↑

Properties

Label 154.3.j.a
Level $154$
Weight $3$
Character orbit 154.j
Analytic conductor $4.196$
Analytic rank $0$
Dimension $48$
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] = [154,3,Mod(29,154)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(154, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 7]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("154.29");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 154 = 2 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 154.j (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: \(4.19619607115\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(12\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 48 q + 4 q^{3} + 24 q^{4} - 12 q^{5} + 40 q^{6} - 52 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 48 q + 4 q^{3} + 24 q^{4} - 12 q^{5} + 40 q^{6} - 52 q^{9} - 16 q^{11} - 48 q^{12} - 60 q^{13} - 96 q^{15} - 48 q^{16} - 80 q^{18} + 60 q^{19} + 24 q^{20} + 16 q^{22} + 168 q^{23} + 80 q^{24} + 48 q^{25} - 16 q^{26} - 128 q^{27} + 180 q^{29} + 120 q^{30} + 28 q^{31} + 280 q^{33} - 160 q^{34} + 104 q^{36} + 28 q^{37} - 136 q^{38} - 340 q^{39} - 128 q^{44} + 320 q^{46} - 240 q^{47} + 16 q^{48} + 84 q^{49} + 160 q^{50} - 20 q^{51} + 80 q^{52} - 44 q^{53} + 172 q^{55} - 380 q^{57} - 16 q^{58} + 76 q^{59} - 248 q^{60} + 160 q^{61} - 320 q^{62} + 96 q^{64} - 544 q^{66} - 432 q^{67} - 220 q^{69} - 112 q^{70} - 60 q^{71} - 320 q^{73} - 308 q^{75} - 56 q^{77} + 112 q^{78} - 560 q^{79} - 48 q^{80} + 260 q^{81} + 320 q^{82} + 720 q^{83} + 280 q^{84} - 320 q^{85} + 456 q^{86} - 32 q^{88} + 816 q^{89} + 800 q^{90} + 252 q^{91} - 56 q^{92} + 1112 q^{93} + 800 q^{95} - 308 q^{97} + 776 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
29.1 −0.831254 + 1.14412i −1.14569 + 3.52606i −0.618034 − 1.90211i −7.31561 + 5.31510i −3.08189 − 4.24185i 2.51626 − 0.817582i 2.68999 + 0.874032i −3.83934 − 2.78944i − 12.7882i
29.2 −0.831254 + 1.14412i −0.199720 + 0.614674i −0.618034 − 1.90211i 0.273658 − 0.198824i −0.537245 − 0.739454i 2.51626 − 0.817582i 2.68999 + 0.874032i 6.94322 + 5.04454i 0.478372i
29.3 −0.831254 + 1.14412i 0.145353 − 0.447350i −0.618034 − 1.90211i 1.34475 − 0.977016i 0.390998 + 0.538163i −2.51626 + 0.817582i 2.68999 + 0.874032i 7.10216 + 5.16002i 2.35070i
29.4 −0.831254 + 1.14412i 1.00158 − 3.08256i −0.618034 − 1.90211i −5.85638 + 4.25491i 2.69425 + 3.70832i −2.51626 + 0.817582i 2.68999 + 0.874032i −1.21784 − 0.884814i − 10.2373i
29.5 −0.831254 + 1.14412i 1.11303 − 3.42556i −0.618034 − 1.90211i −0.282988 + 0.205603i 2.99405 + 4.12096i 2.51626 − 0.817582i 2.68999 + 0.874032i −3.21447 − 2.33545i − 0.494681i
29.6 −0.831254 + 1.14412i 1.73096 − 5.32734i −0.618034 − 1.90211i 6.98248 − 5.07307i 4.65626 + 6.40880i −2.51626 + 0.817582i 2.68999 + 0.874032i −18.1032 − 13.1527i 12.2058i
