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Properties

Label 841.2.e.j
Level $841$
Weight $2$
Character orbit 841.e
Analytic conductor $6.715$
Analytic rank $0$
Dimension $24$
Inner twists $12$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [841,2,Mod(63,841)]
 
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([11]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("841.63");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 841 = 29^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 841.e (of order \(14\), 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 \(\Q(\zeta_{14})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{14}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 2 q^{4} + 2 q^{5} - 6 q^{6} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q - 2 q^{4} + 2 q^{5} - 6 q^{6} - 6 q^{9} + 8 q^{13} + 6 q^{16} + 16 q^{20} + 10 q^{22} - 4 q^{23} - 10 q^{24} - 26 q^{25} - 60 q^{28} + 72 q^{30} - 10 q^{33} + 16 q^{34} - 30 q^{35} - 8 q^{36} - 12 q^{38} - 10 q^{42} + 18 q^{45} + 8 q^{49} - 16 q^{51} - 6 q^{52} + 8 q^{53} - 22 q^{54} - 72 q^{57} + 12 q^{59} - 16 q^{62} + 10 q^{63} + 8 q^{64} + 26 q^{65} - 24 q^{67} + 24 q^{71} - 34 q^{74} + 22 q^{78} + 42 q^{80} + 4 q^{81} - 14 q^{82} + 4 q^{83} - 60 q^{88} + 20 q^{91} + 8 q^{92} + 16 q^{93} - 14 q^{94} + 4 q^{96}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
63.1 −1.26503 + 1.00883i −1.57747 + 0.360046i 0.137526 − 0.602539i 1.77950 + 2.23143i 1.63232 − 2.04686i −0.497572 − 2.18001i −0.970194 − 2.01463i −0.344139 + 0.165729i −4.50225 − 1.02761i
63.2 −0.483198 + 0.385338i −0.602539 + 0.137526i −0.360046 + 1.57747i −2.40299 − 3.01326i 0.238152 − 0.298633i 0.497572 + 2.18001i −0.970194 − 2.01463i −2.35877 + 1.13592i 2.32225 + 0.530037i
63.3 0.483198 − 0.385338i 0.602539 − 0.137526i −0.360046 + 1.57747i −2.40299 − 3.01326i 0.238152 − 0.298633i 0.497572 + 2.18001i 0.970194 + 2.01463i −2.35877 + 1.13592i −2.32225 − 0.530037i
63.4 1.26503 − 1.00883i 1.57747 − 0.360046i 0.137526 − 0.602539i 1.77950 + 2.23143i 1.63232 − 2.04686i −0.497572 − 2.18001i 0.970194 + 2.01463i −0.344139 + 0.165729i 4.50225 + 1.02761i
196.1 −1.57747 + 0.360046i 0.702039 − 1.45780i 0.556829 − 0.268155i −0.635097 − 2.78254i −0.582567 + 2.55239i −2.01463 − 0.970194i 1.74823 − 1.39417i 0.238152 + 0.298633i 2.00369 + 4.16070i
196.2 −0.602539 + 0.137526i 0.268155 − 0.556829i −1.45780 + 0.702039i 0.857618 + 3.75747i −0.0849954 + 0.372389i 2.01463 + 0.970194i 1.74823 − 1.39417i 1.63232 + 2.04686i −1.03350 − 2.14608i
196.3 0.602539 − 0.137526i −0.268155 + 0.556829i −1.45780 + 0.702039i 0.857618 + 3.75747i −0.0849954 + 0.372389i 2.01463 + 0.970194i −1.74823 + 1.39417i 1.63232 + 2.04686i 1.03350 + 2.14608i
196.4 1.57747 − 0.360046i −0.702039 + 1.45780i 0.556829 − 0.268155i −0.635097 − 2.78254i −0.582567 + 2.55239i −2.01463 − 0.970194i −1.74823 + 1.39417i 0.238152 + 0.298633i −2.00369 − 4.16070i
236.1 −1.57747 − 0.360046i 0.702039 + 1.45780i 0.556829 + 0.268155i −0.635097 + 2.78254i −0.582567 − 2.55239i −2.01463 + 0.970194i 1.74823 + 1.39417i 0.238152 − 0.298633i 2.00369 − 4.16070i
236.2 −0.602539 − 0.137526i 0.268155 + 0.556829i −1.45780 − 0.702039i 0.857618 − 3.75747i −0.0849954 − 0.372389i 2.01463 − 0.970194i 1.74823 + 1.39417i 1.63232 − 2.04686i −1.03350 + 2.14608i
