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Properties

Label 891.2.v.a
Level $891$
Weight $2$
Character orbit 891.v
Analytic conductor $7.115$
Analytic rank $0$
Dimension $816$
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] = [891,2,Mod(37,891)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(891, base_ring=CyclotomicField(90))
 
chi = DirichletCharacter(H, H._module([70, 18]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("891.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 891 = 3^{4} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 891.v (of order \(45\), degree \(24\), not 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: \(7.11467082010\)
Analytic rank: \(0\)
Dimension: \(816\)
Relative dimension: \(34\) over \(\Q(\zeta_{45})\)
Twist minimal: no (minimal twist has level 297)
Sato-Tate group: $\mathrm{SU}(2)[C_{45}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 816 q + 18 q^{2} - 18 q^{4} + 21 q^{5} - 18 q^{7} + 27 q^{8}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 816 q + 18 q^{2} - 18 q^{4} + 21 q^{5} - 18 q^{7} + 27 q^{8} - 24 q^{10} + 33 q^{11} - 18 q^{13} + 18 q^{14} - 30 q^{16} + 33 q^{17} - 9 q^{19} - 24 q^{20} - 33 q^{22} + 12 q^{23} - 27 q^{25} + 36 q^{26} - 36 q^{28} + 72 q^{29} - 27 q^{31} + 72 q^{32} - 78 q^{34} + 57 q^{35} - 9 q^{37} - 6 q^{38} - 12 q^{40} + 60 q^{41} - 66 q^{43} - 12 q^{44} - 9 q^{46} + 30 q^{47} - 18 q^{49} + 21 q^{50} + 6 q^{52} + 96 q^{53} - 48 q^{55} - 102 q^{56} - 18 q^{58} + 177 q^{59} - 18 q^{61} - 9 q^{62} + 51 q^{64} - 48 q^{65} - 138 q^{67} - 159 q^{68} + 33 q^{70} + 9 q^{71} - 9 q^{73} - 66 q^{74} + 36 q^{76} - 75 q^{77} + 54 q^{79} + 72 q^{80} - 36 q^{82} + 51 q^{83} + 24 q^{85} - 93 q^{86} + 66 q^{89} - 9 q^{91} - 24 q^{92} - 18 q^{94} - 24 q^{95} + 81 q^{97} - 216 q^{98}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
37.1 −2.74023 + 0.191616i 0 5.49162 − 0.771796i 0.144399 − 0.214080i 0 −2.45668 + 1.30624i −9.52662 + 2.02495i 0 −0.354665 + 0.614297i
37.2 −2.52782 + 0.176762i 0 4.37809 − 0.615300i 2.22430 − 3.29766i 0 −1.56704 + 0.833208i −6.00102 + 1.27556i 0 −5.03973 + 8.72907i
37.3 −2.52170 + 0.176335i 0 4.34735 − 0.610980i −1.10153 + 1.63309i 0 −1.70717 + 0.907720i −5.90975 + 1.25616i 0 2.48977 − 4.31241i
37.4 −2.33937 + 0.163584i 0 3.46533 − 0.487021i 0.501724 − 0.743836i 0 3.33947 − 1.77563i −3.43935 + 0.731056i 0 −1.05203 + 1.82218i
37.5 −2.12697 + 0.148732i 0 2.52135 − 0.354353i 0.856748 − 1.27018i 0 1.44365 − 0.767605i −1.13900 + 0.242102i 0 −1.63336 + 2.82907i
37.6 −1.90693 + 0.133346i 0 1.63808 − 0.230217i −1.60717 + 2.38273i 0 −2.89769 + 1.54073i 0.646625 − 0.137444i 0 2.74704 − 4.75802i
