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Properties

Label 124.3.k.a
Level $124$
Weight $3$
Character orbit 124.k
Analytic conductor $3.379$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [124,3,Mod(29,124)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(124, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("124.29");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 124 = 2^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 124.k (of order \(10\), degree \(4\), 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: \(3.37875527807\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 6 q^{5} - 6 q^{7} + 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q - 6 q^{5} - 6 q^{7} + 14 q^{9} - 5 q^{11} + 15 q^{13} - 35 q^{15} - 40 q^{17} + 34 q^{19} + 80 q^{23} + 158 q^{25} - 90 q^{27} + 10 q^{29} - 139 q^{31} + 183 q^{33} - 108 q^{35} - 152 q^{39} - 127 q^{41} - 70 q^{43} + 198 q^{45} - 134 q^{49} - 154 q^{51} - 130 q^{53} - 320 q^{55} + 110 q^{59} - 76 q^{63} + 25 q^{65} + 84 q^{67} + 240 q^{69} - 48 q^{71} + 230 q^{73} + 840 q^{75} + 485 q^{77} - 335 q^{79} - 263 q^{81} + 555 q^{83} + 790 q^{85} + 284 q^{87} - 20 q^{89} - 895 q^{91} - 613 q^{93} + 191 q^{95} + 302 q^{97}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
29.1 0 −3.24972 − 4.47285i 0 6.03496 0 −2.69393 − 8.29107i 0 −6.66460 + 20.5115i 0
29.2 0 −2.12267 − 2.92161i 0 −6.31780 0 3.25667 + 10.0230i 0 −1.24891 + 3.84375i 0
29.3 0 −0.700789 − 0.964553i 0 3.20583 0 2.35581 + 7.25043i 0 2.34190 − 7.20761i 0
29.4 0 −0.221154 − 0.304393i 0 −3.74775 0 −3.57465 − 11.0017i 0 2.73741 − 8.42487i 0
29.5 0 1.97990 + 2.72510i 0 5.50686 0 −0.0794018 − 0.244374i 0 −0.725016 + 2.23137i 0
29.6 0 3.19640 + 4.39947i 0 −9.53620 0 1.47158 + 4.52907i 0 −6.35718 + 19.5654i 0
77.1 0 −3.24972 + 4.47285i 0 6.03496 0 −2.69393 + 8.29107i 0 −6.66460 − 20.5115i 0
77.2 0 −2.12267 + 2.92161i 0 −6.31780 0 3.25667 − 10.0230i 0 −1.24891 − 3.84375i 0
77.3 0 −0.700789 + 0.964553i 0 3.20583 0 2.35581 − 7.25043i 0 2.34190 + 7.20761i 0
77.4 0 −0.221154 + 0.304393i 0 −3.74775 0 −3.57465 + 11.0017i 0 2.73741 + 8.42487i 0
77.5 0 1.97990 − 2.72510i 0 5.50686 0 −0.0794018 + 0.244374i 0 −0.725016 − 2.23137i 0
77.6 0 3.19640 − 4.39947i 0 −9.53620 0 1.47158 − 4.52907i 0 −6.35718 − 19.5654i 0
85.1 0 −5.44557 + 1.76937i 0 1.66378 0 −3.96780 − 2.88278i 0 19.2424 − 13.9804i 0
85.2 0 −1.93009 + 0.627125i 0 −2.24878 0 4.39783 + 3.19521i 0 −3.94919 + 2.86925i 0
85.3 0 −0.169610 + 0.0551098i 0 4.55181 0 3.81338 + 2.77058i 0 −7.25542 + 5.27137i 0
85.4 0 0.419139 − 0.136186i 0 −7.36786 0 −8.13896 − 5.91330i 0 −7.12402 + 5.17591i 0
85.5 0 3.81424 − 1.23932i 0 8.12481 0 −7.64216 − 5.55235i 0 5.73138 − 4.16409i 0
85.6 0 4.42992 − 1.43937i 0 −2.86966 0 7.80163 + 5.66822i 0 10.2713 − 7.46251i 0
89.1 0 −5.44557 − 1.76937i 0 1.66378 0 −3.96780 + 2.88278i 0 19.2424 + 13.9804i 0
89.2 0 −1.93009 − 0.627125i 0 −2.24878 0 4.39783 − 3.19521i 0 −3.94919 − 2.86925i 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 29.6
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
31.f odd 10 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 124.3.k.a ✓ 24
31.f odd 10 1 inner 124.3.k.a ✓ 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
124.3.k.a ✓ 24 1.a even 1 1 trivial
124.3.k.a ✓ 24 31.f odd 10 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(124, [\chi])\).