↑

Properties

Label 1055.2.b.f
Level $1055$
Weight $2$
Character orbit 1055.b
Analytic conductor $8.424$
Analytic rank $0$
Dimension $58$
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [1055,2,Mod(634,1055)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1055.634"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1055, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 1055 = 5 \cdot 211 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1055.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [58,0,0,-66] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(8.42421741325\)
Analytic rank: \(0\)
Dimension: \(58\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 58 q - 66 q^{4} - q^{5} + 16 q^{6} - 80 q^{9} + 24 q^{11} - 42 q^{14} + 2 q^{15} + 86 q^{16} - 10 q^{19} + 46 q^{21} - 42 q^{24} + q^{25} + 64 q^{26} - 90 q^{29} + 3 q^{30} + 22 q^{31} - 34 q^{34} - q^{35}+ \cdots - 62 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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.

Copy content comment:embeddings in the coefficient field
 
Copy content gp:mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
634.1 − 2.73297i − 2.44232i −5.46911 −2.19795 − 0.411133i −6.67479 − 4.42098i 9.48097i −2.96495 −1.12361 + 6.00692i
634.2 − 2.71246i 1.20572i −5.35745 1.19375 − 1.89076i 3.27048 0.239875i 9.10695i 1.54623 −5.12860 − 3.23800i
634.3 − 2.66867i − 0.954906i −5.12181 2.07983 + 0.821164i −2.54833 − 1.44798i 8.33109i 2.08815 2.19142 − 5.55038i
634.4 − 2.65136i 2.81016i −5.02973 0.452229 + 2.18986i 7.45075 1.51838i 8.03292i −4.89698 5.80612 − 1.19902i
634.5 − 2.51043i − 0.366736i −4.30224 −1.62088 − 1.54037i −0.920663 1.68656i 5.77960i 2.86550 −3.86700 + 4.06910i
634.6 − 2.43265i 1.96810i −3.91777 −2.19536 + 0.424723i 4.78770 − 2.83967i 4.66527i −0.873427 1.03320 + 5.34054i
634.7 − 2.40461i 2.55830i −3.78213 2.22390 − 0.232996i 6.15171 − 4.75690i 4.28532i −3.54492 −0.560264 − 5.34759i
634.8 − 2.36784i 3.40903i −3.60665 −1.30301 − 1.81719i 8.07202 0.901252i 3.80428i −8.62147 −4.30280 + 3.08531i
634.9 − 2.13366i − 2.39523i −2.55250 −0.600393 + 2.15396i −5.11060 − 3.70764i 1.17885i −2.73712 4.59581 + 1.28103i
634.10 − 2.13084i − 0.398367i −2.54049 0.0402943 + 2.23570i −0.848858 − 0.277316i 1.15171i 2.84130 4.76394 − 0.0858608i
634.11 − 2.09413i − 3.08538i −2.38540 −2.23389 + 0.0987661i −6.46121 2.70508i 0.807079i −6.51959 0.206829 + 4.67806i
634.12 − 1.97550i − 1.16651i −1.90261 1.87035 − 1.22548i −2.30444 4.82158i − 0.192395i 1.63925 −2.42093 − 3.69488i
634.13 − 1.81045i − 1.29136i −1.27772 2.23549 + 0.0508875i −2.33794 − 4.36156i − 1.30764i 1.33238 0.0921291 − 4.04724i
634.14 − 1.78631i 2.00871i −1.19089 0.971751 − 2.01388i 3.58818 − 2.69981i − 1.44532i −1.03493 −3.59740 − 1.73584i
634.15 − 1.68875i 1.95652i −0.851888 −0.827078 + 2.07748i 3.30408 4.65798i − 1.93888i −0.827973 3.50836 + 1.39673i
634.16 − 1.47953i − 3.39961i −0.189007 1.88043 + 1.20995i −5.02982 1.16654i − 2.67942i −8.55732 1.79016 − 2.78215i
634.17 − 1.37976i − 0.764357i 0.0962556 −2.23264 + 0.123701i −1.05463 3.72391i − 2.89233i 2.41576 0.170678 + 3.08052i
634.18 − 1.31411i 0.589410i 0.273107 1.32836 − 1.79874i 0.774552 − 0.176501i − 2.98712i 2.65260 −2.36374 − 1.74562i
634.19 − 1.28462i 3.10265i 0.349744 0.435127 + 2.19332i 3.98573 − 2.90980i − 3.01854i −6.62642 2.81759 − 0.558974i
634.20 − 1.25741i − 2.35917i 0.418917 2.18401 + 0.479679i −2.96645 − 1.97457i − 3.04157i −2.56570 0.603153 − 2.74620i
See all 58 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 634.58
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1055.2.b.f ✓ 58
5.b even 2 1 inner 1055.2.b.f ✓ 58
5.c odd 4 2 5275.2.a.w 58
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1055.2.b.f ✓ 58 1.a even 1 1 trivial
1055.2.b.f ✓ 58 5.b even 2 1 inner
5275.2.a.w 58 5.c odd 4 2

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{58} + 91 T_{2}^{56} + 3904 T_{2}^{54} + 105009 T_{2}^{52} + 1986701 T_{2}^{50} + 28115020 T_{2}^{48} + \cdots + 576 \) acting on \(S_{2}^{\mathrm{new}}(1055, [\chi])\). Copy content Toggle raw display