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Properties

Label 152.2.v.b
Level $152$
Weight $2$
Character orbit 152.v
Analytic conductor $1.214$
Analytic rank $0$
Dimension $96$
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] = [152,2,Mod(3,152)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(152, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 9, 13]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("152.3");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 152 = 2^{3} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 152.v (of order \(18\), degree \(6\), 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: \(1.21372611072\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(16\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 96 q - 6 q^{2} - 6 q^{3} - 12 q^{4} - 12 q^{6} - 9 q^{8} - 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 96 q - 6 q^{2} - 6 q^{3} - 12 q^{4} - 12 q^{6} - 9 q^{8} - 18 q^{9} - 3 q^{10} - 6 q^{11} - 9 q^{12} - 21 q^{14} - 12 q^{17} - 12 q^{19} + 18 q^{20} - 24 q^{22} - 12 q^{24} - 12 q^{25} + 21 q^{26} + 72 q^{27} - 36 q^{28} - 6 q^{30} - 51 q^{32} - 24 q^{33} + 48 q^{34} - 42 q^{35} - 39 q^{36} + 6 q^{38} - 48 q^{40} - 42 q^{41} + 69 q^{42} - 12 q^{43} + 81 q^{44} + 36 q^{46} - 9 q^{48} + 54 q^{49} + 18 q^{50} - 78 q^{51} - 45 q^{52} - 15 q^{54} - 12 q^{57} - 84 q^{58} + 6 q^{59} + 24 q^{60} + 66 q^{62} - 9 q^{64} - 18 q^{65} + 66 q^{66} - 54 q^{67} - 36 q^{68} + 81 q^{70} + 6 q^{72} - 24 q^{73} + 9 q^{74} + 66 q^{76} + 81 q^{78} + 51 q^{80} - 96 q^{81} + 87 q^{82} - 6 q^{83} + 99 q^{84} + 12 q^{86} + 63 q^{88} - 12 q^{89} + 114 q^{90} - 54 q^{91} - 48 q^{92} - 66 q^{96} + 18 q^{97} - 123 q^{98} + 72 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
3.1 −1.41042 − 0.103530i −0.958816 − 2.63432i 1.97856 + 0.292041i 3.73931 + 0.659341i 1.07960 + 3.81477i 0.569121 − 0.328582i −2.76037 − 0.616741i −3.72221 + 3.12330i −5.20573 − 1.31708i
3.2 −1.37324 + 0.337937i −0.479110 − 1.31634i 1.77160 − 0.928139i −2.77583 − 0.489454i 1.10278 + 1.64575i −1.81886 + 1.05012i −2.11918 + 1.87325i 0.794916 − 0.667014i 3.97729 − 0.265916i
3.3 −1.33777 − 0.458672i 0.735462 + 2.02067i 1.57924 + 1.22719i 2.19693 + 0.387378i −0.0570532 − 3.04052i −3.18527 + 1.83902i −1.54977 − 2.36605i −1.24405 + 1.04389i −2.76130 − 1.52589i
3.4 −1.18349 − 0.774180i −0.0275002 − 0.0755562i 0.801292 + 1.83247i −1.54307 − 0.272084i −0.0259479 + 0.110710i 2.54721 − 1.47063i 0.470338 − 2.78905i 2.29318 − 1.92421i 1.61556 + 1.51662i
3.5 −1.17222 + 0.791131i 0.750355 + 2.06158i 0.748222 − 1.85477i 1.96163 + 0.345888i −2.51057 − 1.82301i 3.50473 − 2.02345i 0.590281 + 2.76615i −1.38896 + 1.16547i −2.57311 + 1.14645i
3.6 −0.575558 + 1.29179i 0.750355 + 2.06158i −1.33747 − 1.48700i −1.96163 − 0.345888i −3.09501 − 0.217255i −3.50473 + 2.02345i 2.69069 − 0.871875i −1.38896 + 1.16547i 1.57584 − 2.33494i
3.7 −0.255869 − 1.39087i 0.445775 + 1.22476i −1.86906 + 0.711763i 1.64533 + 0.290115i 1.58942 − 0.933393i 0.994127 − 0.573959i 1.46821 + 2.41751i 0.996822 − 0.836433i −0.0174740 − 2.36267i
3.8 −0.0943415 + 1.41106i −0.479110 − 1.31634i −1.98220 − 0.266244i 2.77583 + 0.489454i 1.90265 − 0.551869i 1.81886 − 1.05012i 0.562690 − 2.77189i 0.794916 − 0.667014i −0.952526 + 3.87069i
