LMFDB - Newform orbit 7938.2.a.a

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7938,2,Mod(1,7938)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7938, 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("7938.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7938 = 2 \cdot 3^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7938.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:	$63.3852491245$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1134)
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} - 4 q^{5} - q^{8}+O(q^{10}) $

$ q - q^{2} + q^{4} - 4 q^{5} - q^{8} + 4 q^{10} - 2 q^{11} + 6 q^{13} + q^{16} - 2 q^{17} - 4 q^{19} - 4 q^{20} + 2 q^{22} + q^{23} + 11 q^{25} - 6 q^{26} - 4 q^{29} - 9 q^{31} - q^{32} + 2 q^{34} + 8 q^{37} + 4 q^{38} + 4 q^{40} - 3 q^{41} + 2 q^{43} - 2 q^{44} - q^{46} + 9 q^{47} - 11 q^{50} + 6 q^{52} + 12 q^{53} + 8 q^{55} + 4 q^{58} - 4 q^{59} + 6 q^{61} + 9 q^{62} + q^{64} - 24 q^{65} - 14 q^{67} - 2 q^{68} + q^{71} + 7 q^{73} - 8 q^{74} - 4 q^{76} - 3 q^{79} - 4 q^{80} + 3 q^{82} - 14 q^{83} + 8 q^{85} - 2 q^{86} + 2 q^{88} + 3 q^{89} + q^{92} - 9 q^{94} + 16 q^{95} + 10 q^{97}+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

−4.00000

−1.00000

4.00000

Atkin-Lehner signs

$ p $	Sign
$2$	$ +1 $
$3$	$ +1 $
$7$	$ +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	7938.2.a.a		1
3.b	odd	2	1		7938.2.a.bf		1
7.b	odd	2	1		7938.2.a.p		1
7.c	even	3	2		1134.2.g.h	yes	2
21.c	even	2	1		7938.2.a.q		1
21.h	odd	6	2		1134.2.g.a	✓	2
63.g	even	3	2		1134.2.h.i		2
63.h	even	3	2		1134.2.e.h		2
63.j	odd	6	2		1134.2.e.i		2
63.n	odd	6	2		1134.2.h.h		2

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1134.2.e.h		2	63.h	even	3	2
1134.2.e.i		2	63.j	odd	6	2
1134.2.g.a	✓	2	21.h	odd	6	2
1134.2.g.h	yes	2	7.c	even	3	2
1134.2.h.h		2	63.n	odd	6	2
1134.2.h.i		2	63.g	even	3	2
7938.2.a.a		1	1.a	even	1	1	trivial
7938.2.a.p		1	7.b	odd	2	1
7938.2.a.q		1	21.c	even	2	1
7938.2.a.bf		1	3.b	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{2}^{\mathrm{new}}(\Gamma_0(7938))$:

$ T_{5} + 4 $

$ T_{11} + 2 $

$ T_{13} - 6 $

$ T_{17} + 2 $

$ T_{23} - 1 $

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T + 1 $ T + 1
$3$	$ T $ T
$5$	$ T + 4 $ T + 4
$7$	$ T $ T
$11$	$ T + 2 $ T + 2
$13$	$ T - 6 $ T - 6
$17$	$ T + 2 $ T + 2
$19$	$ T + 4 $ T + 4
$23$	$ T - 1 $ T - 1
$29$	$ T + 4 $ T + 4
$31$	$ T + 9 $ T + 9
$37$	$ T - 8 $ T - 8
$41$	$ T + 3 $ T + 3
$43$	$ T - 2 $ T - 2
$47$	$ T - 9 $ T - 9
$53$	$ T - 12 $ T - 12
$59$	$ T + 4 $ T + 4
$61$	$ T - 6 $ T - 6
$67$	$ T + 14 $ T + 14
$71$	$ T - 1 $ T - 1
$73$	$ T - 7 $ T - 7
$79$	$ T + 3 $ T + 3
$83$	$ T + 14 $ T + 14
$89$	$ T - 3 $ T - 3
$97$	$ T - 10 $ T - 10
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Elliptic curves over $\Q$
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Level:	\( N \)	\(=\)	\( 7938 = 2 \cdot 3^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7938.a (trivial)

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