LMFDB - Newform orbit 950.4.a.c

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [950,4,Mod(1,950)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(950, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("950.1"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	950.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,2,2,4,0,4,-8,8,-23] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	yes
Analytic conductor:	$56.0518145055$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
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} + 2 q^{3} + 4 q^{4} + 4 q^{6} - 8 q^{7} + 8 q^{8} - 23 q^{9} + 44 q^{11} + 8 q^{12} - 16 q^{14} + 16 q^{16} + 74 q^{17} - 46 q^{18} + 19 q^{19} - 16 q^{21} + 88 q^{22} - 84 q^{23} + 16 q^{24}+ \cdots - 1012 q^{99}+O(q^{100}) $

q + 2 * q^2 + 2 * q^3 + 4 * q^4 + 4 * q^6 - 8 * q^7 + 8 * q^8 - 23 * q^9 + 44 * q^11 + 8 * q^12 - 16 * q^14 + 16 * q^16 + 74 * q^17 - 46 * q^18 + 19 * q^19 - 16 * q^21 + 88 * q^22 - 84 * q^23 + 16 * q^24 - 100 * q^27 - 32 * q^28 + 266 * q^29 + 136 * q^31 + 32 * q^32 + 88 * q^33 + 148 * q^34 - 92 * q^36 - 424 * q^37 + 38 * q^38 + 470 * q^41 - 32 * q^42 + 236 * q^43 + 176 * q^44 - 168 * q^46 + 240 * q^47 + 32 * q^48 - 279 * q^49 + 148 * q^51 - 36 * q^53 - 200 * q^54 - 64 * q^56 + 38 * q^57 + 532 * q^58 + 736 * q^59 + 650 * q^61 + 272 * q^62 + 184 * q^63 + 64 * q^64 + 176 * q^66 + 830 * q^67 + 296 * q^68 - 168 * q^69 - 216 * q^71 - 184 * q^72 - 254 * q^73 - 848 * q^74 + 76 * q^76 - 352 * q^77 - 1220 * q^79 + 421 * q^81 + 940 * q^82 + 688 * q^83 - 64 * q^84 + 472 * q^86 + 532 * q^87 + 352 * q^88 + 102 * q^89 - 336 * q^92 + 272 * q^93 + 480 * q^94 + 64 * q^96 + 1280 * q^97 - 558 * q^98 - 1012 * 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

2.00000

4.00000

−8.00000

8.00000

−23.0000

Atkin-Lehner signs

$ p $	Sign
$2$	$ -1 $
$5$	$ +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	950.4.a.c		1
5.b	even	2	1		190.4.a.a	✓	1
5.c	odd	4	2		950.4.b.c		2
15.d	odd	2	1		1710.4.a.i		1
20.d	odd	2	1		1520.4.a.f		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
190.4.a.a	✓	1	5.b	even	2	1
950.4.a.c		1	1.a	even	1	1	trivial
950.4.b.c		2	5.c	odd	4	2
1520.4.a.f		1	20.d	odd	2	1
1710.4.a.i		1	15.d	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{4}^{\mathrm{new}}(\Gamma_0(950))$:

$ T_{3} - 2 $

T3 - 2

$ T_{7} + 8 $

T7 + 8

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T - 2 $ T - 2
$3$	$ T - 2 $ T - 2
$5$	$ T $ T
$7$	$ T + 8 $ T + 8
$11$	$ T - 44 $ T - 44
$13$	$ T $ T
$17$	$ T - 74 $ T - 74
$19$	$ T - 19 $ T - 19
$23$	$ T + 84 $ T + 84
$29$	$ T - 266 $ T - 266
$31$	$ T - 136 $ T - 136
$37$	$ T + 424 $ T + 424
$41$	$ T - 470 $ T - 470
$43$	$ T - 236 $ T - 236
$47$	$ T - 240 $ T - 240
$53$	$ T + 36 $ T + 36
$59$	$ T - 736 $ T - 736
$61$	$ T - 650 $ T - 650
$67$	$ T - 830 $ T - 830
$71$	$ T + 216 $ T + 216
$73$	$ T + 254 $ T + 254
$79$	$ T + 1220 $ T + 1220
$83$	$ T - 688 $ T - 688
$89$	$ T - 102 $ T - 102
$97$	$ T - 1280 $ T - 1280
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Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	950.a (trivial)

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