3.9 −0.0489554 − 1.41337i −0.964940 − 2.65115i −1.99521 + 0.138384i −0.372991 − 0.0657685i −3.69981 + 1.49360i 2.52984 − 1.46060i 0.293263 + 2.81318i −3.79935 + 3.18804i −0.0746950 + 0.530393i
3.10 0.346874 + 1.37101i −0.958816 − 2.63432i −1.75936 + 0.951138i −3.73931 − 0.659341i 3.27911 − 2.22833i −0.569121 + 0.328582i −1.91430 − 2.08218i −3.72221 + 3.12330i −0.393103 − 5.35535i
3.11 0.684005 + 1.23780i 0.735462 + 2.02067i −1.06427 + 1.69332i −2.19693 − 0.387378i −1.99811 + 2.29250i 3.18527 − 1.83902i −2.82395 − 0.159118i −1.24405 + 1.04389i −1.02322 − 2.98432i
3.12 0.818566 − 1.15323i −0.174874 − 0.480461i −0.659899 − 1.88800i 3.32869 + 0.586938i −0.697230 − 0.191619i −2.05325 + 1.18545i −2.71747 − 0.784432i 2.09787 − 1.76032i 3.40163 − 3.35832i
3.13 0.967929 + 1.03107i −0.0275002 − 0.0755562i −0.126228 + 1.99601i 1.54307 + 0.272084i 0.0512858 − 0.101488i −2.54721 + 1.47063i −2.18022 + 1.80185i 2.29318 − 1.92421i 1.21304 + 1.85437i
3.14 0.993572 − 1.00639i −0.174874 − 0.480461i −0.0256305 − 1.99984i −3.32869 − 0.586938i −0.657280 − 0.301382i 2.05325 − 1.18545i −2.03807 − 1.96119i 2.09787 − 1.76032i −3.89798 + 2.76679i
3.15 1.40039 − 0.197217i −0.964940 − 2.65115i 1.92221 − 0.552363i 0.372991 + 0.0657685i −1.87415 − 3.52235i −2.52984 + 1.46060i 2.58292 − 1.15262i −3.79935 + 3.18804i 0.535306 + 0.0185416i
3.16 1.41417 + 0.0104591i 0.445775 + 1.22476i 1.99978 + 0.0295819i −1.64533 − 0.290115i 0.617593 + 1.73668i −0.994127 + 0.573959i 2.82773 + 0.0627498i 0.996822 − 0.836433i −2.32374 − 0.427482i
51.1 −1.41042 + 0.103530i −0.958816 + 2.63432i 1.97856 − 0.292041i 3.73931 − 0.659341i 1.07960 − 3.81477i 0.569121 + 0.328582i −2.76037 + 0.616741i −3.72221 − 3.12330i −5.20573 + 1.31708i
51.2 −1.37324 − 0.337937i −0.479110 + 1.31634i 1.77160 + 0.928139i −2.77583 + 0.489454i 1.10278 − 1.64575i −1.81886 − 1.05012i −2.11918 − 1.87325i 0.794916 + 0.667014i 3.97729 + 0.265916i
51.3 −1.33777 + 0.458672i 0.735462 − 2.02067i 1.57924 − 1.22719i 2.19693 − 0.387378i −0.0570532 + 3.04052i −3.18527 − 1.83902i −1.54977 + 2.36605i −1.24405 − 1.04389i −2.76130 + 1.52589i
51.4 −1.18349 + 0.774180i −0.0275002 + 0.0755562i 0.801292 − 1.83247i −1.54307 + 0.272084i −0.0259479 − 0.110710i 2.54721 + 1.47063i 0.470338 + 2.78905i 2.29318 + 1.92421i 1.61556 − 1.51662i
See all 96 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 3.16
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
8.d odd 2 1 inner
19.f odd 18 1 inner
152.v even 18 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 152.2.v.b ✓ 96
4.b odd 2 1 608.2.bh.b 96
8.b even 2 1 608.2.bh.b 96
8.d odd 2 1 inner 152.2.v.b ✓ 96
19.f odd 18 1 inner 152.2.v.b ✓ 96
76.k even 18 1 608.2.bh.b 96
152.s odd 18 1 608.2.bh.b 96
152.v even 18 1 inner 152.2.v.b ✓ 96
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
152.2.v.b ✓ 96 1.a even 1 1 trivial
152.2.v.b ✓ 96 8.d odd 2 1 inner
152.2.v.b ✓ 96 19.f odd 18 1 inner
152.2.v.b ✓ 96 152.v even 18 1 inner
608.2.bh.b 96 4.b odd 2 1
608.2.bh.b 96 8.b even 2 1
608.2.bh.b 96 76.k even 18 1
608.2.bh.b 96 152.s odd 18 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{48} + 3 T_{3}^{47} + 9 T_{3}^{46} + 6 T_{3}^{45} + 30 T_{3}^{44} + 138 T_{3}^{43} - 101 T_{3}^{42} + \cdots + 3249 \) acting on \(S_{2}^{\mathrm{new}}(152, [\chi])\). Copy content Toggle raw display