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Properties

Label 124.6.e.a
Level $124$
Weight $6$
Character orbit 124.e
Analytic conductor $19.888$
Analytic rank $0$
Dimension $26$
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] = [124,6,Mod(5,124)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(124, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("124.5");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 124 = 2^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 124.e (of order \(3\), degree \(2\), 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: \(19.8875936568\)
Analytic rank: \(0\)
Dimension: \(26\)
Relative dimension: \(13\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 26 q - 7 q^{3} + 29 q^{5} - 85 q^{7} - 910 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 26 q - 7 q^{3} + 29 q^{5} - 85 q^{7} - 910 q^{9} - 331 q^{11} - 1223 q^{13} + 1006 q^{15} + 289 q^{17} - 255 q^{19} - 3965 q^{21} + 8736 q^{23} - 11044 q^{25} - 7090 q^{27} + 3740 q^{29} - 4378 q^{31} - 8610 q^{33} + 33618 q^{35} + 19709 q^{37} - 25190 q^{39} + 12665 q^{41} - 24803 q^{43} + 3174 q^{45} - 43400 q^{47} - 47710 q^{49} - 11195 q^{51} - 44939 q^{53} + 1097 q^{55} - 61689 q^{57} - 21165 q^{59} + 106308 q^{61} + 124784 q^{63} + 8599 q^{65} + 40445 q^{67} - 96540 q^{69} + 3127 q^{71} - 61171 q^{73} + 102168 q^{75} + 135766 q^{77} + 45663 q^{79} - 184525 q^{81} - 17961 q^{83} + 204058 q^{85} + 76632 q^{87} - 4460 q^{89} - 62434 q^{91} - 21117 q^{93} + 53446 q^{95} + 407108 q^{97} - 335752 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
5.1 0 −13.5997 + 23.5554i 0 −19.1795 − 33.2198i 0 −124.154 + 215.041i 0 −248.403 − 430.247i 0
5.2 0 −12.9559 + 22.4403i 0 15.0532 + 26.0729i 0 80.3996 − 139.256i 0 −214.211 − 371.024i 0
5.3 0 −8.14152 + 14.1015i 0 44.1737 + 76.5112i 0 −56.7307 + 98.2605i 0 −11.0688 − 19.1718i 0
5.4 0 −7.23210 + 12.5264i 0 −44.7489 − 77.5073i 0 44.2998 − 76.7295i 0 16.8935 + 29.2603i 0
5.5 0 −6.95972 + 12.0546i 0 4.16771 + 7.21869i 0 12.0417 − 20.8568i 0 24.6245 + 42.6508i 0
5.6 0 −1.18571 + 2.05371i 0 −36.2567 − 62.7984i 0 −61.0465 + 105.736i 0 118.688 + 205.574i 0
5.7 0 −0.335033 + 0.580294i 0 −3.20366 − 5.54890i 0 23.1351 − 40.0711i 0 121.276 + 210.055i 0
5.8 0 1.77651 − 3.07701i 0 23.3335 + 40.4149i 0 −88.0895 + 152.575i 0 115.188 + 199.511i 0
5.9 0 2.55181 − 4.41986i 0 54.6006 + 94.5710i 0 95.4995 − 165.410i 0 108.477 + 187.887i 0
5.10 0 8.12182 − 14.0674i 0 9.34608 + 16.1879i 0 −36.3878 + 63.0254i 0 −10.4280 − 18.0618i 0
5.11 0 8.26083 − 14.3082i 0 −19.0131 − 32.9317i 0 119.279 − 206.597i 0 −14.9827 − 25.9509i 0
5.12 0 10.9970 − 19.0473i 0 −45.3408 − 78.5326i 0 −51.4992 + 89.1993i 0 −120.367 − 208.481i 0
5.13 0 15.2017 − 26.3302i 0 31.5677 + 54.6769i 0 0.753021 − 1.30427i 0 −340.686 − 590.085i 0
25.1 0 −13.5997 − 23.5554i 0 −19.1795 + 33.2198i 0 −124.154 − 215.041i 0 −248.403 + 430.247i 0
25.2 0 −12.9559 − 22.4403i 0 15.0532 − 26.0729i 0 80.3996 + 139.256i 0 −214.211 + 371.024i 0
25.3 0 −8.14152 − 14.1015i 0 44.1737 − 76.5112i 0 −56.7307 − 98.2605i 0 −11.0688 + 19.1718i 0
25.4 0 −7.23210 − 12.5264i 0 −44.7489 + 77.5073i 0 44.2998 + 76.7295i 0 16.8935 − 29.2603i 0
25.5 0 −6.95972 − 12.0546i 0 4.16771 − 7.21869i 0 12.0417 + 20.8568i 0 24.6245 − 42.6508i 0
25.6 0 −1.18571 − 2.05371i 0 −36.2567 + 62.7984i 0 −61.0465 − 105.736i 0 118.688 − 205.574i 0
25.7 0 −0.335033 − 0.580294i 0 −3.20366 + 5.54890i 0 23.1351 + 40.0711i 0 121.276 − 210.055i 0
See all 26 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 5.13
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
31.c even 3 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 124.6.e.a ✓ 26
31.c even 3 1 inner 124.6.e.a ✓ 26
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
124.6.e.a ✓ 26 1.a even 1 1 trivial
124.6.e.a ✓ 26 31.c even 3 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{6}^{\mathrm{new}}(124, [\chi])\).