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Properties

Label 841.2.d.l
Level $841$
Weight $2$
Character orbit 841.d
Analytic conductor $6.715$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [841,2,Mod(190,841)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(841, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("841.190");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 841 = 29^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 841.d (of order \(7\), degree \(6\), not 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: \(6.71541880999\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(4\) over \(\Q(\zeta_{7})\)
Twist minimal: no (minimal twist has level 29)
Sato-Tate group: $\mathrm{SU}(2)[C_{7}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 2 q^{4} - 12 q^{5} - 22 q^{6} - 8 q^{7} + 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q + 2 q^{4} - 12 q^{5} - 22 q^{6} - 8 q^{7} + 20 q^{9} - 4 q^{13} - 66 q^{16} - 64 q^{20} - 20 q^{22} + 4 q^{23} - 22 q^{24} + 12 q^{25} - 24 q^{28} + 4 q^{30} - 36 q^{33} - 72 q^{34} - 24 q^{35} + 32 q^{36} + 42 q^{38} + 54 q^{42} - 10 q^{45} + 12 q^{49} + 44 q^{51} - 12 q^{52} - 20 q^{53} + 22 q^{54} + 28 q^{57} + 88 q^{59} + 66 q^{62} + 12 q^{63} + 38 q^{64} - 54 q^{65} - 52 q^{67} - 56 q^{71} - 14 q^{74} - 22 q^{78} + 12 q^{80} + 44 q^{81} - 26 q^{82} - 32 q^{83} + 88 q^{86} - 132 q^{88} - 8 q^{91} - 2 q^{92} + 4 q^{93} - 36 q^{94} + 10 q^{96}+O(q^{100}) \) Copy content Toggle raw display

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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
190.1 −2.04317 − 0.983939i 1.77107 − 2.22085i 1.95943 + 2.45704i −0.0521506 − 0.0251144i −5.80376 + 2.79495i −0.973866 + 1.22119i −0.576620 − 2.52634i −1.12792 − 4.94174i 0.0818415 + 0.102626i
190.2 −0.495421 − 0.238582i −1.23002 + 1.54240i −1.05846 − 1.32727i −2.47231 − 1.19060i 0.977367 − 0.470675i 2.78938 − 3.49777i 0.452439 + 1.98226i −0.198476 − 0.869580i 0.940777 + 1.17970i
190.3 0.495421 + 0.238582i 1.23002 − 1.54240i −1.05846 − 1.32727i −2.47231 − 1.19060i 0.977367 − 0.470675i 2.78938 − 3.49777i −0.452439 − 1.98226i −0.198476 − 0.869580i −0.940777 − 1.17970i
190.4 2.04317 + 0.983939i −1.77107 + 2.22085i 1.95943 + 2.45704i −0.0521506 − 0.0251144i −5.80376 + 2.79495i −0.973866 + 1.22119i 0.576620 + 2.52634i −1.12792 − 4.94174i −0.0818415 − 0.102626i
571.1 −2.04317 + 0.983939i 1.77107 + 2.22085i 1.95943 − 2.45704i −0.0521506 + 0.0251144i −5.80376 − 2.79495i −0.973866 − 1.22119i −0.576620 + 2.52634i −1.12792 + 4.94174i 0.0818415 − 0.102626i
571.2 −0.495421 + 0.238582i −1.23002 − 1.54240i −1.05846 + 1.32727i −2.47231 + 1.19060i 0.977367 + 0.470675i 2.78938 + 3.49777i 0.452439 − 1.98226i −0.198476 + 0.869580i 0.940777 − 1.17970i
571.3 0.495421 − 0.238582i 1.23002 + 1.54240i −1.05846 + 1.32727i −2.47231 + 1.19060i 0.977367 + 0.470675i 2.78938 + 3.49777i −0.452439 + 1.98226i −0.198476 + 0.869580i −0.940777 + 1.17970i
571.4 2.04317 − 0.983939i −1.77107 − 2.22085i 1.95943 − 2.45704i −0.0521506 + 0.0251144i −5.80376 − 2.79495i −0.973866 − 1.22119i 0.576620 − 2.52634i −1.12792 + 4.94174i −0.0818415 + 0.102626i
574.1 −1.62259 + 2.03467i 0.0977621 − 0.428324i −1.06202 − 4.65303i 1.60887 − 2.01746i 0.712869 + 0.893909i −0.0167182 + 0.0732474i 6.50118 + 3.13080i 2.52900 + 1.21790i 1.49432 + 6.54703i
574.2 −0.106623 + 0.133701i −0.250186 + 1.09614i 0.438534 + 1.92134i −1.76286 + 2.21055i −0.119878 − 0.150323i 0.651093 − 2.85263i −0.611791 − 0.294623i 1.56399 + 0.753177i −0.107592 − 0.471390i
574.3 0.106623 − 0.133701i 0.250186 − 1.09614i 0.438534 + 1.92134i −1.76286 + 2.21055i −0.119878 − 0.150323i 0.651093 − 2.85263i 0.611791 + 0.294623i 1.56399 + 0.753177i 0.107592 + 0.471390i
