Properties

Label 430.3.v.a
Level $430$
Weight $3$
Character orbit 430.v
Analytic conductor $11.717$
Analytic rank $0$
Dimension $528$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [430,3,Mod(19,430)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(430, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([21, 19]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("430.19");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 430 = 2 \cdot 5 \cdot 43 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 430.v (of order \(42\), degree \(12\), minimal)

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: no
Analytic conductor: \(11.7166513675\)
Analytic rank: \(0\)
Dimension: \(528\)
Relative dimension: \(44\) over \(\Q(\zeta_{42})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{42}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 528 q - 176 q^{4} - 4 q^{6} + 196 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 528 q - 176 q^{4} - 4 q^{6} + 196 q^{9} - 40 q^{11} - 60 q^{14} - 96 q^{15} - 352 q^{16} + 144 q^{19} - 24 q^{21} - 8 q^{24} + 52 q^{25} + 184 q^{29} - 36 q^{30} - 312 q^{31} - 48 q^{34} + 384 q^{35} - 1568 q^{36} - 504 q^{39} - 104 q^{41} - 80 q^{44} - 756 q^{45} + 96 q^{46} - 1576 q^{49} - 528 q^{50} + 560 q^{51} + 232 q^{54} - 416 q^{55} + 48 q^{56} - 32 q^{59} - 24 q^{60} + 588 q^{61} - 704 q^{64} + 168 q^{65} - 272 q^{66} + 140 q^{69} + 156 q^{71} + 176 q^{74} + 742 q^{75} - 272 q^{76} - 20 q^{79} + 460 q^{81} - 48 q^{84} - 220 q^{86} + 1296 q^{89} + 416 q^{90} - 408 q^{91} + 280 q^{95} - 16 q^{96} + 456 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
19.1 −0.881748 + 1.10568i −5.53717 + 0.834594i −0.445042 1.94986i 2.46053 4.35267i 3.95960 6.85822i −6.78387 11.7500i 2.54832 + 1.22721i 21.3636 6.58979i 2.64308 + 6.55852i
19.2 −0.881748 + 1.10568i −5.18599 + 0.781662i −0.445042 1.94986i −3.48247 + 3.58781i 3.70847 6.42326i −0.255468 0.442483i 2.54832 + 1.22721i 17.6833 5.45459i −0.896301 7.01403i
19.3 −0.881748 + 1.10568i −4.62376 + 0.696920i −0.445042 1.94986i −4.07322 2.89980i 3.30642 5.72689i 5.10344 + 8.83943i 2.54832 + 1.22721i 12.2933 3.79199i 6.79780 1.94678i
19.4 −0.881748 + 1.10568i −4.45936 + 0.672141i −0.445042 1.94986i 4.97131 0.534821i 3.18886 5.52327i 5.76015 + 9.97687i 2.54832 + 1.22721i 10.8340 3.34185i −3.79211 + 5.96824i
19.5 −0.881748 + 1.10568i −3.74963 + 0.565166i −0.445042 1.94986i 1.61914 + 4.73058i 2.68134 4.64421i −1.29937 2.25058i 2.54832 + 1.22721i 5.14017 1.58553i −6.65816 2.38094i
19.6 −0.881748 + 1.10568i −3.14566 + 0.474132i −0.445042 1.94986i −1.74550 4.68543i 2.24944 3.89615i 1.15128 + 1.99407i 2.54832 + 1.22721i 1.07023 0.330121i 6.71966 + 2.20141i
19.7 −0.881748 + 1.10568i −1.98509 + 0.299204i −0.445042 1.94986i −4.80167 + 1.39426i 1.41953 2.45869i −1.77310 3.07109i 2.54832 + 1.22721i −4.74910 + 1.46490i 2.69227 6.53848i
