↑

Properties

Label 124.4.m.a
Level $124$
Weight $4$
Character orbit 124.m
Analytic conductor $7.316$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [124,4,Mod(9,124)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(124, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("124.9");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 124 = 2^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 124.m (of order \(15\), degree \(8\), 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: \(7.31623684071\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(8\) over \(\Q(\zeta_{15})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 64 q + 4 q^{3} + 4 q^{5} + 46 q^{7} + 40 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 64 q + 4 q^{3} + 4 q^{5} + 46 q^{7} + 40 q^{9} - 82 q^{11} - 52 q^{13} - 62 q^{15} - 54 q^{17} - 152 q^{19} - 502 q^{21} + 342 q^{23} - 856 q^{25} + 424 q^{27} + 840 q^{29} + 724 q^{31} + 1350 q^{33} + 200 q^{35} - 90 q^{37} - 1264 q^{39} - 524 q^{41} - 1122 q^{43} + 1130 q^{45} - 246 q^{47} + 1950 q^{49} + 1924 q^{51} + 208 q^{53} - 1596 q^{55} - 510 q^{57} - 1802 q^{59} - 1692 q^{61} - 7124 q^{63} - 2248 q^{65} - 30 q^{67} - 476 q^{69} + 1788 q^{71} + 96 q^{73} + 5862 q^{75} + 322 q^{77} - 1854 q^{79} + 1308 q^{81} - 1162 q^{83} + 3044 q^{85} + 60 q^{87} + 5026 q^{89} + 3720 q^{91} + 6236 q^{93} + 4970 q^{95} + 3452 q^{97} + 900 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
9.1 0 −8.64213 − 1.83694i 0 2.76404 + 4.78746i 0 −21.3605 + 9.51032i 0 46.6463 + 20.7683i 0
9.2 0 −6.47113 − 1.37548i 0 −5.18536 − 8.98130i 0 12.6504 − 5.63230i 0 15.3179 + 6.81996i 0
9.3 0 −2.63900 − 0.560936i 0 0.589414 + 1.02090i 0 8.31895 − 3.70384i 0 −18.0161 − 8.02127i 0
9.4 0 −0.583083 − 0.123938i 0 10.1759 + 17.6252i 0 −11.1641 + 4.97056i 0 −24.3411 − 10.8374i 0
9.5 0 2.58240 + 0.548905i 0 −5.46077 − 9.45833i 0 −31.4822 + 14.0168i 0 −18.2983 − 8.14691i 0
9.6 0 4.19347 + 0.891350i 0 4.02689 + 6.97477i 0 21.7090 − 9.66545i 0 −7.87502 − 3.50618i 0
9.7 0 5.17620 + 1.10023i 0 −7.90202 − 13.6867i 0 11.4478 − 5.09687i 0 0.916762 + 0.408169i 0
9.8 0 9.54863 + 2.02962i 0 3.66840 + 6.35385i 0 −7.21841 + 3.21384i 0 62.3912 + 27.7783i 0
41.1 0 −0.797975 − 7.59223i 0 9.70753 + 16.8139i 0 27.5180 + 5.84913i 0 −30.5951 + 6.50320i 0
41.2 0 −0.712172 − 6.77586i 0 −10.1582 − 17.5946i 0 23.4601 + 4.98659i 0 −18.9952 + 4.03754i 0
41.3 0 −0.696512 − 6.62687i 0 −1.00841 − 1.74661i 0 −26.1276 − 5.55359i 0 −17.0203 + 3.61778i 0
41.4 0 −0.250899 − 2.38714i 0 1.12384 + 1.94655i 0 −3.51521 − 0.747181i 0 20.7745 − 4.41576i 0
41.5 0 0.226255 + 2.15268i 0 −2.95203 − 5.11307i 0 10.2309 + 2.17464i 0 21.8272 − 4.63951i 0
41.6 0 0.343209 + 3.26541i 0 8.86299 + 15.3511i 0 −13.5223 − 2.87425i 0 15.8649 − 3.37218i 0
41.7 0 0.775171 + 7.37526i 0 −7.07670 − 12.2572i 0 −17.8286 − 3.78958i 0 −27.3836 + 5.82056i 0
41.8 0 0.983719 + 9.35946i 0 5.15522 + 8.92910i 0 29.4938 + 6.26909i 0 −60.2218 + 12.8005i 0
45.1 0 −6.37726 + 7.08266i 0 −9.68267 + 16.7709i 0 −1.03034 + 9.80304i 0 −6.67243 − 63.4839i 0
45.2 0 −4.25543 + 4.72613i 0 6.59845 − 11.4289i 0 −2.98033 + 28.3560i 0 −1.40539 − 13.3714i 0
45.3 0 −3.34595 + 3.71605i 0 3.09755 − 5.36511i 0 2.06573 − 19.6541i 0 0.208598 + 1.98467i 0
45.4 0 −1.40788 + 1.56361i 0 −3.83787 + 6.64739i 0 1.68148 − 15.9983i 0 2.35952 + 22.4493i 0
See all 64 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 9.8
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
31.g even 15 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 124.4.m.a ✓ 64
31.g even 15 1 inner 124.4.m.a ✓ 64
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
124.4.m.a ✓ 64 1.a even 1 1 trivial
124.4.m.a ✓ 64 31.g even 15 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(124, [\chi])\).