29.7 0.831254 − 1.14412i −1.72607 + 5.31230i −0.618034 − 1.90211i −3.10775 + 2.25792i 4.64312 + 6.39071i 2.51626 − 0.817582i −2.68999 − 0.874032i −17.9601 − 13.0488i 5.43255i
29.8 0.831254 − 1.14412i −0.756843 + 2.32932i −0.618034 − 1.90211i 3.07045 − 2.23081i 2.03590 + 2.80218i 2.51626 − 0.817582i −2.68999 − 0.874032i 2.42822 + 1.76420i − 5.36735i
29.9 0.831254 − 1.14412i −0.503896 + 1.55083i −0.618034 − 1.90211i −5.86834 + 4.26360i 1.35548 + 1.86566i −2.51626 + 0.817582i −2.68999 − 0.874032i 5.12998 + 3.72715i 10.2582i
29.10 0.831254 − 1.14412i 0.632393 − 1.94630i −0.618034 − 1.90211i 4.76027 − 3.45854i −1.70113 − 2.34141i −2.51626 + 0.817582i −2.68999 − 0.874032i 3.89297 + 2.82841i − 8.32126i
29.11 0.831254 − 1.14412i 1.22305 − 3.76417i −0.618034 − 1.90211i 2.50815 − 1.82227i −3.29001 − 4.52831i 2.51626 − 0.817582i −2.68999 − 0.874032i −5.39200 − 3.91752i − 4.38440i
29.12 0.831254 − 1.14412i 1.72191 − 5.29950i −0.618034 − 1.90211i −6.21688 + 4.51683i −4.63193 − 6.37531i −2.51626 + 0.817582i −2.68999 − 0.874032i −17.8385 − 12.9605i 10.8675i
57.1 −1.34500 − 0.437016i −3.89298 + 2.82842i 1.61803 + 1.17557i −2.10473 − 6.47769i 6.47211 − 2.10292i −1.55513 + 2.14046i −1.66251 − 2.28825i 4.37421 − 13.4624i 9.63227i
57.2 −1.34500 − 0.437016i −3.41646 + 2.48220i 1.61803 + 1.17557i 2.80979 + 8.64764i 5.67989 − 1.84551i 1.55513 − 2.14046i −1.66251 − 2.28825i 2.72970 − 8.40116i − 12.8590i
57.3 −1.34500 − 0.437016i −2.51501 + 1.82726i 1.61803 + 1.17557i 0.457745 + 1.40879i 4.18122 − 1.35856i −1.55513 + 2.14046i −1.66251 − 2.28825i 0.205234 − 0.631645i − 2.09487i
57.4 −1.34500 − 0.437016i −1.07269 + 0.779354i 1.61803 + 1.17557i −0.422699 − 1.30093i 1.78335 − 0.579447i 1.55513 − 2.14046i −1.66251 − 2.28825i −2.23788 + 6.88750i 1.93448i
57.5 −1.34500 − 0.437016i 1.40646 − 1.02185i 1.61803 + 1.17557i 1.85944 + 5.72277i −2.33825 + 0.759745i −1.55513 + 2.14046i −1.66251 − 2.28825i −1.84720 + 5.68511i − 8.50972i
57.6 −1.34500 − 0.437016i 4.52014 − 3.28407i 1.61803 + 1.17557i −0.745447 − 2.29425i −7.51476 + 2.44169i 1.55513 − 2.14046i −1.66251 − 2.28825i 6.86536 − 21.1294i 3.41153i
57.7 1.34500 + 0.437016i −4.09582 + 2.97578i 1.61803 + 1.17557i 0.526132 + 1.61927i −6.80933 + 2.21248i −1.55513 + 2.14046i 1.66251 + 2.28825i 5.13926 − 15.8170i 2.40784i
57.8 1.34500 + 0.437016i −1.39909 + 1.01650i 1.61803 + 1.17557i 1.03045 + 3.17139i −2.32599 + 0.755761i 1.55513 − 2.14046i 1.66251 + 2.28825i −1.85697 + 5.71517i 4.71584i
See all 48 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 29.12
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
11.d odd 10 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 154.3.j.a ✓ 48
11.d odd 10 1 inner 154.3.j.a ✓ 48
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
154.3.j.a ✓ 48 1.a even 1 1 trivial
154.3.j.a ✓ 48 11.d odd 10 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(154, [\chi])\).