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Properties

Label 855.2.ci.a
Level $855$
Weight $2$
Character orbit 855.ci
Analytic conductor $6.827$
Analytic rank $0$
Dimension $464$
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(182,855)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(855, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([2, 3, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("855.182");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 855.ci (of order \(12\), 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: \(6.82720937282\)
Analytic rank: \(0\)
Dimension: \(464\)
Relative dimension: \(116\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 464 q - 6 q^{2} - 2 q^{3} - 4 q^{6} - 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 464 q - 6 q^{2} - 2 q^{3} - 4 q^{6} - 4 q^{7} - 4 q^{10} - 24 q^{11} + 2 q^{12} + 2 q^{13} + 10 q^{15} + 212 q^{16} + 18 q^{17} - 24 q^{18} - 12 q^{20} - 4 q^{21} - 20 q^{22} + 18 q^{23} - 4 q^{25} - 2 q^{27} - 20 q^{28} + 2 q^{30} - 8 q^{31} - 30 q^{32} + 10 q^{33} - 68 q^{36} - 16 q^{37} + 30 q^{38} - 36 q^{40} - 14 q^{42} + 2 q^{43} + 6 q^{45} - 56 q^{46} + 42 q^{48} - 108 q^{50} + 12 q^{51} - 34 q^{52} - 14 q^{55} - 24 q^{56} - 78 q^{57} - 12 q^{58} - 42 q^{60} - 8 q^{61} - 12 q^{62} + 92 q^{63} - 84 q^{65} - 52 q^{66} + 2 q^{67} - 60 q^{68} - 84 q^{70} - 118 q^{72} - 4 q^{73} + 98 q^{75} - 60 q^{76} - 12 q^{77} + 92 q^{78} + 120 q^{80} - 12 q^{81} + 4 q^{82} - 12 q^{83} + 2 q^{85} - 264 q^{86} + 102 q^{87} + 48 q^{88} - 34 q^{90} - 8 q^{91} + 54 q^{92} - 52 q^{93} - 36 q^{95} + 96 q^{96} + 2 q^{97} + 42 q^{98}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
182.1 −2.70052 − 0.723603i 1.70366 − 0.312339i 5.03717 + 2.90821i −2.07206 − 0.840570i −4.82677 − 0.389291i 2.14621 − 0.575074i −7.54477 − 7.54477i 2.80489 − 1.06424i 4.98741 + 3.76933i
182.2 −2.64907 − 0.709817i −1.67832 + 0.428065i 4.78169 + 2.76071i 1.47253 − 1.68275i 4.74984 + 0.0573243i 3.03796 − 0.814018i −6.82893 − 6.82893i 2.63352 − 1.43686i −5.09528 + 3.41250i
182.3 −2.63630 − 0.706393i −1.21340 − 1.23598i 4.71901 + 2.72452i 1.52807 + 1.63249i 2.32580 + 4.11556i −1.07631 + 0.288396i −6.65633 − 6.65633i −0.0553068 + 2.99949i −2.87526 − 5.38313i
182.4 −2.56255 − 0.686633i 1.63233 + 0.579224i 4.36315 + 2.51907i 2.07118 − 0.842734i −3.78521 − 2.60510i −0.701876 + 0.188067i −5.69928 − 5.69928i 2.32900 + 1.89097i −5.88616 + 0.737405i
182.5 −2.55473 − 0.684539i 0.721089 + 1.57481i 4.32602 + 2.49763i −1.88291 + 1.20609i −0.764171 − 4.51684i −3.99747 + 1.07112i −5.60173 − 5.60173i −1.96006 + 2.27116i 5.63595 − 1.79233i
182.6 −2.51258 − 0.673244i −0.200386 − 1.72042i 4.12775 + 2.38316i −2.14878 + 0.618674i −0.654775 + 4.45760i −0.809553 + 0.216919i −5.08819 − 5.08819i −2.91969 + 0.689498i 5.81549 − 0.107817i
182.7 −2.49445 − 0.668387i −0.535609 + 1.64716i 4.04351 + 2.33452i 2.17188 + 0.531926i 2.43699 − 3.75076i −2.77687 + 0.744061i −4.87385 − 4.87385i −2.42625 − 1.76446i −5.06212 − 2.77852i
182.8 −2.40979 − 0.645700i −0.659782 + 1.60146i 3.65809 + 2.11200i −0.119609 + 2.23287i 2.62400 − 3.43317i 3.38143 − 0.906053i −3.92333 − 3.92333i −2.12937 − 2.11323i 1.72999 − 5.30350i
