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Properties

Label 154.4.c.a
Level $154$
Weight $4$
Character orbit 154.c
Analytic conductor $9.086$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [154,4,Mod(153,154)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(154, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("154.153");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 154 = 2 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 154.c (of order \(2\), degree \(1\), 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: \(9.08629414088\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 96 q^{4} - 152 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q - 96 q^{4} - 152 q^{9} + 36 q^{11} - 32 q^{14} - 248 q^{15} + 384 q^{16} + 184 q^{22} - 392 q^{23} - 56 q^{25} + 608 q^{36} + 720 q^{37} + 576 q^{42} - 144 q^{44} - 1472 q^{49} - 2744 q^{53} + 128 q^{56} + 1680 q^{58} + 992 q^{60} - 1536 q^{64} + 2048 q^{67} + 672 q^{70} - 760 q^{71} + 2532 q^{77} - 1040 q^{78} - 3984 q^{81} + 736 q^{86} - 736 q^{88} - 824 q^{91} + 1568 q^{92} + 4560 q^{93} + 4220 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
153.1 − 2.00000i − 8.81399i −4.00000 − 3.81914i −17.6280 −6.10201 + 17.4862i 8.00000i −50.6865 −7.63828
153.2 − 2.00000i − 7.37278i −4.00000 − 19.4906i −14.7456 −1.31020 − 18.4739i 8.00000i −27.3578 −38.9812
153.3 − 2.00000i − 6.22079i −4.00000 7.04818i −12.4416 −15.3222 − 10.4034i 8.00000i −11.6982 14.0964
153.4 − 2.00000i − 3.65107i −4.00000 9.62869i −7.30215 −1.84269 + 18.4284i 8.00000i 13.6697 19.2574
153.5 − 2.00000i − 3.50992i −4.00000 13.7268i −7.01983 18.5195 − 0.170481i 8.00000i 14.6805 27.4536
153.6 − 2.00000i − 1.89937i −4.00000 − 6.22238i −3.79874 14.9971 − 10.8668i 8.00000i 23.3924 −12.4448
153.7 − 2.00000i 1.89937i −4.00000 6.22238i 3.79874 −14.9971 − 10.8668i 8.00000i 23.3924 12.4448
153.8 − 2.00000i 3.50992i −4.00000 − 13.7268i 7.01983 −18.5195 − 0.170481i 8.00000i 14.6805 −27.4536
153.9 − 2.00000i 3.65107i −4.00000 − 9.62869i 7.30215 1.84269 + 18.4284i 8.00000i 13.6697 −19.2574
153.10 − 2.00000i 6.22079i −4.00000 − 7.04818i 12.4416 15.3222 − 10.4034i 8.00000i −11.6982 −14.0964
153.11 − 2.00000i 7.37278i −4.00000 19.4906i 14.7456 1.31020 − 18.4739i 8.00000i −27.3578 38.9812
153.12 − 2.00000i 8.81399i −4.00000 3.81914i 17.6280 6.10201 + 17.4862i 8.00000i −50.6865 7.63828
153.13 2.00000i − 8.81399i −4.00000 − 3.81914i 17.6280 6.10201 − 17.4862i − 8.00000i −50.6865 7.63828
153.14 2.00000i − 7.37278i −4.00000 − 19.4906i 14.7456 1.31020 + 18.4739i − 8.00000i −27.3578 38.9812
153.15 2.00000i − 6.22079i −4.00000 7.04818i 12.4416 15.3222 + 10.4034i − 8.00000i −11.6982 −14.0964
153.16 2.00000i − 3.65107i −4.00000 9.62869i 7.30215 1.84269 − 18.4284i − 8.00000i 13.6697 −19.2574
153.17 2.00000i − 3.50992i −4.00000 13.7268i 7.01983 −18.5195 + 0.170481i − 8.00000i 14.6805 −27.4536
153.18 2.00000i − 1.89937i −4.00000 − 6.22238i 3.79874 −14.9971 + 10.8668i − 8.00000i 23.3924 12.4448
153.19 2.00000i 1.89937i −4.00000 6.22238i −3.79874 14.9971 + 10.8668i − 8.00000i 23.3924 −12.4448
153.20 2.00000i 3.50992i −4.00000 − 13.7268i −7.01983 18.5195 + 0.170481i − 8.00000i 14.6805 27.4536
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 153.24
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
7.b odd 2 1 inner
11.b odd 2 1 inner
77.b even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 154.4.c.a ✓ 24
7.b odd 2 1 inner 154.4.c.a ✓ 24
11.b odd 2 1 inner 154.4.c.a ✓ 24
77.b even 2 1 inner 154.4.c.a ✓ 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
154.4.c.a ✓ 24 1.a even 1 1 trivial
154.4.c.a ✓ 24 7.b odd 2 1 inner
154.4.c.a ✓ 24 11.b odd 2 1 inner
154.4.c.a ✓ 24 77.b even 2 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(154, [\chi])\).