LMFDB - Newform orbit 234.10.a.b

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [234,10,Mod(1,234)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(234, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 10, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("234.1"); S:= CuspForms(chi, 10); N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	234.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,16,0,256,-1015] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$120.518385662$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 26)
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 + 16 q^{2} + 256 q^{4} - 1015 q^{5} + 3955 q^{7} + 4096 q^{8} - 16240 q^{10} + 50998 q^{11} - 28561 q^{13} + 63280 q^{14} + 65536 q^{16} - 509757 q^{17} - 626574 q^{19} - 259840 q^{20} + 815968 q^{22}+ \cdots - 395385312 q^{98}+O(q^{100}) $

q + 16 * q^2 + 256 * q^4 - 1015 * q^5 + 3955 * q^7 + 4096 * q^8 - 16240 * q^10 + 50998 * q^11 - 28561 * q^13 + 63280 * q^14 + 65536 * q^16 - 509757 * q^17 - 626574 * q^19 - 259840 * q^20 + 815968 * q^22 - 653524 * q^23 - 922900 * q^25 - 456976 * q^26 + 1012480 * q^28 + 4943006 * q^29 + 4071700 * q^31 + 1048576 * q^32 - 8156112 * q^34 - 4014325 * q^35 + 2348883 * q^37 - 10025184 * q^38 - 4157440 * q^40 + 13350960 * q^41 - 7834847 * q^43 + 13055488 * q^44 - 10456384 * q^46 + 39637681 * q^47 - 24711582 * q^49 - 14766400 * q^50 - 7311616 * q^52 - 73200924 * q^53 - 51762970 * q^55 + 16199680 * q^56 + 79088096 * q^58 + 141141614 * q^59 - 132061256 * q^61 + 65147200 * q^62 + 16777216 * q^64 + 28989415 * q^65 - 185673110 * q^67 - 130497792 * q^68 - 64229200 * q^70 - 224452625 * q^71 - 172523674 * q^73 + 37582128 * q^74 - 160402944 * q^76 + 201697090 * q^77 - 643288156 * q^79 - 66519040 * q^80 + 213615360 * q^82 - 720077280 * q^83 + 517403355 * q^85 - 125357552 * q^86 + 208887808 * q^88 + 73028106 * q^89 - 112958755 * q^91 - 167302144 * q^92 + 634202896 * q^94 + 635972610 * q^95 - 15879778 * q^97 - 395385312 * q^98

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

16.0000

256.000

−1015.00

3955.00

4096.00

−16240.0

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	234.10.a.b		1
3.b	odd	2	1		26.10.a.a	✓	1
12.b	even	2	1		208.10.a.c		1
39.d	odd	2	1		338.10.a.c		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
26.10.a.a	✓	1	3.b	odd	2	1
208.10.a.c		1	12.b	even	2	1
234.10.a.b		1	1.a	even	1	1	trivial
338.10.a.c		1	39.d	odd	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $ T_{5} + 1015 $ T5 + 1015 acting on $S_{10}^{\mathrm{new}}(\Gamma_0(234))$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T - 16 $ T - 16
$3$	$ T $ T
$5$	$ T + 1015 $ T + 1015
$7$	$ T - 3955 $ T - 3955
$11$	$ T - 50998 $ T - 50998
$13$	$ T + 28561 $ T + 28561
$17$	$ T + 509757 $ T + 509757
$19$	$ T + 626574 $ T + 626574
$23$	$ T + 653524 $ T + 653524
$29$	$ T - 4943006 $ T - 4943006
$31$	$ T - 4071700 $ T - 4071700
$37$	$ T - 2348883 $ T - 2348883
$41$	$ T - 13350960 $ T - 13350960
$43$	$ T + 7834847 $ T + 7834847
$47$	$ T - 39637681 $ T - 39637681
$53$	$ T + 73200924 $ T + 73200924
$59$	$ T - 141141614 $ T - 141141614
$61$	$ T + 132061256 $ T + 132061256
$67$	$ T + 185673110 $ T + 185673110
$71$	$ T + 224452625 $ T + 224452625
$73$	$ T + 172523674 $ T + 172523674
$79$	$ T + 643288156 $ T + 643288156
$83$	$ T + 720077280 $ T + 720077280
$89$	$ T - 73028106 $ T - 73028106
$97$	$ T + 15879778 $ T + 15879778
show more
show less

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	234.a (trivial)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more