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Properties

Label 155.3.l.b
Level $155$
Weight $3$
Character orbit 155.l
Analytic conductor $4.223$
Analytic rank $0$
Dimension $40$
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] = [155,3,Mod(46,155)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(155, 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("155.46");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 155 = 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 155.l (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: \(4.22344409758\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(10\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 40 q - 18 q^{4} + 15 q^{7} + 47 q^{8} + 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 40 q - 18 q^{4} + 15 q^{7} + 47 q^{8} + 14 q^{9} - 10 q^{10} + 25 q^{11} - 60 q^{12} - 15 q^{13} - 44 q^{14} + 62 q^{16} - 25 q^{17} - 14 q^{18} - 52 q^{19} - 60 q^{20} + 70 q^{21} - 120 q^{22} + 5 q^{23} - 110 q^{24} + 200 q^{25} - 45 q^{27} - 72 q^{28} + 115 q^{29} + 34 q^{31} - 182 q^{32} + 99 q^{33} - 200 q^{34} + 15 q^{35} + 390 q^{36} + 71 q^{38} - 130 q^{39} + 145 q^{40} - 12 q^{41} - 130 q^{42} - 15 q^{43} - 35 q^{44} + 110 q^{45} + 180 q^{46} + 32 q^{47} - 180 q^{48} - 383 q^{49} + 126 q^{51} - 145 q^{52} - 20 q^{53} + 55 q^{54} - 105 q^{55} + 336 q^{56} + 120 q^{58} + 28 q^{59} + 120 q^{62} - 578 q^{63} + 297 q^{64} - 125 q^{65} + 48 q^{66} - 22 q^{67} + 14 q^{69} - 40 q^{70} + 229 q^{71} + 277 q^{72} - 95 q^{73} + 775 q^{74} - 425 q^{76} + 35 q^{77} + 503 q^{78} - 475 q^{79} - 60 q^{80} - 586 q^{81} + 228 q^{82} - 120 q^{83} + 195 q^{84} + 15 q^{85} - 830 q^{86} + 276 q^{87} - 135 q^{89} + 30 q^{90} - 700 q^{91} + 418 q^{93} + 346 q^{94} + 70 q^{95} - 195 q^{96} - 181 q^{97} - 300 q^{98}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
46.1 −2.45218 + 1.78162i 1.83627 − 2.52741i 1.60298 − 4.93347i −2.23607 9.46919i −1.80279 + 5.54842i 1.11214 + 3.42280i −0.234753 − 0.722495i 5.48325 − 3.98381i
46.2 −2.11638 + 1.53764i −1.45025 + 1.99610i 0.878657 − 2.70423i −2.23607 − 6.45447i 3.73059 − 11.4816i −0.934983 − 2.87758i 0.899967 + 2.76981i 4.73237 − 3.43827i
46.3 −1.26699 + 0.920520i −2.46288 + 3.38986i −0.478169 + 1.47165i −2.23607 − 6.56204i −3.84205 + 11.8246i −2.68464 − 8.26246i −2.64425 − 8.13815i 2.83307 − 2.05834i
46.4 −1.11262 + 0.808364i 0.752097 − 1.03517i −0.651602 + 2.00543i −2.23607 1.75972i −0.618313 + 1.90297i −2.59606 − 7.98985i 2.27522 + 7.00241i 2.48789 − 1.80756i
46.5 −0.197020 + 0.143143i 3.12860 − 4.30614i −1.21774 + 3.74782i −2.23607 1.29623i 2.75109 − 8.46700i −0.597576 − 1.83915i −5.97361 − 18.3849i 0.440550 − 0.320078i
46.6 0.414439 − 0.301108i 0.347460 − 0.478238i −1.15497 + 3.55464i −2.23607 − 0.302824i 0.305256 − 0.939482i 1.22487 + 3.76977i 2.67317 + 8.22717i −0.926714 + 0.673297i