182.9 −2.38103 − 0.637995i −1.70423 − 0.309196i 3.53022 + 2.03817i −1.30158 − 1.81821i 3.86056 + 1.82350i −4.79769 + 1.28554i −3.61914 − 3.61914i 2.80880 + 1.05388i 1.93908 + 5.15962i
182.10 −2.36887 − 0.634736i 0.925734 − 1.46390i 3.47659 + 2.00721i 1.58102 − 1.58126i −3.12213 + 2.88020i −3.25666 + 0.872620i −3.49327 − 3.49327i −1.28603 − 2.71037i −4.74891 + 2.74226i
182.11 −2.34685 − 0.628836i 0.712618 + 1.57866i 3.38021 + 1.95157i −0.554835 − 2.16614i −0.679687 − 4.15300i 2.47049 − 0.661967i −3.26960 − 3.26960i −1.98435 + 2.24997i −0.0600336 + 5.43250i
182.12 −2.32431 − 0.622797i 0.246529 − 1.71442i 3.28249 + 1.89515i −0.132181 − 2.23216i −1.64074 + 3.83130i 1.22539 − 0.328341i −3.04621 − 3.04621i −2.87845 − 0.845307i −1.08295 + 5.27055i
182.13 −2.30747 − 0.618286i −1.18916 + 1.25932i 3.21011 + 1.85336i −2.04227 − 0.910568i 3.52258 − 2.17061i 0.475464 − 0.127400i −2.88296 − 2.88296i −0.171788 − 2.99508i 4.14949 + 3.36382i
182.14 −2.27720 − 0.610173i 1.09806 − 1.33950i 3.08126 + 1.77897i −0.234541 + 2.22373i −3.31782 + 2.38031i 3.31665 − 0.888694i −2.59711 − 2.59711i −0.588539 − 2.94170i 1.89096 − 4.92077i
182.15 −2.14510 − 0.574778i −1.63225 − 0.579449i 2.53904 + 1.46592i −1.44202 + 1.70897i 3.16829 + 2.18116i 2.12013 − 0.568087i −1.46328 − 1.46328i 2.32848 + 1.89161i 4.07556 − 2.83707i
182.16 −2.08526 − 0.558744i −0.369684 − 1.69214i 2.30406 + 1.33025i 2.11340 + 0.730453i −0.174586 + 3.73511i 3.19584 − 0.856322i −1.00827 − 1.00827i −2.72667 + 1.25111i −3.99884 − 2.70403i
182.17 −2.03938 − 0.546450i −1.70698 + 0.293642i 2.12841 + 1.22884i 0.568747 + 2.16253i 3.64164 + 0.333930i −3.03698 + 0.813757i −0.683274 − 0.683274i 2.82755 − 1.00248i 0.0218223 − 4.72101i
182.18 −2.03110 − 0.544232i 1.67740 + 0.431656i 2.09713 + 1.21078i 1.01851 + 1.99064i −3.17205 − 1.78963i −1.44077 + 0.386053i −0.626809 − 0.626809i 2.62735 + 1.44812i −0.985324 − 4.59749i
182.19 −2.03096 − 0.544195i 1.67937 − 0.423924i 2.09661 + 1.21048i −1.48407 + 1.67258i −3.64144 − 0.0529320i −3.29647 + 0.883287i −0.625861 − 0.625861i 2.64058 − 1.42385i 3.92430 − 2.58933i
182.20 −2.02250 − 0.541927i 1.67116 − 0.455213i 2.06477 + 1.19209i 2.16372 − 0.564195i −3.62661 + 0.0150195i 3.00968 − 0.806442i −0.568816 − 0.568816i 2.58556 − 1.52147i −4.68187 − 0.0314942i
See next 80 embeddings (of 464 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 182.116
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.c odd 4 1 inner
171.n odd 6 1 inner
855.ci even 12 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 855.2.ci.a yes 464
5.c odd 4 1 inner 855.2.ci.a yes 464
9.d odd 6 1 855.2.bx.a ✓ 464
19.c even 3 1 855.2.bx.a ✓ 464
45.l even 12 1 855.2.bx.a ✓ 464
95.m odd 12 1 855.2.bx.a ✓ 464
171.n odd 6 1 inner 855.2.ci.a yes 464
855.ci even 12 1 inner 855.2.ci.a yes 464
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
855.2.bx.a ✓ 464 9.d odd 6 1
855.2.bx.a ✓ 464 19.c even 3 1
855.2.bx.a ✓ 464 45.l even 12 1
855.2.bx.a ✓ 464 95.m odd 12 1
855.2.ci.a yes 464 1.a even 1 1 trivial
855.2.ci.a yes 464 5.c odd 4 1 inner
855.2.ci.a yes 464 171.n odd 6 1 inner
855.2.ci.a yes 464 855.ci even 12 1 inner

Hecke kernels

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