19.8 −0.881748 + 1.10568i −1.78481 + 0.269016i −0.445042 1.94986i 4.92419 + 0.867367i 1.27630 2.21062i −4.83720 8.37828i 2.54832 + 1.22721i −5.48699 + 1.69251i −5.30092 + 4.67977i
19.9 −0.881748 + 1.10568i −1.63988 + 0.247173i −0.445042 1.94986i 2.58854 4.27779i 1.17267 2.03113i 0.823044 + 1.42555i 2.54832 + 1.22721i −5.97203 + 1.84213i 2.44741 + 6.63402i
19.10 −0.881748 + 1.10568i −0.779641 + 0.117512i −0.445042 1.94986i 1.01477 + 4.89594i 0.557517 0.965647i 6.88523 + 11.9256i 2.54832 + 1.22721i −8.00612 + 2.46956i −6.30810 3.19498i
19.11 −0.881748 + 1.10568i 0.187544 0.0282677i −0.445042 1.94986i −4.96879 + 0.557772i −0.134111 + 0.232288i 3.01780 + 5.22699i 2.54832 + 1.22721i −8.56578 + 2.64219i 3.76451 5.98569i
19.12 −0.881748 + 1.10568i 0.848146 0.127837i −0.445042 1.94986i 4.27225 + 2.59767i −0.606504 + 1.05050i 3.17378 + 5.49714i 2.54832 + 1.22721i −7.89715 + 2.43595i −6.63923 + 2.43323i
19.13 −0.881748 + 1.10568i 1.49385 0.225161i −0.445042 1.94986i −1.94249 + 4.60725i −1.06824 + 1.85025i −5.73360 9.93089i 2.54832 + 1.22721i −6.41927 + 1.98008i −3.38133 6.21020i
19.14 −0.881748 + 1.10568i 1.56541 0.235948i −0.445042 1.94986i −3.98919 3.01435i −1.11942 + 1.93889i −4.02926 6.97889i 2.54832 + 1.22721i −6.20531 + 1.91408i 6.85036 1.75286i
19.15 −0.881748 + 1.10568i 1.92814 0.290620i −0.445042 1.94986i 4.97927 + 0.454829i −1.37880 + 2.38815i −2.45096 4.24519i 2.54832 + 1.22721i −4.96691 + 1.53209i −4.89335 + 5.10442i
19.16 −0.881748 + 1.10568i 2.53284 0.381764i −0.445042 1.94986i 0.994994 4.90000i −1.81122 + 3.13712i −3.83884 6.64907i 2.54832 + 1.22721i −2.33063 + 0.718904i 4.54048 + 5.42070i
19.17 −0.881748 + 1.10568i 2.54127 0.383034i −0.445042 1.94986i −1.54186 + 4.75633i −1.81724 + 3.14756i −0.460716 0.797984i 2.54832 + 1.22721i −2.28883 + 0.706011i −3.89943 5.89868i
19.18 −0.881748 + 1.10568i 2.92413 0.440742i −0.445042 1.94986i −4.00778 2.98959i −2.09103 + 3.62176i 4.77680 + 8.27366i 2.54832 + 1.22721i −0.243875 + 0.0752254i 6.83938 1.79525i
19.19 −0.881748 + 1.10568i 4.43770 0.668875i −0.445042 1.94986i 0.452191 4.97951i −3.17337 + 5.49644i 4.76870 + 8.25963i 2.54832 + 1.22721i 10.6456 3.28374i 5.10701 + 4.89065i
19.20 −0.881748 + 1.10568i 4.64965 0.700822i −0.445042 1.94986i 4.97525 0.496896i −3.32494 + 5.75896i 2.25382 + 3.90374i 2.54832 + 1.22721i 12.5279 3.86436i −3.83751 + 5.93915i
See next 80 embeddings (of 528 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 19.44
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner
43.h odd 42 1 inner
215.t odd 42 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 430.3.v.a 528
5.b even 2 1 inner 430.3.v.a 528
43.h odd 42 1 inner 430.3.v.a 528
215.t odd 42 1 inner 430.3.v.a 528
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
430.3.v.a 528 1.a even 1 1 trivial
430.3.v.a 528 5.b even 2 1 inner
430.3.v.a 528 43.h odd 42 1 inner
430.3.v.a 528 215.t odd 42 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(430, [\chi])\).