574.4 1.62259 − 2.03467i −0.0977621 + 0.428324i −1.06202 − 4.65303i 1.60887 − 2.01746i 0.712869 + 0.893909i −0.0167182 + 0.0732474i −6.50118 − 3.13080i 2.52900 + 1.21790i −1.49432 − 6.54703i
605.1 −0.344746 + 1.51043i −2.64404 + 1.27330i −0.360619 − 0.173665i 0.101097 − 0.442937i −1.01172 − 4.43261i −3.07524 + 1.48096i −1.54528 + 1.93773i 3.49918 − 4.38784i 0.634173 + 0.305402i
605.2 −0.258810 + 1.13392i −0.887282 + 0.427293i 0.583140 + 0.280826i −0.422650 + 1.85175i −0.254879 − 1.11670i −1.37465 + 0.661994i −1.91970 + 2.40723i −1.26578 + 1.58724i −1.99035 − 0.958504i
605.3 0.258810 − 1.13392i 0.887282 − 0.427293i 0.583140 + 0.280826i −0.422650 + 1.85175i −0.254879 − 1.11670i −1.37465 + 0.661994i 1.91970 − 2.40723i −1.26578 + 1.58724i 1.99035 + 0.958504i
605.4 0.344746 − 1.51043i 2.64404 − 1.27330i −0.360619 − 0.173665i 0.101097 − 0.442937i −1.01172 − 4.43261i −3.07524 + 1.48096i 1.54528 − 1.93773i 3.49918 − 4.38784i −0.634173 − 0.305402i
645.1 −0.344746 − 1.51043i −2.64404 − 1.27330i −0.360619 + 0.173665i 0.101097 + 0.442937i −1.01172 + 4.43261i −3.07524 − 1.48096i −1.54528 − 1.93773i 3.49918 + 4.38784i 0.634173 − 0.305402i
645.2 −0.258810 − 1.13392i −0.887282 − 0.427293i 0.583140 − 0.280826i −0.422650 − 1.85175i −0.254879 + 1.11670i −1.37465 − 0.661994i −1.91970 − 2.40723i −1.26578 − 1.58724i −1.99035 + 0.958504i
645.3 0.258810 + 1.13392i 0.887282 + 0.427293i 0.583140 − 0.280826i −0.422650 − 1.85175i −0.254879 + 1.11670i −1.37465 − 0.661994i 1.91970 + 2.40723i −1.26578 − 1.58724i 1.99035 − 0.958504i
645.4 0.344746 + 1.51043i 2.64404 + 1.27330i −0.360619 + 0.173665i 0.101097 + 0.442937i −1.01172 + 4.43261i −3.07524 − 1.48096i 1.54528 + 1.93773i 3.49918 + 4.38784i −0.634173 + 0.305402i
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 190.4
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
29.b even 2 1 inner
29.d even 7 1 inner
29.e even 14 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 841.2.d.l 24
29.b even 2 1 inner 841.2.d.l 24
29.c odd 4 1 841.2.e.a 12
29.c odd 4 1 841.2.e.h 12
29.d even 7 1 841.2.a.k 12
29.d even 7 2 841.2.d.k 24
29.d even 7 1 inner 841.2.d.l 24
29.d even 7 2 841.2.d.m 24
29.e even 14 1 841.2.a.k 12
29.e even 14 2 841.2.d.k 24
29.e even 14 1 inner 841.2.d.l 24
29.e even 14 2 841.2.d.m 24
29.f odd 28 2 29.2.e.a ✓ 12
29.f odd 28 2 841.2.b.e 12
29.f odd 28 1 841.2.e.a 12
29.f odd 28 2 841.2.e.e 12
29.f odd 28 2 841.2.e.f 12
29.f odd 28 1 841.2.e.h 12
29.f odd 28 2 841.2.e.i 12
87.h odd 14 1 7569.2.a.bp 12
87.j odd 14 1 7569.2.a.bp 12
87.k even 28 2 261.2.o.a 12
116.l even 28 2 464.2.y.d 12
145.o even 28 2 725.2.p.a 24
145.s odd 28 2 725.2.q.a 12
145.t even 28 2 725.2.p.a 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
29.2.e.a ✓ 12 29.f odd 28 2
261.2.o.a 12 87.k even 28 2
464.2.y.d 12 116.l even 28 2
725.2.p.a 24 145.o even 28 2
725.2.p.a 24 145.t even 28 2
725.2.q.a 12 145.s odd 28 2
841.2.a.k 12 29.d even 7 1
841.2.a.k 12 29.e even 14 1
841.2.b.e 12 29.f odd 28 2
841.2.d.k 24 29.d even 7 2
841.2.d.k 24 29.e even 14 2
841.2.d.l 24 1.a even 1 1 trivial
841.2.d.l 24 29.b even 2 1 inner
841.2.d.l 24 29.d even 7 1 inner
841.2.d.l 24 29.e even 14 1 inner
841.2.d.m 24 29.d even 7 2
841.2.d.m 24 29.e even 14 2
841.2.e.a 12 29.c odd 4 1
841.2.e.a 12 29.f odd 28 1
841.2.e.e 12 29.f odd 28 2
841.2.e.f 12 29.f odd 28 2
841.2.e.h 12 29.c odd 4 1
841.2.e.h 12 29.f odd 28 1
841.2.e.i 12 29.f odd 28 2
7569.2.a.bp 12 87.h odd 14 1
7569.2.a.bp 12 87.j odd 14 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{24} + 3 T_{2}^{22} + 47 T_{2}^{20} + 87 T_{2}^{18} + 626 T_{2}^{16} + 5212 T_{2}^{14} + 15925 T_{2}^{12} + \cdots + 1 \) acting on \(S_{2}^{\mathrm{new}}(841, [\chi])\). Copy content Toggle raw display