LMFDB - Newform orbit 468.4.a.c

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [468,4,Mod(1,468)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(468, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("468.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 468 = 2^{2} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	468.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:	$27.6128938827$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 52)
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 + 13 q^{5} - 11 q^{7}+O(q^{10}) $

$ q + 13 q^{5} - 11 q^{7} + 2 q^{11} - 13 q^{13} + 51 q^{17} + 150 q^{19} + 4 q^{23} + 44 q^{25} + 118 q^{29} - 116 q^{31} - 143 q^{35} + 63 q^{37} + 288 q^{41} - 293 q^{43} + 335 q^{47} - 222 q^{49} + 708 q^{53} + 26 q^{55} - 566 q^{59} + 904 q^{61} - 169 q^{65} + 382 q^{67} - 7 q^{71} + 518 q^{73} - 22 q^{77} - 100 q^{79} + 1440 q^{83} + 663 q^{85} - 1254 q^{89} + 143 q^{91} + 1950 q^{95} + 1262 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

13.0000

−11.0000

Atkin-Lehner signs

$ p $	Sign
$2$	$-1$
$3$	$-1$
$13$	$1$

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	468.4.a.c		1
3.b	odd	2	1		52.4.a.a	✓	1
4.b	odd	2	1		1872.4.a.n		1
12.b	even	2	1		208.4.a.f		1
15.d	odd	2	1		1300.4.a.d		1
15.e	even	4	2		1300.4.c.b		2
24.f	even	2	1		832.4.a.f		1
24.h	odd	2	1		832.4.a.n		1
39.d	odd	2	1		676.4.a.a		1
39.f	even	4	2		676.4.d.a		2
39.h	odd	6	2		676.4.e.b		2
39.i	odd	6	2		676.4.e.a		2
39.k	even	12	4		676.4.h.d		4

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
52.4.a.a	✓	1	3.b	odd	2	1
208.4.a.f		1	12.b	even	2	1
468.4.a.c		1	1.a	even	1	1	trivial
676.4.a.a		1	39.d	odd	2	1
676.4.d.a		2	39.f	even	4	2
676.4.e.a		2	39.i	odd	6	2
676.4.e.b		2	39.h	odd	6	2
676.4.h.d		4	39.k	even	12	4
832.4.a.f		1	24.f	even	2	1
832.4.a.n		1	24.h	odd	2	1
1300.4.a.d		1	15.d	odd	2	1
1300.4.c.b		2	15.e	even	4	2
1872.4.a.n		1	4.b	odd	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $ T_{5} - 13 $ T5 - 13 acting on $S_{4}^{\mathrm{new}}(\Gamma_0(468))$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T $ T
$3$	$ T $ T
$5$	$ T - 13 $ T - 13
$7$	$ T + 11 $ T + 11
$11$	$ T - 2 $ T - 2
$13$	$ T + 13 $ T + 13
$17$	$ T - 51 $ T - 51
$19$	$ T - 150 $ T - 150
$23$	$ T - 4 $ T - 4
$29$	$ T - 118 $ T - 118
$31$	$ T + 116 $ T + 116
$37$	$ T - 63 $ T - 63
$41$	$ T - 288 $ T - 288
$43$	$ T + 293 $ T + 293
$47$	$ T - 335 $ T - 335
$53$	$ T - 708 $ T - 708
$59$	$ T + 566 $ T + 566
$61$	$ T - 904 $ T - 904
$67$	$ T - 382 $ T - 382
$71$	$ T + 7 $ T + 7
$73$	$ T - 518 $ T - 518
$79$	$ T + 100 $ T + 100
$83$	$ T - 1440 $ T - 1440
$89$	$ T + 1254 $ T + 1254
$97$	$ T - 1262 $ T - 1262
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Level:	\( N \)	\(=\)	\( 468 = 2^{2} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	468.a (trivial)

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