Properties

Label 855.2.dm.a
Level $855$
Weight $2$
Character orbit 855.dm
Analytic conductor $6.827$
Analytic rank $0$
Dimension $1392$
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(23,855)]
 
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([30, 27, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("855.23");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 855.dm (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: \(1392\)
Relative dimension: \(116\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 1392 q - 18 q^{2} - 12 q^{3} - 18 q^{5} - 24 q^{6} - 12 q^{7}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 1392 q - 18 q^{2} - 12 q^{3} - 18 q^{5} - 24 q^{6} - 12 q^{7} - 24 q^{10} - 36 q^{11} - 6 q^{12} - 6 q^{13} + 6 q^{15} - 12 q^{16} + 54 q^{17} - 48 q^{18} - 36 q^{20} - 24 q^{21} - 30 q^{22} - 18 q^{23} - 6 q^{25} - 144 q^{26} - 6 q^{27} - 6 q^{30} + 12 q^{31} + 54 q^{32} + 6 q^{33} - 24 q^{36} - 48 q^{37} - 18 q^{38} - 6 q^{40} - 36 q^{41} - 84 q^{42} - 6 q^{43} + 12 q^{45} - 24 q^{46} - 18 q^{47} - 30 q^{48} - 162 q^{50} - 72 q^{51} + 6 q^{52} + 6 q^{55} - 72 q^{56} - 90 q^{57} - 12 q^{58} - 84 q^{60} - 12 q^{61} + 36 q^{62} - 72 q^{63} - 18 q^{65} - 144 q^{66} - 6 q^{67} - 6 q^{70} + 96 q^{72} - 24 q^{73} - 192 q^{75} - 12 q^{76} - 36 q^{77} + 30 q^{78} + 252 q^{80} - 24 q^{82} - 6 q^{85} - 36 q^{86} + 42 q^{87} - 204 q^{88} - 168 q^{90} - 48 q^{91} - 234 q^{92} + 102 q^{93} - 18 q^{95} + 96 q^{96} - 6 q^{97} + 378 q^{98}+O(q^{100}) \) 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.

