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Properties

Label 927.2.bh.a
Level $927$
Weight $2$
Character orbit 927.bh
Analytic conductor $7.402$
Analytic rank $0$
Dimension $1088$
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] = [927,2,Mod(35,927)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(927, base_ring=CyclotomicField(102))
 
chi = DirichletCharacter(H, H._module([51, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("927.35");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 927 = 3^{2} \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 927.bh (of order \(102\), degree \(32\), 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: \(7.40213226737\)
Analytic rank: \(0\)
Dimension: \(1088\)
Relative dimension: \(34\) over \(\Q(\zeta_{102})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{102}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 1088 q - 32 q^{4} - 6 q^{7}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 1088 q - 32 q^{4} - 6 q^{7} + 136 q^{10} - 28 q^{13} + 44 q^{16} - 14 q^{19} + 154 q^{25} - 164 q^{28} - 180 q^{34} - 72 q^{40} - 18 q^{43} + 12 q^{49} + 12 q^{52} + 4 q^{55} + 156 q^{58} - 16 q^{61} + 284 q^{64} - 36 q^{67} + 24 q^{70} - 204 q^{73} - 160 q^{76} - 60 q^{79} - 140 q^{82} - 76 q^{85} - 784 q^{88} + 312 q^{91} - 272 q^{94} - 86 q^{97}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
35.1 −1.29903 + 2.41910i 0 −3.05985 − 4.61778i 0.588148 − 3.78891i 0 −0.999592 − 0.707597i 9.67750 − 0.896753i 0 8.40175 + 6.34471i
35.2 −1.26806 + 2.36143i 0 −2.86363 − 4.32165i −0.312806 + 2.01513i 0 0.824185 + 0.583429i 8.49867 − 0.787517i 0 −4.36193 − 3.29397i
35.3 −1.16887 + 2.17671i 0 −2.26707 − 3.42135i 0.593047 − 3.82047i 0 0.485765 + 0.343866i 5.17688 − 0.479709i 0 7.62285 + 5.75651i
35.4 −1.11859 + 2.08307i 0 −1.98322 − 2.99298i −0.0343217 + 0.221104i 0 3.86533 + 2.73621i 3.74436 − 0.346966i 0 −0.422183 − 0.318818i
35.5 −1.04211 + 1.94066i 0 −1.57542 − 2.37755i −0.366576 + 2.36152i 0 −2.61564 − 1.85157i 1.86906 − 0.173194i 0 −4.20089 − 3.17237i
35.6 −1.00483 + 1.87123i 0 −1.38709 − 2.09333i 0.182842 − 1.17789i 0 2.20692 + 1.56225i 1.08111 − 0.100180i 0 2.02038 + 1.52572i
35.7 −0.875733 + 1.63082i 0 −0.787941 − 1.18912i 0.221700 − 1.42821i 0 −0.0878822 − 0.0622105i −1.05709 + 0.0979538i 0 2.13501 + 1.61229i
35.8 −0.857676 + 1.59720i 0 −0.710696 − 1.07255i −0.427017 + 2.75089i 0 −2.09174 − 1.48071i −1.28774 + 0.119326i 0 −4.02747 − 3.04140i
35.9 −0.660074 + 1.22921i 0 0.0294596 + 0.0444590i −0.00141038 + 0.00908580i 0 −1.33920 − 0.947999i −2.85265 + 0.264337i 0 −0.0102374 − 0.00773096i
35.10 −0.639606 + 1.19110i 0 0.0951117 + 0.143538i 0.588869 − 3.79356i 0 −3.10463 − 2.19773i −2.92420 + 0.270967i 0 4.14186 + 3.12778i
35.11 −0.510492 + 0.950656i 0 0.461584 + 0.696600i −0.292845 + 1.88654i 0 0.550203 + 0.389481i −3.04676 + 0.282324i 0 −1.64395 − 1.24146i
35.12 −0.438414 + 0.816431i 0 0.630377 + 0.951334i −0.569383 + 3.66803i 0 2.33321 + 1.65165i −2.89855 + 0.268590i 0 −2.74507 − 2.07298i
35.13 −0.378030 + 0.703981i 0 0.752048 + 1.13495i 0.586684 − 3.77948i 0 1.82473 + 1.29170i −2.67458 + 0.247837i 0 2.43890 + 1.84177i
35.14 −0.356715 + 0.664288i 0 0.790697 + 1.19328i 0.0397188 − 0.255873i 0 3.12602 + 2.21286i −2.57631 + 0.238731i 0 0.155805 + 0.117658i
35.15 −0.223957 + 0.417061i 0 0.980947 + 1.48040i 0.0676516 − 0.435819i 0 −3.23857 − 2.29254i −1.77984 + 0.164927i 0 0.166612 + 0.125819i
35.16 −0.207101 + 0.385672i 0 0.998878 + 1.50746i 0.0226080 − 0.145643i 0 −2.50222 − 1.77129i −1.66004 + 0.153825i 0 0.0514884 + 0.0388822i
35.17 −0.137627 + 0.256295i 0 1.05798 + 1.59666i −0.439578 + 2.83181i 0 0.711815 + 0.503884i −1.13416 + 0.105095i 0 −0.665280 − 0.502396i
35.18 0.137627 − 0.256295i 0 1.05798 + 1.59666i 0.439578 − 2.83181i 0 0.711815 + 0.503884i 1.13416 − 0.105095i 0 −0.665280 − 0.502396i
35.19 0.207101 − 0.385672i 0 0.998878 + 1.50746i −0.0226080 + 0.145643i 0 −2.50222 − 1.77129i 1.66004 − 0.153825i 0 0.0514884 + 0.0388822i
35.20 0.223957 − 0.417061i 0 0.980947 + 1.48040i −0.0676516 + 0.435819i 0 −3.23857 − 2.29254i 1.77984 − 0.164927i 0 0.166612 + 0.125819i
See next 80 embeddings (of 1088 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 35.34
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
103.h odd 102 1 inner
309.o even 102 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 927.2.bh.a ✓ 1088
3.b odd 2 1 inner 927.2.bh.a ✓ 1088
103.h odd 102 1 inner 927.2.bh.a ✓ 1088
309.o even 102 1 inner 927.2.bh.a ✓ 1088
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
927.2.bh.a ✓ 1088 1.a even 1 1 trivial
927.2.bh.a ✓ 1088 3.b odd 2 1 inner
927.2.bh.a ✓ 1088 103.h odd 102 1 inner
927.2.bh.a ✓ 1088 309.o even 102 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(927, [\chi])\).