37.7 −1.86573 + 0.130464i 0 1.48338 − 0.208475i −0.500856 + 0.742549i 0 0.389922 − 0.207325i 0.918445 − 0.195222i 0 0.837583 − 1.45074i
37.8 −1.80934 + 0.126521i 0 1.27715 − 0.179492i −2.43672 + 3.61259i 0 3.23064 − 1.71776i 1.26015 − 0.267853i 0 3.95178 − 6.84468i
37.9 −1.59990 + 0.111876i 0 0.566623 − 0.0796337i 2.10202 − 3.11637i 0 −1.20004 + 0.638071i 2.23989 − 0.476102i 0 −3.01437 + 5.22105i
37.10 −1.44676 + 0.101168i 0 0.102356 − 0.0143851i 0.727232 − 1.07817i 0 3.70974 − 1.97250i 2.69058 − 0.571900i 0 −0.943058 + 1.63342i
37.11 −1.32173 + 0.0924243i 0 −0.242109 + 0.0340262i 0.293572 − 0.435239i 0 −3.64313 + 1.93709i 2.90887 − 0.618298i 0 −0.347797 + 0.602402i
37.12 −1.01688 + 0.0711070i 0 −0.951552 + 0.133732i −0.941946 + 1.39649i 0 1.89328 − 1.00667i 2.95227 − 0.627525i 0 0.858544 − 1.48704i
37.13 −0.679268 + 0.0474990i 0 −1.52139 + 0.213817i 1.93669 − 2.87126i 0 −1.75831 + 0.934911i 2.35537 − 0.500649i 0 −1.17915 + 2.04234i
37.14 −0.624067 + 0.0436390i 0 −1.59298 + 0.223879i −1.50338 + 2.22885i 0 0.335077 − 0.178164i 2.20820 − 0.469367i 0 0.840944 − 1.45656i
37.15 −0.426836 + 0.0298473i 0 −1.79924 + 0.252866i 0.0610138 − 0.0904566i 0 −1.13700 + 0.604556i 1.59749 − 0.339557i 0 −0.0233430 + 0.0404312i
37.16 −0.347449 + 0.0242960i 0 −1.86041 + 0.261463i −0.684329 + 1.01456i 0 1.48131 − 0.787624i 1.32142 − 0.280876i 0 0.213120 − 0.369134i
37.17 −0.111910 + 0.00782552i 0 −1.96807 + 0.276595i 0.545661 − 0.808975i 0 −4.08703 + 2.17311i 0.437547 − 0.0930034i 0 −0.0547343 + 0.0948026i
37.18 0.120434 − 0.00842154i 0 −1.96610 + 0.276318i 2.34157 − 3.47152i 0 3.07773 − 1.63646i −0.470637 + 0.100037i 0 0.252768 − 0.437807i
37.19 0.263917 − 0.0184548i 0 −1.91122 + 0.268605i 1.05480 − 1.56381i 0 0.785027 − 0.417406i −1.01701 + 0.216171i 0 0.249519 − 0.432180i
37.20 0.574262 − 0.0401563i 0 −1.65237 + 0.232226i −1.66152 + 2.46330i 0 −0.0708845 + 0.0376900i −2.06574 + 0.439086i 0 −0.855227 + 1.48130i
See next 80 embeddings (of 816 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 37.34
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
11.c even 5 1 inner
27.e even 9 1 inner
297.u even 45 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 891.2.v.a 816
3.b odd 2 1 297.2.u.a ✓ 816
11.c even 5 1 inner 891.2.v.a 816
27.e even 9 1 inner 891.2.v.a 816
27.f odd 18 1 297.2.u.a ✓ 816
33.h odd 10 1 297.2.u.a ✓ 816
297.u even 45 1 inner 891.2.v.a 816
297.v odd 90 1 297.2.u.a ✓ 816
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
297.2.u.a ✓ 816 3.b odd 2 1
297.2.u.a ✓ 816 27.f odd 18 1
297.2.u.a ✓ 816 33.h odd 10 1
297.2.u.a ✓ 816 297.v odd 90 1
891.2.v.a 816 1.a even 1 1 trivial
891.2.v.a 816 11.c even 5 1 inner
891.2.v.a 816 27.e even 9 1 inner
891.2.v.a 816 297.u even 45 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(891, [\chi])\).