LMFDB - Newform orbit 9025.2.a.h

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9025,2,Mod(1,9025)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9025, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("9025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9025 = 5^{2} \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9025.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$72.0649878242$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$

$=$

$ q + q^{2} - q^{4} + 2 q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) $

$ q + q^{2} - q^{4} + 2 q^{7} - 3 q^{8} - 3 q^{9} - 4 q^{11} + 2 q^{13} + 2 q^{14} - q^{16} + 4 q^{17} - 3 q^{18} - 4 q^{22} - 6 q^{23} + 2 q^{26} - 2 q^{28} + 6 q^{29} + 4 q^{31} + 5 q^{32} + 4 q^{34} + 3 q^{36} + 10 q^{37} + 10 q^{41} + 2 q^{43} + 4 q^{44} - 6 q^{46} - 6 q^{47} - 3 q^{49} - 2 q^{52} - 10 q^{53} - 6 q^{56} + 6 q^{58} + 2 q^{61} + 4 q^{62} - 6 q^{63} + 7 q^{64} - 8 q^{67} - 4 q^{68} - 4 q^{71} + 9 q^{72} + 4 q^{73} + 10 q^{74} - 8 q^{77} - 4 q^{79} + 9 q^{81} + 10 q^{82} - 18 q^{83} + 2 q^{86} + 12 q^{88} + 2 q^{89} + 4 q^{91} + 6 q^{92} - 6 q^{94} - 6 q^{97} - 3 q^{98} + 12 q^{99}+O(q^{100}) $

Display 100 coefficients 10 coefficients

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.

comment: embeddings in the coefficient field

gp: mfembed(f)

Label

$\iota_m(\nu)$

$ a_{2} $

$ a_{3} $

$ a_{4} $

$ a_{5} $

$ a_{6} $

$ a_{7} $

$ a_{8} $

$ a_{9} $

$ a_{10} $

1.1

1.00000

−1.00000

2.00000

−3.00000

Atkin-Lehner signs

$ p $	Sign
$5$	$ -1 $
$19$	$ -1 $

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	9025.2.a.h		1
5.b	even	2	1		9025.2.a.c		1
5.c	odd	4	2		1805.2.b.c		2
19.b	odd	2	1		475.2.a.a		1
57.d	even	2	1		4275.2.a.p		1
76.d	even	2	1		7600.2.a.i		1
95.d	odd	2	1		475.2.a.c		1
95.g	even	4	2		95.2.b.a	✓	2
285.b	even	2	1		4275.2.a.e		1
285.j	odd	4	2		855.2.c.b		2
380.d	even	2	1		7600.2.a.l		1
380.j	odd	4	2		1520.2.d.b		2

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
95.2.b.a	✓	2	95.g	even	4	2
475.2.a.a		1	19.b	odd	2	1
475.2.a.c		1	95.d	odd	2	1
855.2.c.b		2	285.j	odd	4	2
1520.2.d.b		2	380.j	odd	4	2
1805.2.b.c		2	5.c	odd	4	2
4275.2.a.e		1	285.b	even	2	1
4275.2.a.p		1	57.d	even	2	1
7600.2.a.i		1	76.d	even	2	1
7600.2.a.l		1	380.d	even	2	1
9025.2.a.c		1	5.b	even	2	1
9025.2.a.h		1	1.a	even	1	1	trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{2}^{\mathrm{new}}(\Gamma_0(9025))$:

$ T_{2} - 1 $

$ T_{3} $

$ T_{7} - 2 $

$ T_{11} + 4 $

$ T_{29} - 6 $

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T - 1 $ T - 1
$3$	$ T $ T
$5$	$ T $ T
$7$	$ T - 2 $ T - 2
$11$	$ T + 4 $ T + 4
$13$	$ T - 2 $ T - 2
$17$	$ T - 4 $ T - 4
$19$	$ T $ T
$23$	$ T + 6 $ T + 6
$29$	$ T - 6 $ T - 6
$31$	$ T - 4 $ T - 4
$37$	$ T - 10 $ T - 10
$41$	$ T - 10 $ T - 10
$43$	$ T - 2 $ T - 2
$47$	$ T + 6 $ T + 6
$53$	$ T + 10 $ T + 10
$59$	$ T $ T
$61$	$ T - 2 $ T - 2
$67$	$ T + 8 $ T + 8
$71$	$ T + 4 $ T + 4
$73$	$ T - 4 $ T - 4
$79$	$ T + 4 $ T + 4
$83$	$ T + 18 $ T + 18
$89$	$ T - 2 $ T - 2
$97$	$ T + 6 $ T + 6
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Elliptic curves over $\Q$
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Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 9025 = 5^{2} \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9025.a (trivial)

\(n\):		e.g. 2-40 or 990-1000
Significant digits:
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