LMFDB - Newform orbit 1050.4.a.d

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,4,Mod(1,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, 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("1050.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1050.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:	$61.9520055060$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
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 - 2 q^{2} - 3 q^{3} + 4 q^{4} + 6 q^{6} + 7 q^{7} - 8 q^{8} + 9 q^{9}+O(q^{10}) $

$ q - 2 q^{2} - 3 q^{3} + 4 q^{4} + 6 q^{6} + 7 q^{7} - 8 q^{8} + 9 q^{9} - 8 q^{11} - 12 q^{12} + 42 q^{13} - 14 q^{14} + 16 q^{16} + 2 q^{17} - 18 q^{18} - 124 q^{19} - 21 q^{21} + 16 q^{22} - 76 q^{23} + 24 q^{24} - 84 q^{26} - 27 q^{27} + 28 q^{28} + 254 q^{29} - 72 q^{31} - 32 q^{32} + 24 q^{33} - 4 q^{34} + 36 q^{36} - 398 q^{37} + 248 q^{38} - 126 q^{39} + 462 q^{41} + 42 q^{42} - 212 q^{43} - 32 q^{44} + 152 q^{46} + 264 q^{47} - 48 q^{48} + 49 q^{49} - 6 q^{51} + 168 q^{52} + 162 q^{53} + 54 q^{54} - 56 q^{56} + 372 q^{57} - 508 q^{58} - 772 q^{59} + 30 q^{61} + 144 q^{62} + 63 q^{63} + 64 q^{64} - 48 q^{66} + 764 q^{67} + 8 q^{68} + 228 q^{69} - 236 q^{71} - 72 q^{72} - 418 q^{73} + 796 q^{74} - 496 q^{76} - 56 q^{77} + 252 q^{78} + 552 q^{79} + 81 q^{81} - 924 q^{82} - 1036 q^{83} - 84 q^{84} + 424 q^{86} - 762 q^{87} + 64 q^{88} + 30 q^{89} + 294 q^{91} - 304 q^{92} + 216 q^{93} - 528 q^{94} + 96 q^{96} + 1190 q^{97} - 98 q^{98} - 72 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

−2.00000

−3.00000

4.00000

6.00000

7.00000

−8.00000

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	1050.4.a.d		1
5.b	even	2	1		42.4.a.b	✓	1
5.c	odd	4	2		1050.4.g.n		2
15.d	odd	2	1		126.4.a.c		1
20.d	odd	2	1		336.4.a.d		1
35.c	odd	2	1		294.4.a.h		1
35.i	odd	6	2		294.4.e.d		2
35.j	even	6	2		294.4.e.a		2
40.e	odd	2	1		1344.4.a.t		1
40.f	even	2	1		1344.4.a.f		1
60.h	even	2	1		1008.4.a.j		1
105.g	even	2	1		882.4.a.d		1
105.o	odd	6	2		882.4.g.s		2
105.p	even	6	2		882.4.g.r		2
140.c	even	2	1		2352.4.a.ba		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
42.4.a.b	✓	1	5.b	even	2	1
126.4.a.c		1	15.d	odd	2	1
294.4.a.h		1	35.c	odd	2	1
294.4.e.a		2	35.j	even	6	2
294.4.e.d		2	35.i	odd	6	2
336.4.a.d		1	20.d	odd	2	1
882.4.a.d		1	105.g	even	2	1
882.4.g.r		2	105.p	even	6	2
882.4.g.s		2	105.o	odd	6	2
1008.4.a.j		1	60.h	even	2	1
1050.4.a.d		1	1.a	even	1	1	trivial
1050.4.g.n		2	5.c	odd	4	2
1344.4.a.f		1	40.f	even	2	1
1344.4.a.t		1	40.e	odd	2	1
2352.4.a.ba		1	140.c	even	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{4}^{\mathrm{new}}(\Gamma_0(1050))$:

$ T_{11} + 8 $

$ T_{13} - 42 $

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T + 2 $ T + 2
$3$	$ T + 3 $ T + 3
$5$	$ T $ T
$7$	$ T - 7 $ T - 7
$11$	$ T + 8 $ T + 8
$13$	$ T - 42 $ T - 42
$17$	$ T - 2 $ T - 2
$19$	$ T + 124 $ T + 124
$23$	$ T + 76 $ T + 76
$29$	$ T - 254 $ T - 254
$31$	$ T + 72 $ T + 72
$37$	$ T + 398 $ T + 398
$41$	$ T - 462 $ T - 462
$43$	$ T + 212 $ T + 212
$47$	$ T - 264 $ T - 264
$53$	$ T - 162 $ T - 162
$59$	$ T + 772 $ T + 772
$61$	$ T - 30 $ T - 30
$67$	$ T - 764 $ T - 764
$71$	$ T + 236 $ T + 236
$73$	$ T + 418 $ T + 418
$79$	$ T - 552 $ T - 552
$83$	$ T + 1036 $ T + 1036
$89$	$ T - 30 $ T - 30
$97$	$ T - 1190 $ T - 1190
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Overview	Random
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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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1050.a (trivial)

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