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Properties

Label 855.2.dc.a
Level $855$
Weight $2$
Character orbit 855.dc
Analytic conductor $6.827$
Analytic rank $0$
Dimension $696$
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] = [855,2,Mod(454,855)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(855, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([6, 9, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("855.454");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 855.dc (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: \(6.82720937282\)
Analytic rank: \(0\)
Dimension: \(696\)
Relative dimension: \(116\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 696 q - 6 q^{4} - 3 q^{5} - 12 q^{6} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 696 q - 6 q^{4} - 3 q^{5} - 12 q^{6} - 12 q^{9} - 12 q^{10} - 12 q^{11} - 30 q^{14} - 36 q^{15} + 6 q^{16} - 24 q^{19} - 6 q^{20} - 30 q^{21} - 3 q^{25} - 36 q^{26} - 6 q^{29} - 45 q^{30} - 12 q^{31} + 30 q^{34} + 21 q^{35} - 24 q^{36} - 12 q^{39} - 45 q^{40} - 6 q^{41} - 48 q^{44} + 33 q^{45} - 12 q^{46} + 282 q^{49} - 54 q^{50} + 6 q^{51} + 48 q^{54} - 27 q^{55} - 198 q^{56} - 102 q^{59} + 69 q^{60} - 6 q^{61} + 270 q^{64} + 54 q^{65} - 72 q^{66} - 6 q^{69} - 45 q^{70} - 60 q^{71} + 90 q^{74} + 72 q^{75} - 6 q^{76} - 6 q^{79} - 78 q^{80} + 120 q^{81} - 162 q^{84} - 3 q^{85} - 60 q^{86} - 24 q^{89} + 27 q^{90} + 18 q^{91} - 12 q^{94} + 9 q^{95} - 192 q^{96} - 132 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
454.1 −0.952518 − 2.61702i 0.236072 + 1.71589i −4.40943 + 3.69995i 0.841986 + 2.07149i 4.26565 − 2.25222i 2.47370 + 1.42819i 9.05919 + 5.23032i −2.88854 + 0.810146i 4.61912 − 4.17663i
454.2 −0.950979 − 2.61279i 1.72954 − 0.0931855i −4.39024 + 3.68384i −1.88379 + 1.20471i −1.88823 − 4.43032i −1.41933 − 0.819451i 8.98422 + 5.18704i 2.98263 − 0.322337i 4.93911 + 3.77630i
454.3 −0.920611 − 2.52936i −1.73197 − 0.0170343i −4.01803 + 3.37153i 2.15898 + 0.582088i 1.55138 + 4.39644i 0.702690 + 0.405698i 7.56471 + 4.36749i 2.99942 + 0.0590058i −0.515268 − 5.99669i
454.4 −0.911885 − 2.50538i 0.869155 − 1.49819i −3.91332 + 3.28366i −0.607143 − 2.15206i −4.54611 − 0.811391i 2.05673 + 1.18746i 7.17739 + 4.14387i −1.48914 − 2.60432i −4.83810 + 3.48356i
454.5 −0.899898 − 2.47245i −1.59845 − 0.667056i −3.77110 + 3.16433i −0.932378 − 2.03241i −0.210823 + 4.55236i −1.49007 − 0.860295i 6.65999 + 3.84515i 2.11007 + 2.13251i −4.18597 + 4.13421i
454.6 −0.884711 − 2.43072i −1.13935 + 1.30456i −3.59362 + 3.01541i −2.22696 − 0.201573i 4.17902 + 1.61530i −3.44398 − 1.98838i 6.02860 + 3.48061i −0.403742 − 2.97271i 1.48025 + 5.59147i
454.7 −0.880048 − 2.41791i 1.12201 + 1.31950i −3.53972 + 2.97018i 1.75018 − 1.39171i 2.20302 − 3.87415i −3.72030 − 2.14791i 5.84004 + 3.37175i −0.482174 + 2.96100i −4.90528 − 3.00702i
454.8 −0.878636 − 2.41403i −0.0685320 − 1.73069i −3.52346 + 2.95654i 0.828386 + 2.07696i −4.11774 + 1.68609i −4.06124 − 2.34476i 5.78345 + 3.33908i −2.99061 + 0.237216i 4.28601 − 3.82465i