comment: embeddings in the coefficient field
 
gp: mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
23.1 −1.59218 + 2.27387i 1.72050 0.199721i −1.95139 5.36141i 0.349170 + 2.20864i −2.28520 + 4.23017i −0.906543 + 0.906543i 9.93551 + 2.66221i 2.92022 0.687238i −5.57808 2.72258i
23.2 −1.56831 + 2.23979i 1.06544 + 1.36559i −1.87299 5.14599i 0.136322 2.23191i −4.72958 + 0.244681i −0.497242 + 0.497242i 9.18115 + 2.46008i −0.729676 + 2.90991i 4.78520 + 3.80567i
23.3 −1.56629 + 2.23690i −0.759229 + 1.55678i −1.86640 5.12789i −2.19457 + 0.428784i −2.29319 4.13670i 1.04965 1.04965i 9.11850 + 2.44330i −1.84714 2.36391i 2.47820 5.58064i
23.4 −1.55563 + 2.22167i 0.173604 1.72333i −1.83179 5.03281i −2.23603 0.0130878i 3.55860 + 3.06655i 2.79066 2.79066i 8.79135 + 2.35564i −2.93972 0.598353i 3.50751 4.94736i
23.5 −1.52991 + 2.18494i −1.70742 0.291075i −1.74929 4.80612i 1.54920 + 1.61245i 3.24817 3.28528i 1.73999 1.73999i 8.02446 + 2.15015i 2.83055 + 0.993975i −5.89323 + 0.917997i
23.6 −1.52131 + 2.17265i −0.567477 1.63645i −1.72199 4.73114i 2.18223 0.487740i 4.41874 + 1.25661i −2.45590 + 2.45590i 7.77491 + 2.08328i −2.35594 + 1.85730i −2.26014 + 5.48321i
23.7 −1.50312 + 2.14667i −1.71871 0.214558i −1.66481 4.57402i −2.11765 0.718012i 3.04401 3.36700i −3.08170 + 3.08170i 7.25871 + 1.94497i 2.90793 + 0.737527i 4.72442 3.46666i
23.8 −1.43964 + 2.05602i 1.41154 1.00377i −1.47062 4.04050i 1.69445 1.45905i 0.0316545 + 4.34723i 3.00329 3.00329i 5.57569 + 1.49400i 0.984899 2.83372i 0.560430 + 5.58435i
23.9 −1.39379 + 1.99054i 1.30945 1.13373i −1.33556 3.66943i −0.411456 2.19789i 0.431635 + 4.18670i −1.73617 + 1.73617i 4.47124 + 1.19807i 0.429315 2.96912i 4.94847 + 2.24438i
23.10 −1.38197 + 1.97366i 0.494643 + 1.65992i −1.30144 3.57568i 1.86774 + 1.22945i −3.95969 1.31770i 3.08858 3.08858i 4.20114 + 1.12569i −2.51066 + 1.64214i −5.00767 + 1.98722i
23.11 −1.35498 + 1.93512i −1.21999 + 1.22948i −1.22466 3.36472i 0.0895790 + 2.23427i −0.726112 4.02676i −2.22451 + 2.22451i 3.60684 + 0.966449i −0.0232303 2.99991i −4.44496 2.85406i
23.12 −1.33479 + 1.90628i −1.37861 + 1.04854i −1.16820 3.20959i 1.60441 1.55752i −0.158641 4.02760i −1.89917 + 1.89917i 3.18200 + 0.852615i 0.801148 2.89105i 0.827521 + 5.13742i
23.13 −1.32656 + 1.89453i 1.36695 + 1.06369i −1.14543 3.14704i −1.71105 + 1.43955i −3.82854 + 1.17868i 1.25759 1.25759i 3.01366 + 0.807508i 0.737120 + 2.90803i −0.457458 5.15129i
23.14 −1.30398 + 1.86227i −0.278008 + 1.70959i −1.08366 2.97734i −0.802200 2.08722i −2.82121 2.74700i 0.0328215 0.0328215i 2.56579 + 0.687500i −2.84542 0.950560i 4.93302 + 1.22777i
23.15 −1.27465 + 1.82039i 0.514103 1.65399i −1.00504 2.76132i −1.41493 + 1.73147i 2.35561 + 3.04413i −2.97934 + 2.97934i 2.01462 + 0.539816i −2.47140 1.70065i −1.34840 4.78273i
23.16 −1.27321 + 1.81834i −0.671321 1.59666i −1.00124 2.75089i −1.34077 1.78951i 3.75801 + 0.812204i −0.0538499 + 0.0538499i 1.98855 + 0.532830i −2.09866 + 2.14374i 4.96102 0.159555i
23.17 −1.26950 + 1.81303i −1.51913 0.832010i −0.991417 2.72390i −1.47644 + 1.67932i 3.43700 1.69800i 0.703811 0.703811i 1.92134 + 0.514822i 1.61552 + 2.52787i −1.17033 4.80873i
23.18 −1.25732 + 1.79565i 1.55144 + 0.770089i −0.959438 2.63604i 2.08904 0.797428i −3.33347 + 1.81758i −0.518266 + 0.518266i 1.70494 + 0.456838i 1.81393 + 2.38949i −1.19471 + 4.75381i
23.19 −1.22192 + 1.74508i −0.146112 + 1.72588i −0.868180 2.38531i 0.636498 + 2.14356i −2.83326 2.36386i −1.26059 + 1.26059i 1.10787 + 0.296854i −2.95730 0.504343i −4.51844 1.50852i
23.20 −1.20798 + 1.72518i 1.17981 + 1.26809i −0.832974 2.28858i −2.23348 + 0.107608i −3.61286 + 0.503553i −3.54890 + 3.54890i 0.885837 + 0.237359i −0.216097 + 2.99221i 2.51236 3.98313i
See next 80 embeddings (of 1392 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 23.116
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.c odd 4 1 inner
171.bf odd 18 1 inner
855.dm 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.dm.a yes 1392
5.c odd 4 1 inner 855.2.dm.a yes 1392
9.d odd 6 1 855.2.dh.a 1392
19.e even 9 1 855.2.dh.a 1392
45.l even 12 1 855.2.dh.a 1392
95.q odd 36 1 855.2.dh.a 1392
171.bf odd 18 1 inner 855.2.dm.a yes 1392
855.dm even 36 1 inner 855.2.dm.a yes 1392
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
855.2.dh.a 1392 9.d odd 6 1
855.2.dh.a 1392 19.e even 9 1
855.2.dh.a 1392 45.l even 12 1
855.2.dh.a 1392 95.q odd 36 1
855.2.dm.a yes 1392 1.a even 1 1 trivial
855.2.dm.a yes 1392 5.c odd 4 1 inner
855.2.dm.a yes 1392 171.bf odd 18 1 inner
855.2.dm.a yes 1392 855.dm even 36 1 inner

Hecke kernels

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