LMFDB - Newform orbit 2880.1.p.b

Newspace parameters

Level:	$ N $	$=$	$ 2880 = 2^{6} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2880.p (of order $2$, degree $1$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$1.43730723638$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{2}$
Projective field:	Galois closure of $\Q(\sqrt{5}, \sqrt{-6})$
Artin image:	$D_4:C_2$
Artin field:	Galois closure of 8.0.19110297600.5

$q$-expansion

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

$f(q)$	$=$	$ q - i q^{5} +O(q^{10}) $ q - z * q^5	$ q - i q^{5} + q^{11} - q^{25} - i q^{29} + i q^{31} - q^{49} - 2 i q^{55} + q^{59} - i q^{79} +O(q^{100}) $ q - z * q^5 + q^11 - q^25 - z * q^29 + z * q^31 - q^49 - 2z q^55 + q^59 - z * q^79
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q+O(q^{10}) $ 2 * q	$ 2 q + 4 q^{11} - 2 q^{25} - 2 q^{49} + 4 q^{59}+O(q^{100}) $ 2 * q + 4 * q^11 - 2 * q^25 - 2 * q^49 + 4 * q^59

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2880\mathbb{Z}\right)^\times$.

$n$	$577$	$641$	$901$	$2431$
$\chi(n)$	$-1$	$1$	$-1$	$-1$

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} $

2719.1

		1.00000i
	−	1.00000i

−

1.00000i

2719.2

1.00000i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	RM by $\Q(\sqrt{5}) $
24.h	odd	2	1	CM by $\Q(\sqrt{-6}) $
120.i	odd	2	1	CM by $\Q(\sqrt{-30}) $
8.d	odd	2	1	inner
12.b	even	2	1	inner
40.e	odd	2	1	inner
60.h	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2880.1.p.b	yes	2
3.b	odd	2	1		2880.1.p.a	✓	2
4.b	odd	2	1		2880.1.p.a	✓	2
5.b	even	2	1	RM	2880.1.p.b	yes	2
8.b	even	2	1		2880.1.p.a	✓	2
8.d	odd	2	1	inner	2880.1.p.b	yes	2
12.b	even	2	1	inner	2880.1.p.b	yes	2
15.d	odd	2	1		2880.1.p.a	✓	2
20.d	odd	2	1		2880.1.p.a	✓	2
24.f	even	2	1		2880.1.p.a	✓	2
24.h	odd	2	1	CM	2880.1.p.b	yes	2
40.e	odd	2	1	inner	2880.1.p.b	yes	2
40.f	even	2	1		2880.1.p.a	✓	2
60.h	even	2	1	inner	2880.1.p.b	yes	2
120.i	odd	2	1	CM	2880.1.p.b	yes	2
120.m	even	2	1		2880.1.p.a	✓	2

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
2880.1.p.a	✓	2	3.b	odd	2	1
2880.1.p.a	✓	2	4.b	odd	2	1
2880.1.p.a	✓	2	8.b	even	2	1
2880.1.p.a	✓	2	15.d	odd	2	1
2880.1.p.a	✓	2	20.d	odd	2	1
2880.1.p.a	✓	2	24.f	even	2	1
2880.1.p.a	✓	2	40.f	even	2	1
2880.1.p.a	✓	2	120.m	even	2	1
2880.1.p.b	yes	2	1.a	even	1	1	trivial
2880.1.p.b	yes	2	5.b	even	2	1	RM
2880.1.p.b	yes	2	8.d	odd	2	1	inner
2880.1.p.b	yes	2	12.b	even	2	1	inner
2880.1.p.b	yes	2	24.h	odd	2	1	CM
2880.1.p.b	yes	2	40.e	odd	2	1	inner
2880.1.p.b	yes	2	60.h	even	2	1	inner
2880.1.p.b	yes	2	120.i	odd	2	1	CM

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $ T_{11} - 2 $ T11 - 2 acting on $S_{1}^{\mathrm{new}}(2880, [\chi])$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T^{2} $ T^2
$3$	$ T^{2} $ T^2
$5$	$ T^{2} + 1 $ T^2 + 1
$7$	$ T^{2} $ T^2
$11$	$ (T - 2)^{2} $ (T - 2)^2
$13$	$ T^{2} $ T^2
$17$	$ T^{2} $ T^2
$19$	$ T^{2} $ T^2
$23$	$ T^{2} $ T^2
$29$	$ T^{2} + 4 $ T^2 + 4
$31$	$ T^{2} + 4 $ T^2 + 4
$37$	$ T^{2} $ T^2
$41$	$ T^{2} $ T^2
$43$	$ T^{2} $ T^2
$47$	$ T^{2} $ T^2
$53$	$ T^{2} $ T^2
$59$	$ (T - 2)^{2} $ (T - 2)^2
$61$	$ T^{2} $ T^2
$67$	$ T^{2} $ T^2
$71$	$ T^{2} $ T^2
$73$	$ T^{2} $ T^2
$79$	$ T^{2} + 4 $ T^2 + 4
$83$	$ T^{2} $ T^2
$89$	$ T^{2} $ T^2
$97$	$ T^{2} $ T^2
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Classical	Maass
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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2880.p (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\( q - i q^{5} +O(q^{10}) \) q - z * q^5	\( q - i q^{5} + q^{11} - q^{25} - i q^{29} + i q^{31} - q^{49} - 2 i q^{55} + q^{59} - i q^{79} +O(q^{100}) \) q - z * q^5 + q^11 - q^25 - z * q^29 + z * q^31 - q^49 - 2z q^55 + q^59 - z * q^79
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q+O(q^{10}) \) 2 * q	\( 2 q + 4 q^{11} - 2 q^{25} - 2 q^{49} + 4 q^{59}+O(q^{100}) \) 2 * q + 4 * q^11 - 2 * q^25 - 2 * q^49 + 4 * q^59

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