Newform orbit 2128.1.cw.b

• Label: 2128.1.cw.b
• Level: $2128$
• Weight: $1$
• Character orbit: 2128.cw
• Analytic conductor: $1.062$
• Analytic rank: $0$
• Dimension: $2$
• Projective image: $D_{6}$
• CM discriminant: -19
• Inner twists: $4$

Newspace parameters

Level:	$N$	$=$	$2128 = 2^{4} \cdot 7 \cdot 19$
Weight:	$k$	$=$	$1$
Character orbit:	$[\chi]$	$=$	2128.cw (of order $6$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$1.06201034688$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
Defining polynomial:	$x^{2} - x + 1$
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$1$
Twist minimal:	yes
Projective image:	$D_{6}$
Projective field:	Galois closure of 6.2.1553235712.2

$q$-expansion

The $q$-expansion and trace form are shown below.

$f(q)$	$=$	q + (-z - 1) * q^5 + q^7 + z^2 * q^9 + (-z^2 + 1) * q^17 - z^2 * q^19 + (-z - 1) * q^23 + (z^2 + z + 1) * q^25 + (-z - 1) * q^35 + (-z^2 - z) * q^43 + (-z^2 + 1) * q^45 - 2*z^2 * q^47 + q^49 + z^2 * q^63 - z * q^81 - q^83 + (z^2 - z - 2) * q^85 + (z^2 - 1) * q^95
$\operatorname{Tr}(f)(q)$	$=$	$2 q - 3 q^{5} + 2 q^{7} - q^{9} + 3 q^{17} + q^{19} - 3 q^{23} + 2 q^{25} - 3 q^{35} + 3 q^{45} + 2 q^{47} + 2 q^{49} - q^{63} - q^{81} - 2 q^{83} - 6 q^{85} - 3 q^{95}+O(q^{100})$

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2128\mathbb{Z}\right)^\times$.

$n$	$533$	$799$	$913$	$1009$
$\chi(n)$	$1$	$-1$	$-\zeta_{6}^{2}$	$-1$

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  

$\iota_m(\nu)$

$a_{2}$

$a_{3}$

$a_{4}$

$a_{5}$

$a_{6}$

$a_{7}$

$a_{8}$

$a_{9}$

$a_{10}$

607.1

0.500000	+	0.866025i
0.500000	−	0.866025i

0

0

0

−1.50000

−

0.866025i

0

1.00000

0

−0.500000

+

0.866025i

0

1823.1

0

0

0

−1.50000

+

0.866025i

0

1.00000

0

−0.500000

−

0.866025i

0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
19.b	odd	2	1	CM by $\Q(\sqrt{-19})$
28.f	even	6	1	inner
532.bh	odd	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2128.1.cw.b	yes	2
4.b	odd	2	1		2128.1.cw.a	✓	2
7.d	odd	6	1		2128.1.cw.a	✓	2
19.b	odd	2	1	CM	2128.1.cw.b	yes	2
28.f	even	6	1	inner	2128.1.cw.b	yes	2
76.d	even	2	1		2128.1.cw.a	✓	2
133.o	even	6	1		2128.1.cw.a	✓	2
532.bh	odd	6	1	inner	2128.1.cw.b	yes	2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
2128.1.cw.a	✓	2	4.b	odd	2	1
2128.1.cw.a	✓	2	7.d	odd	6	1
2128.1.cw.a	✓	2	76.d	even	2	1
2128.1.cw.a	✓	2	133.o	even	6	1
2128.1.cw.b	yes	2	1.a	even	1	1	trivial
2128.1.cw.b	yes	2	19.b	odd	2	1	CM
2128.1.cw.b	yes	2	28.f	even	6	1	inner
2128.1.cw.b	yes	2	532.bh	odd	6	1	inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{1}^{\mathrm{new}}(2128, [\chi])$:

$T_{5}^{2} + 3T_{5} + 3$

$T_{11}$

$T_{23}^{2} + 3T_{23} + 3$

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T^{2}$
$3$	$T^{2}$
$5$	$T^{2} + 3T + 3$
$7$	$(T - 1)^{2}$
$11$	$T^{2}$