Newform orbit 2527.1.d.f

• Label: 2527.1.d.f
• Level: $2527$
• Weight: $1$
• Character orbit: 2527.d
• Self dual: yes
• Analytic conductor: $1.261$
• Analytic rank: $0$
• Dimension: $4$
• Projective image: $D_{10}$
• CM discriminant: -7
• Inner twists: $4$

Newspace parameters

Level:	$N$	$=$	$2527 = 7 \cdot 19^{2}$
Weight:	$k$	$=$	$1$
Character orbit:	$[\chi]$	$=$	2527.d (of order $2$, degree $1$, minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	$1.26113728692$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{20})^+$
Defining polynomial:	$x^{4} - 5x^{2} + 5$
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$1$
Twist minimal:	yes
Projective image:	$D_{10}$
Projective field:	Galois closure of 10.0.774773162367379.1

$q$-expansion

Coefficients of the $q$-expansion are expressed in terms of a basis $1,\beta_1,\beta_2,\beta_3$ for the coefficient ring described below. We also show the integral $q$-expansion of the trace form.

$f(q)$	$=$	q - b1 * q^2 + (b2 + 2) * q^4 - q^7 + (-b3 - b1) * q^8 + q^9 - b2 * q^11 + b1 * q^14 + (2*b2 + 2) * q^16 - b1 * q^18 + b3 * q^22 + (-b2 - 1) * q^23 + q^25 + (-b2 - 2) * q^28 + b3 * q^29 + (-b3 - b1) * q^32 + (b2 + 2) * q^36 + b2 * q^43 + (-b2 - 1) * q^44 + (b3 + b1) * q^46 + q^49 - b1 * q^50 + b1 * q^53 + (b3 + b1) * q^56 + (-2*b2 - 1) * q^58 - q^63 + (b2 + 2) * q^64 + b1 * q^67 + (-b3 - b1) * q^72 + b2 * q^77 - b3 * q^79 + q^81 - b3 * q^86 + b1 * q^88 + (-2*b2 - 3) * q^92 - b1 * q^98 - b2 * q^99
$\operatorname{Tr}(f)(q)$	$=$	$4 q + 6 q^{4} - 4 q^{7} + 4 q^{9} + 2 q^{11} + 4 q^{16} - 2 q^{23} + 4 q^{25} - 6 q^{28} + 6 q^{36} - 2 q^{43} - 2 q^{44} + 4 q^{49} - 4 q^{63} + 6 q^{64} - 2 q^{77} + 4 q^{81} - 8 q^{92} + 2 q^{99}+O(q^{100})$

Basis of coefficient ring in terms of $\nu = \zeta_{20} + \zeta_{20}^{-1}$:

$\beta_{1}$	$=$	$\nu$
$\beta_{2}$	$=$	$\nu^{2} - 3$
$\beta_{3}$	$=$	$\nu^{3} - 3\nu$

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2527\mathbb{Z}\right)^\times$.

$n$	$1445$	$1807$
$\chi(n)$	$-1$	$1$

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  

$\iota_m(\nu)$

$a_{2}$

$a_{3}$

$a_{4}$

$a_{5}$

$a_{6}$

$a_{7}$

$a_{8}$

$a_{9}$

$a_{10}$

1084.1

1.90211
1.17557
−1.17557
−1.90211

−1.90211

0

2.61803

0

0

−1.00000

−3.07768

1.00000

0

1084.2

−1.17557

0

0.381966

0

0

−1.00000

0.726543

1.00000

0

1084.3

1.17557

0

0.381966

0

0

−1.00000

−0.726543

1.00000

0

1084.4

1.90211

0

2.61803

0

0

−1.00000

3.07768

1.00000

0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.b	odd	2	1	CM by $\Q(\sqrt{-7})$
19.b	odd	2	1	inner
133.c	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2527.1.d.f	✓	4
7.b	odd	2	1	CM	2527.1.d.f	✓	4
19.b	odd	2	1	inner	2527.1.d.f	✓	4
19.c	even	3	2		2527.1.m.e		8
19.d	odd	6	2		2527.1.m.e		8
19.e	even	9	6		2527.1.y.f		24
19.f	odd	18	6		2527.1.y.f		24
133.c	even	2	1	inner	2527.1.d.f	✓	4
133.m	odd	6	2		2527.1.m.e		8
133.p	even	6	2		2527.1.m.e		8
133.y	odd	18	6		2527.1.y.f		24
133.ba	even	18	6		2527.1.y.f		24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
2527.1.d.f	✓	4	1.a	even	1	1	trivial
2527.1.d.f	✓	4	7.b	odd	2	1	CM
2527.1.d.f	✓	4	19.b	odd	2	1	inner
2527.1.d.f	✓	4	133.c	even	2	1	inner
2527.1.m.e		8	19.c	even	3	2
2527.1.m.e		8	19.d	odd	6	2
2527.1.m.e		8	133.m	odd	6	2
2527.1.m.e		8	133.p	even	6	2
2527.1.y.f		24	19.e	even	9	6
2527.1.y.f		24	19.f	odd	18	6
2527.1.y.f		24	133.y	odd	18	6
2527.1.y.f		24	133.ba	even	18	6

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $T_{2}^{4} - 5T_{2}^{2} + 5$ acting on $S_{1}^{\mathrm{new}}(2527, [\chi])$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T^{4} - 5T^{2} + 5$
$3$	$T^{4}$
$5$	$T^{4}$
$7$	$(T + 1)^{4}$
$11$	$(T^{2} - T - 1)^{2}$