LMFDB - Newform orbit 2100.4.a.d

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2100,4,Mod(1,2100)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2100.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2100, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2100.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,0,-3,0,0,0,7,0,9,0,-44] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	yes
Analytic conductor:	$123.904011012$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 420)
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 - 3 q^{3} + 7 q^{7} + 9 q^{9} - 44 q^{11} + 42 q^{13} + 94 q^{17} - 36 q^{19} - 21 q^{21} - 24 q^{23} - 27 q^{27} + 54 q^{29} - 112 q^{31} + 132 q^{33} + 322 q^{37} - 126 q^{39} - 22 q^{41} - 292 q^{43}+ \cdots - 396 q^{99}+O(q^{100}) $

q - 3 * q^3 + 7 * q^7 + 9 * q^9 - 44 * q^11 + 42 * q^13 + 94 * q^17 - 36 * q^19 - 21 * q^21 - 24 * q^23 - 27 * q^27 + 54 * q^29 - 112 * q^31 + 132 * q^33 + 322 * q^37 - 126 * q^39 - 22 * q^41 - 292 * q^43 - 272 * q^47 + 49 * q^49 - 282 * q^51 + 578 * q^53 + 108 * q^57 - 44 * q^59 - 26 * q^61 + 63 * q^63 - 12 * q^67 + 72 * q^69 - 280 * q^71 - 410 * q^73 - 308 * q^77 - 320 * q^79 + 81 * q^81 + 1252 * q^83 - 162 * q^87 - 38 * q^89 + 294 * q^91 + 336 * q^93 - 1250 * q^97 - 396 * q^99

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

−3.00000

7.00000

9.00000

Atkin-Lehner signs

$ p $	Sign
$2$	$ -1 $
$3$	$ +1 $
$5$	$ +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	2100.4.a.d		1
5.b	even	2	1		420.4.a.d	✓	1
5.c	odd	4	2		2100.4.k.a		2
15.d	odd	2	1		1260.4.a.c		1
20.d	odd	2	1		1680.4.a.k		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
420.4.a.d	✓	1	5.b	even	2	1
1260.4.a.c		1	15.d	odd	2	1
1680.4.a.k		1	20.d	odd	2	1
2100.4.a.d		1	1.a	even	1	1	trivial
2100.4.k.a		2	5.c	odd	4	2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{4}^{\mathrm{new}}(\Gamma_0(2100))$:

$ T_{11} + 44 $

T11 + 44

$ T_{13} - 42 $

T13 - 42

$ T_{17} - 94 $

T17 - 94

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T $ T
$3$	$ T + 3 $ T + 3
$5$	$ T $ T
$7$	$ T - 7 $ T - 7
$11$	$ T + 44 $ T + 44
$13$	$ T - 42 $ T - 42
$17$	$ T - 94 $ T - 94
$19$	$ T + 36 $ T + 36
$23$	$ T + 24 $ T + 24
$29$	$ T - 54 $ T - 54
$31$	$ T + 112 $ T + 112
$37$	$ T - 322 $ T - 322
$41$	$ T + 22 $ T + 22
$43$	$ T + 292 $ T + 292
$47$	$ T + 272 $ T + 272
$53$	$ T - 578 $ T - 578
$59$	$ T + 44 $ T + 44
$61$	$ T + 26 $ T + 26
$67$	$ T + 12 $ T + 12
$71$	$ T + 280 $ T + 280
$73$	$ T + 410 $ T + 410
$79$	$ T + 320 $ T + 320
$83$	$ T - 1252 $ T - 1252
$89$	$ T + 38 $ T + 38
$97$	$ T + 1250 $ T + 1250
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Elliptic curves over $\Q$
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Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2100.a (trivial)

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