LMFDB - Newform orbit 190.4.a.c

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [190,4,Mod(1,190)] 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("190.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(190, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 190 = 2 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	190.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,2,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	yes
Analytic conductor:	$11.2103629011$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
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} - 4 q^{3} + 4 q^{4} + 5 q^{5} - 8 q^{6} - 20 q^{7} + 8 q^{8} - 11 q^{9} + 10 q^{10} - 44 q^{11} - 16 q^{12} + 42 q^{13} - 40 q^{14} - 20 q^{15} + 16 q^{16} - 86 q^{17} - 22 q^{18} + 19 q^{19}+ \cdots + 484 q^{99}+O(q^{100}) $

q + 2 * q^2 - 4 * q^3 + 4 * q^4 + 5 * q^5 - 8 * q^6 - 20 * q^7 + 8 * q^8 - 11 * q^9 + 10 * q^10 - 44 * q^11 - 16 * q^12 + 42 * q^13 - 40 * q^14 - 20 * q^15 + 16 * q^16 - 86 * q^17 - 22 * q^18 + 19 * q^19 + 20 * q^20 + 80 * q^21 - 88 * q^22 - 164 * q^23 - 32 * q^24 + 25 * q^25 + 84 * q^26 + 152 * q^27 - 80 * q^28 - 162 * q^29 - 40 * q^30 - 312 * q^31 + 32 * q^32 + 176 * q^33 - 172 * q^34 - 100 * q^35 - 44 * q^36 + 226 * q^37 + 38 * q^38 - 168 * q^39 + 40 * q^40 + 34 * q^41 + 160 * q^42 - 432 * q^43 - 176 * q^44 - 55 * q^45 - 328 * q^46 + 580 * q^47 - 64 * q^48 + 57 * q^49 + 50 * q^50 + 344 * q^51 + 168 * q^52 + 506 * q^53 + 304 * q^54 - 220 * q^55 - 160 * q^56 - 76 * q^57 - 324 * q^58 + 364 * q^59 - 80 * q^60 + 518 * q^61 - 624 * q^62 + 220 * q^63 + 64 * q^64 + 210 * q^65 + 352 * q^66 + 924 * q^67 - 344 * q^68 + 656 * q^69 - 200 * q^70 + 320 * q^71 - 88 * q^72 - 542 * q^73 + 452 * q^74 - 100 * q^75 + 76 * q^76 + 880 * q^77 - 336 * q^78 - 1208 * q^79 + 80 * q^80 - 311 * q^81 + 68 * q^82 - 1120 * q^83 + 320 * q^84 - 430 * q^85 - 864 * q^86 + 648 * q^87 - 352 * q^88 - 1022 * q^89 - 110 * q^90 - 840 * q^91 - 656 * q^92 + 1248 * q^93 + 1160 * q^94 + 95 * q^95 - 128 * q^96 + 1166 * q^97 + 114 * q^98 + 484 * 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

4.00000

5.00000

−8.00000

−20.0000

8.00000

−11.0000

10.0000

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	190.4.a.c	✓	1
3.b	odd	2	1		1710.4.a.b		1
4.b	odd	2	1		1520.4.a.g		1
5.b	even	2	1		950.4.a.a		1
5.c	odd	4	2		950.4.b.a		2

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
190.4.a.c	✓	1	1.a	even	1	1	trivial
950.4.a.a		1	5.b	even	2	1
950.4.b.a		2	5.c	odd	4	2
1520.4.a.g		1	4.b	odd	2	1
1710.4.a.b		1	3.b	odd	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $ T_{3} + 4 $ T3 + 4 acting on $S_{4}^{\mathrm{new}}(\Gamma_0(190))$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T - 2 $ T - 2
$3$	$ T + 4 $ T + 4
$5$	$ T - 5 $ T - 5
$7$	$ T + 20 $ T + 20
$11$	$ T + 44 $ T + 44
$13$	$ T - 42 $ T - 42
$17$	$ T + 86 $ T + 86
$19$	$ T - 19 $ T - 19
$23$	$ T + 164 $ T + 164
$29$	$ T + 162 $ T + 162
$31$	$ T + 312 $ T + 312
$37$	$ T - 226 $ T - 226
$41$	$ T - 34 $ T - 34
$43$	$ T + 432 $ T + 432
$47$	$ T - 580 $ T - 580
$53$	$ T - 506 $ T - 506
$59$	$ T - 364 $ T - 364
$61$	$ T - 518 $ T - 518
$67$	$ T - 924 $ T - 924
$71$	$ T - 320 $ T - 320
$73$	$ T + 542 $ T + 542
$79$	$ T + 1208 $ T + 1208
$83$	$ T + 1120 $ T + 1120
$89$	$ T + 1022 $ T + 1022
$97$	$ T - 1166 $ T - 1166
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Level:	\( N \)	\(=\)	\( 190 = 2 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	190.a (trivial)

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