 - q^3 + q^4 - q^5 + q^6 - q^8 + q^9 + q^10 - q^12 + q^15 + q^16 - q^18 - q^19 - q^20 + q^24 + q^25 - q^27 - q^30 - q^32 + q^36 + q^38 + q^40 - q^45 - q^48 - q^49 - q^50 + 2 * q^53 + q^54 + q^57 + q^60 + q^64 + 2 * q^67 - q^72 - q^75 - q^76 - q^80 + q^81 + q^90 + q^95 + q^96 + 2 * q^97 + q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2280\mathbb{Z}\right)^\times$.

$n$	$457$	$761$	$1141$	$1711$	$1921$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$	$-1$

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  

$\iota_m(\nu)$

$a_{2}$

$a_{3}$

$a_{4}$

$a_{5}$

$a_{6}$

$a_{7}$

$a_{8}$

$a_{9}$

$a_{10}$

1139.1

0

−1.00000

−1.00000

1.00000

−1.00000

1.00000

0

−1.00000

1.00000

1.00000

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
24.f	even	2	1	RM by $\Q(\sqrt{6})$
95.d	odd	2	1	CM by $\Q(\sqrt{-95})$
2280.t	odd	2	1	CM by $\Q(\sqrt{-570})$

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2280.1.t.a	✓	1
3.b	odd	2	1		2280.1.t.c	yes	1
5.b	even	2	1		2280.1.t.d	yes	1
8.d	odd	2	1		2280.1.t.c	yes	1
15.d	odd	2	1		2280.1.t.b	yes	1
19.b	odd	2	1		2280.1.t.d	yes	1
24.f	even	2	1	RM	2280.1.t.a	✓	1
40.e	odd	2	1		2280.1.t.b	yes	1
57.d	even	2	1		2280.1.t.b	yes	1
95.d	odd	2	1	CM	2280.1.t.a	✓	1
120.m	even	2	1		2280.1.t.d	yes	1
152.b	even	2	1		2280.1.t.b	yes	1
285.b	even	2	1		2280.1.t.c	yes	1
456.l	odd	2	1		2280.1.t.d	yes	1
760.p	even	2	1		2280.1.t.c	yes	1
2280.t	odd	2	1	CM	2280.1.t.a	✓	1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
2280.1.t.a	✓	1	1.a	even	1	1	trivial
2280.1.t.a	✓	1	24.f	even	2	1	RM
2280.1.t.a	✓	1	95.d	odd	2	1	CM
2280.1.t.a	✓	1	2280.t	odd	2	1	CM
2280.1.t.b	yes	1	15.d	odd	2	1
2280.1.t.b	yes	1	40.e	odd	2	1
2280.1.t.b	yes	1	57.d	even	2	1
2280.1.t.b	yes	1	152.b	even	2	1
2280.1.t.c	yes	1	3.b	odd	2	1
2280.1.t.c	yes	1	8.d	odd	2	1
2280.1.t.c	yes	1	285.b	even	2	1
2280.1.t.c	yes	1	760.p	even	2	1
2280.1.t.d	yes	1	5.b	even	2	1
2280.1.t.d	yes	1	19.b	odd	2	1
2280.1.t.d	yes	1	120.m	even	2	1
2280.1.t.d	yes	1	456.l	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{1}^{\mathrm{new}}(2280, [\chi])$:

$T_{11}$

$T_{13}$

$T_{23}$

$T_{31}$

$T_{53} - 2$

$T_{67} - 2$

$T_{101} - 2$

$T_{191} - 2$

Hecke characteristic polynomials

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