46.7 0.977865 − 0.710460i −3.36719 + 4.63453i −0.784603 + 2.41476i −2.23607 6.92420i 2.29024 − 7.04865i 2.44240 + 7.51693i −7.35981 − 22.6512i −2.18657 + 1.58864i
46.8 1.66402 − 1.20898i −1.17523 + 1.61756i 0.0712575 − 0.219308i −2.23607 4.11248i −2.78578 + 8.57375i 2.39583 + 7.37361i 1.54581 + 4.75750i −3.72086 + 2.70336i
46.9 2.48034 − 1.80207i 2.48744 − 3.42366i 1.66854 − 5.13524i −2.23607 − 12.9744i −1.77286 + 5.45631i −1.32591 − 4.08072i −2.75297 − 8.47278i −5.54620 + 4.02955i
46.10 2.72656 − 1.98096i −0.0963141 + 0.132565i 2.27386 − 6.99821i −2.23607 0.552241i 3.81756 − 11.7492i −3.49757 − 10.7644i 2.77286 + 8.53397i −6.09678 + 4.42957i
91.1 −2.45218 − 1.78162i 1.83627 + 2.52741i 1.60298 + 4.93347i −2.23607 − 9.46919i −1.80279 − 5.54842i 1.11214 − 3.42280i −0.234753 + 0.722495i 5.48325 + 3.98381i
91.2 −2.11638 − 1.53764i −1.45025 − 1.99610i 0.878657 + 2.70423i −2.23607 6.45447i 3.73059 + 11.4816i −0.934983 + 2.87758i 0.899967 − 2.76981i 4.73237 + 3.43827i
91.3 −1.26699 − 0.920520i −2.46288 − 3.38986i −0.478169 − 1.47165i −2.23607 6.56204i −3.84205 − 11.8246i −2.68464 + 8.26246i −2.64425 + 8.13815i 2.83307 + 2.05834i
91.4 −1.11262 − 0.808364i 0.752097 + 1.03517i −0.651602 − 2.00543i −2.23607 − 1.75972i −0.618313 − 1.90297i −2.59606 + 7.98985i 2.27522 − 7.00241i 2.48789 + 1.80756i
91.5 −0.197020 − 0.143143i 3.12860 + 4.30614i −1.21774 − 3.74782i −2.23607 − 1.29623i 2.75109 + 8.46700i −0.597576 + 1.83915i −5.97361 + 18.3849i 0.440550 + 0.320078i
91.6 0.414439 + 0.301108i 0.347460 + 0.478238i −1.15497 − 3.55464i −2.23607 0.302824i 0.305256 + 0.939482i 1.22487 − 3.76977i 2.67317 − 8.22717i −0.926714 − 0.673297i
91.7 0.977865 + 0.710460i −3.36719 − 4.63453i −0.784603 − 2.41476i −2.23607 − 6.92420i 2.29024 + 7.04865i 2.44240 − 7.51693i −7.35981 + 22.6512i −2.18657 − 1.58864i
91.8 1.66402 + 1.20898i −1.17523 − 1.61756i 0.0712575 + 0.219308i −2.23607 − 4.11248i −2.78578 − 8.57375i 2.39583 − 7.37361i 1.54581 − 4.75750i −3.72086 − 2.70336i
91.9 2.48034 + 1.80207i 2.48744 + 3.42366i 1.66854 + 5.13524i −2.23607 12.9744i −1.77286 − 5.45631i −1.32591 + 4.08072i −2.75297 + 8.47278i −5.54620 − 4.02955i
91.10 2.72656 + 1.98096i −0.0963141 − 0.132565i 2.27386 + 6.99821i −2.23607 − 0.552241i 3.81756 + 11.7492i −3.49757 + 10.7644i 2.77286 − 8.53397i −6.09678 − 4.42957i
See all 40 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 46.10
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
31.f odd 10 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 155.3.l.b ✓ 40
31.f odd 10 1 inner 155.3.l.b ✓ 40
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
155.3.l.b ✓ 40 1.a even 1 1 trivial
155.3.l.b ✓ 40 31.f odd 10 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{40} + 29 T_{2}^{38} - 29 T_{2}^{37} + 494 T_{2}^{36} - 331 T_{2}^{35} + 6966 T_{2}^{34} + \cdots + 23338561 \) acting on \(S_{3}^{\mathrm{new}}(155, [\chi])\). Copy content Toggle raw display