236.3 0.602539 + 0.137526i −0.268155 − 0.556829i −1.45780 − 0.702039i 0.857618 − 3.75747i −0.0849954 − 0.372389i 2.01463 − 0.970194i −1.74823 − 1.39417i 1.63232 − 2.04686i 1.03350 − 2.14608i
236.4 1.57747 + 0.360046i −0.702039 − 1.45780i 0.556829 + 0.268155i −0.635097 + 2.78254i −0.582567 − 2.55239i −2.01463 + 0.970194i −1.74823 − 1.39417i 0.238152 − 0.298633i −2.00369 + 4.16070i
267.1 −1.26503 − 1.00883i −1.57747 − 0.360046i 0.137526 + 0.602539i 1.77950 − 2.23143i 1.63232 + 2.04686i −0.497572 + 2.18001i −0.970194 + 2.01463i −0.344139 − 0.165729i −4.50225 + 1.02761i
267.2 −0.483198 − 0.385338i −0.602539 − 0.137526i −0.360046 − 1.57747i −2.40299 + 3.01326i 0.238152 + 0.298633i 0.497572 − 2.18001i −0.970194 + 2.01463i −2.35877 − 1.13592i 2.32225 − 0.530037i
267.3 0.483198 + 0.385338i 0.602539 + 0.137526i −0.360046 − 1.57747i −2.40299 + 3.01326i 0.238152 + 0.298633i 0.497572 − 2.18001i 0.970194 − 2.01463i −2.35877 − 1.13592i −2.32225 + 0.530037i
267.4 1.26503 + 1.00883i 1.57747 + 0.360046i 0.137526 + 0.602539i 1.77950 − 2.23143i 1.63232 + 2.04686i −0.497572 + 2.18001i 0.970194 − 2.01463i −0.344139 − 0.165729i 4.50225 − 1.02761i
270.1 −0.702039 − 1.45780i 1.26503 − 1.00883i −0.385338 + 0.483198i −2.57146 + 1.23835i −2.35877 − 1.13592i 1.39417 + 1.74823i −2.18001 − 0.497572i −0.0849954 + 0.372389i 3.61052 + 2.87930i
270.2 −0.268155 − 0.556829i 0.483198 − 0.385338i 1.00883 − 1.26503i 3.47243 − 1.67223i −0.344139 − 0.165729i −1.39417 − 1.74823i −2.18001 − 0.497572i −0.582567 + 2.55239i −1.86230 − 1.48513i
270.3 0.268155 + 0.556829i −0.483198 + 0.385338i 1.00883 − 1.26503i 3.47243 − 1.67223i −0.344139 − 0.165729i −1.39417 − 1.74823i 2.18001 + 0.497572i −0.582567 + 2.55239i 1.86230 + 1.48513i
270.4 0.702039 + 1.45780i −1.26503 + 1.00883i −0.385338 + 0.483198i −2.57146 + 1.23835i −2.35877 − 1.13592i 1.39417 + 1.74823i 2.18001 + 0.497572i −0.0849954 + 0.372389i −3.61052 − 2.87930i
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 63.4
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 5 inner
29.e even 14 5 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 841.2.e.j 24
29.b even 2 1 inner 841.2.e.j 24
29.c odd 4 1 841.2.d.g 12
29.c odd 4 1 841.2.d.i 12
29.d even 7 1 841.2.b.b 4
29.d even 7 5 inner 841.2.e.j 24
29.e even 14 1 841.2.b.b 4
29.e even 14 5 inner 841.2.e.j 24
29.f odd 28 1 841.2.a.a ✓ 2
29.f odd 28 1 841.2.a.c yes 2
29.f odd 28 5 841.2.d.g 12
29.f odd 28 5 841.2.d.i 12
87.k even 28 1 7569.2.a.d 2
87.k even 28 1 7569.2.a.l 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
841.2.a.a ✓ 2 29.f odd 28 1
841.2.a.c yes 2 29.f odd 28 1
841.2.b.b 4 29.d even 7 1
841.2.b.b 4 29.e even 14 1
841.2.d.g 12 29.c odd 4 1
841.2.d.g 12 29.f odd 28 5
841.2.d.i 12 29.c odd 4 1
841.2.d.i 12 29.f odd 28 5
841.2.e.j 24 1.a even 1 1 trivial
841.2.e.j 24 29.b even 2 1 inner
841.2.e.j 24 29.d even 7 5 inner
841.2.e.j 24 29.e even 14 5 inner
7569.2.a.d 2 87.k even 28 1
7569.2.a.l 2 87.k even 28 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{24} - 3 T_{2}^{22} + 8 T_{2}^{20} - 21 T_{2}^{18} + 55 T_{2}^{16} - 144 T_{2}^{14} + 377 T_{2}^{12} + \cdots + 1 \) acting on \(S_{2}^{\mathrm{new}}(841, [\chi])\). Copy content Toggle raw display