454.9 −0.863024 − 2.37114i −0.173304 − 1.72336i −3.34540 + 2.80713i 2.17374 − 0.524277i −3.93676 + 1.89823i 2.02236 + 1.16761i 5.17274 + 2.98648i −2.93993 + 0.597331i −3.11912 − 4.70177i
454.10 −0.838977 − 2.30507i 0.518347 + 1.65267i −3.07738 + 2.58222i −1.66508 − 1.49249i 3.37464 − 2.58138i 0.0407165 + 0.0235077i 4.28533 + 2.47413i −2.46263 + 1.71331i −2.04332 + 5.09028i
454.11 −0.817948 − 2.24729i −0.611592 + 1.62048i −2.84921 + 2.39077i 0.888283 − 2.05206i 4.14195 + 0.0489597i 2.05283 + 1.18520i 3.56103 + 2.05596i −2.25191 − 1.98215i −5.33816 − 0.317753i
454.12 −0.807906 − 2.21970i −1.69758 − 0.343828i −2.74228 + 2.30105i −0.681458 + 2.12970i 0.608290 + 4.04591i −0.248972 − 0.143744i 3.23177 + 1.86586i 2.76356 + 1.16735i 5.27785 − 0.207961i
454.13 −0.806576 − 2.21605i 1.55504 − 0.762791i −2.72822 + 2.28925i 0.494030 − 2.18081i −2.94464 − 2.83080i −2.61371 − 1.50902i 3.18896 + 1.84115i 1.83630 − 2.37234i −5.23126 + 0.664195i
454.14 −0.778740 − 2.13957i 1.69532 + 0.354801i −2.43924 + 2.04676i −2.21627 − 0.296924i −0.561094 − 3.90356i 2.87344 + 1.65898i 2.33505 + 1.34814i 2.74823 + 1.20300i 1.09060 + 4.97309i
454.15 −0.776506 − 2.13343i 1.71207 + 0.262299i −2.41649 + 2.02767i 2.21729 − 0.289166i −0.769840 − 3.85627i 2.61064 + 1.50725i 2.26995 + 1.31056i 2.86240 + 0.898149i −2.33866 − 4.50590i
454.16 −0.735975 − 2.02207i 1.47707 + 0.904587i −2.01503 + 1.69081i 1.21926 + 1.87441i 0.742059 − 3.65249i −1.05623 − 0.609814i 1.17486 + 0.678306i 1.36344 + 2.67227i 2.89286 − 3.84494i
454.17 −0.730499 − 2.00703i −1.21219 + 1.23717i −1.96245 + 1.64669i −1.05350 + 1.97234i 3.36855 + 1.52914i 0.781741 + 0.451338i 1.03915 + 0.599951i −0.0611996 − 2.99938i 4.72813 + 0.673608i
454.18 −0.728853 − 2.00251i −0.849012 − 1.50969i −1.94672 + 1.63349i −2.07883 − 0.823682i −2.40437 + 2.80050i −0.0431364 − 0.0249048i 0.998902 + 0.576716i −1.55836 + 2.56350i −0.134266 + 4.76322i
454.19 −0.716058 − 1.96735i 0.874155 − 1.49528i −1.82565 + 1.53190i −1.19790 + 1.88813i −3.56768 − 0.649065i 3.12896 + 1.80651i 0.694811 + 0.401149i −1.47171 − 2.61421i 4.57238 + 1.00469i
454.20 −0.706945 − 1.94232i 0.634303 − 1.61173i −1.74073 + 1.46065i −2.23476 + 0.0764103i −3.57890 − 0.0926144i −2.21539 − 1.27906i 0.487544 + 0.281484i −2.19532 − 2.04464i 1.72827 + 4.28660i
See next 80 embeddings (of 696 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 454.116
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner
171.v even 9 1 inner
855.dc even 18 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 855.2.dc.a yes 696
5.b even 2 1 inner 855.2.dc.a yes 696
9.c even 3 1 855.2.cn.a ✓ 696
19.e even 9 1 855.2.cn.a ✓ 696
45.j even 6 1 855.2.cn.a ✓ 696
95.p even 18 1 855.2.cn.a ✓ 696
171.v even 9 1 inner 855.2.dc.a yes 696
855.dc even 18 1 inner 855.2.dc.a yes 696
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
855.2.cn.a ✓ 696 9.c even 3 1
855.2.cn.a ✓ 696 19.e even 9 1
855.2.cn.a ✓ 696 45.j even 6 1
855.2.cn.a ✓ 696 95.p even 18 1
855.2.dc.a yes 696 1.a even 1 1 trivial
855.2.dc.a yes 696 5.b even 2 1 inner
855.2.dc.a yes 696 171.v even 9 1 inner
855.2.dc.a yes 696 855.dc even 18 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(855, [\chi])\).