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Properties

Label 855.2.dn.a
Level $855$
Weight $2$
Character orbit 855.dn
Analytic conductor $6.827$
Analytic rank $0$
Dimension $480$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [855,2,Mod(17,855)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(855, base_ring=CyclotomicField(36))
 
chi = DirichletCharacter(H, H._module([18, 9, 20]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("855.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 855.dn (of order \(36\), degree \(12\), 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: \(480\)
Relative dimension: \(40\) over \(\Q(\zeta_{36})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 480 q+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 480 q + 120 q^{16} + 48 q^{22} - 48 q^{25} + 24 q^{43} - 192 q^{55} - 288 q^{58} - 48 q^{61} + 192 q^{67} - 96 q^{70} + 240 q^{76} + 144 q^{82} - 48 q^{85} - 96 q^{91} + 48 q^{97}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
17.1 −1.51687 − 2.16632i 0 −1.70800 + 4.69268i 1.30382 − 1.81660i 0 −0.333478 + 1.24456i 7.64771 − 2.04920i 0 −5.91308 − 0.0689427i
17.2 −1.50897 − 2.15503i 0 −1.68313 + 4.62435i −0.793097 + 2.09069i 0 −0.628220 + 2.34455i 7.42307 − 1.98901i 0 5.70226 − 1.44564i
17.3 −1.41893 − 2.02644i 0 −1.40906 + 3.87137i 1.24801 − 1.85539i 0 −0.212520 + 0.793137i 5.06539 − 1.35727i 0 −5.53068 + 0.103660i
17.4 −1.36179 − 1.94483i 0 −1.24387 + 3.41751i −1.83653 + 1.27560i 0 1.17647 − 4.39064i 3.75377 − 1.00582i 0 4.98179 + 1.83465i
17.5 −1.33008 − 1.89955i 0 −1.15514 + 3.17371i 1.87236 + 1.22240i 0 1.07848 − 4.02496i 3.08523 − 0.826685i 0 −0.168377 − 5.18253i
17.6 −1.28120 − 1.82975i 0 −1.02245 + 2.80916i −2.20659 − 0.361856i 0 −1.16077 + 4.33204i 2.13483 − 0.572025i 0 2.16499 + 4.50112i
17.7 −1.20080 − 1.71492i 0 −0.814982 + 2.23915i −1.84634 − 1.26136i 0 0.149356 − 0.557403i 0.774193 − 0.207444i 0 0.0539615 + 4.68095i
17.8 −1.06000 − 1.51384i 0 −0.484065 + 1.32996i 2.13829 + 0.653992i 0 −0.0957887 + 0.357488i −1.04372 + 0.279664i 0 −1.27656 − 3.93026i
17.9 −0.960827 − 1.37220i 0 −0.275713 + 0.757514i −0.123542 − 2.23265i 0 1.12714 − 4.20656i −1.93177 + 0.517615i 0 −2.94495 + 2.31472i
17.10 −0.913704 − 1.30490i 0 −0.183880 + 0.505207i 1.83927 + 1.27165i 0 −0.671757 + 2.50703i −2.25017 + 0.602931i 0 −0.0211704 − 3.56198i
17.11 −0.864188 − 1.23419i 0 −0.0923591 + 0.253754i −1.92397 + 1.13945i 0 0.163686 − 0.610883i −2.51766 + 0.674604i 0 3.06896 + 1.38985i
17.12 −0.740105 − 1.05698i 0 0.114590 − 0.314833i −0.865175 + 2.06191i 0 −0.198336 + 0.740198i −2.91031 + 0.779816i 0 2.81972 − 0.611558i
17.13 −0.674280 − 0.962971i 0 0.211380 − 0.580761i 1.42689 + 1.72162i 0 0.476310 − 1.77761i −2.97281 + 0.796563i 0 0.695745 − 2.53491i
17.14 −0.512845 − 0.732419i 0 0.410613 − 1.12815i −0.0916859 − 2.23419i 0 −0.492567 + 1.83828i −2.76416 + 0.740656i 0 −1.58934 + 1.21295i
17.15 −0.471016 − 0.672681i 0 0.453397 − 1.24570i −0.491070 − 2.18148i 0 −1.24570 + 4.64901i −2.63794 + 0.706833i 0 −1.23614 + 1.35785i
17.16 −0.321381 − 0.458979i 0 0.576664 − 1.58437i 2.04550 − 0.903296i 0 0.507440 − 1.89379i −1.99496 + 0.534547i 0 −1.07198 − 0.648538i
17.17 −0.264315 − 0.377481i 0 0.611411 − 1.67984i 2.17555 − 0.516698i 0 −1.14934 + 4.28939i −1.68595 + 0.451748i 0 −0.770075 − 0.684658i
17.18 −0.252822 − 0.361067i 0 0.617590 − 1.69681i −2.23484 − 0.0739883i 0 −0.127744 + 0.476749i −1.62033 + 0.434166i 0 0.538303 + 0.825634i
17.19 −0.211211 − 0.301640i 0 0.637664 − 1.75197i −0.727431 + 2.11444i 0 0.810305 − 3.02410i −1.37452 + 0.368301i 0 0.791440 − 0.227169i
17.20 −0.188899 − 0.269775i 0 0.646944 − 1.77746i −1.16498 − 1.90862i 0 0.827022 − 3.08649i −1.23795 + 0.331707i 0 −0.294835 + 0.674818i
See next 80 embeddings (of 480 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 17.40
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
5.c odd 4 1 inner
15.e even 4 1 inner
19.e even 9 1 inner
57.l odd 18 1 inner
95.q odd 36 1 inner
285.bi even 36 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 855.2.dn.a ✓ 480
3.b odd 2 1 inner 855.2.dn.a ✓ 480
5.c odd 4 1 inner 855.2.dn.a ✓ 480
15.e even 4 1 inner 855.2.dn.a ✓ 480
19.e even 9 1 inner 855.2.dn.a ✓ 480
57.l odd 18 1 inner 855.2.dn.a ✓ 480
95.q odd 36 1 inner 855.2.dn.a ✓ 480
285.bi even 36 1 inner 855.2.dn.a ✓ 480
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
855.2.dn.a ✓ 480 1.a even 1 1 trivial
855.2.dn.a ✓ 480 3.b odd 2 1 inner
855.2.dn.a ✓ 480 5.c odd 4 1 inner
855.2.dn.a ✓ 480 15.e even 4 1 inner
855.2.dn.a ✓ 480 19.e even 9 1 inner
855.2.dn.a ✓ 480 57.l odd 18 1 inner
855.2.dn.a ✓ 480 95.q odd 36 1 inner
855.2.dn.a ✓ 480 285.bi even 36 1 inner

Hecke kernels

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