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Properties

Label 833.2.k.c
Level $833$
Weight $2$
Character orbit 833.k
Analytic conductor $6.652$
Analytic rank $0$
Dimension $234$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [833,2,Mod(120,833)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(833, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([8, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("833.120");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 833 = 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 833.k (of order \(7\), degree \(6\), 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: \(6.65153848837\)
Analytic rank: \(0\)
Dimension: \(234\)
Relative dimension: \(39\) over \(\Q(\zeta_{7})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{7}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 234 q + q^{2} - 7 q^{3} - 39 q^{4} + 2 q^{5} + 7 q^{6} - 13 q^{7} - 23 q^{8} - 42 q^{9} + 21 q^{10} - 7 q^{11} + q^{12} - 15 q^{13} - 22 q^{14} + 36 q^{15} - 55 q^{16} - 39 q^{17} + 62 q^{18} - 4 q^{19}+ \cdots + 72 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
120.1 −2.50182 + 1.20481i −0.171341 + 0.750694i 3.56055 − 4.46478i 0.877681 − 3.84537i −0.475782 − 2.08454i 0.315183 + 2.62691i −2.29282 + 10.0455i 2.16872 + 1.04440i 2.43715 + 10.6779i
120.2 −2.43956 + 1.17483i −0.760566 + 3.33226i 3.32426 − 4.16849i −0.286235 + 1.25408i −2.05939 − 9.02278i 2.05845 − 1.66216i −2.00742 + 8.79508i −7.82256 − 3.76715i −0.775040 − 3.39567i
120.3 −2.37785 + 1.14511i 0.690513 − 3.02534i 3.09592 − 3.88216i −0.837852 + 3.67087i 1.82241 + 7.98452i 2.27520 − 1.35035i −1.74156 + 7.63029i −5.97295 − 2.87642i −2.21127 − 9.68822i
120.4 −2.37198 + 1.14228i 0.0745220 − 0.326502i 3.07448 − 3.85528i 0.126569 − 0.554535i 0.196194 + 0.859581i 2.08018 − 1.63489i −1.71712 + 7.52319i 2.60186 + 1.25299i 0.333218 + 1.45992i
120.5 −2.26588 + 1.09119i 0.619080 − 2.71237i 2.69652 − 3.38133i 0.778175 − 3.40941i 1.55694 + 6.82142i −1.62207 − 2.09019i −1.30107 + 5.70034i −4.27077 − 2.05669i 1.95706 + 8.57443i
120.6 −2.09590 + 1.00933i −0.366696 + 1.60660i 2.12706 − 2.66725i −0.829036 + 3.63224i −0.853033 − 3.73738i −2.52695 + 0.783922i −0.730672 + 3.20128i 0.256213 + 0.123386i −1.92856 − 8.44958i
120.7 −1.89747 + 0.913774i −0.429516 + 1.88183i 1.51844 − 1.90406i −0.158555 + 0.694674i −0.904575 − 3.96320i 1.77019 + 1.96633i −0.204037 + 0.893943i −0.653899 − 0.314901i −0.333922 − 1.46301i
120.8 −1.87670 + 0.903770i 0.219850 − 0.963228i 1.45822 − 1.82855i 0.469031 − 2.05496i 0.457944 + 2.00638i −2.41920 + 1.07119i −0.157035 + 0.688016i 1.82343 + 0.878119i 0.976982 + 4.28044i
120.9 −1.84959 + 0.890715i 0.302495 − 1.32532i 1.38063 − 1.73125i −0.656828 + 2.87775i 0.620989 + 2.72073i 0.0701726 + 2.64482i −0.0979182 + 0.429007i 1.03794 + 0.499847i −1.34840 − 5.90771i
120.10 −1.52554 + 0.734659i −0.245038 + 1.07358i 0.540556 − 0.677835i 0.390090 − 1.70910i −0.414902 − 1.81780i −2.19439 − 1.47806i 0.426894 − 1.87034i 1.61038 + 0.775517i 0.660507 + 2.89387i
120.11 −1.47390 + 0.709793i −0.503806 + 2.20732i 0.421595 − 0.528664i −0.472460 + 2.06998i −0.824180 − 3.61097i 0.428847 − 2.61076i 0.481899 − 2.11134i −1.91554 − 0.922474i −0.772900 − 3.38630i
120.12 −1.43433 + 0.690739i 0.146861 − 0.643439i 0.333216 − 0.417840i 0.0319535 − 0.139998i 0.233801 + 1.02435i 0.161382 − 2.64082i 0.519178 − 2.27467i 2.31046 + 1.11266i 0.0508698 + 0.222875i
120.13 −1.26981 + 0.611506i −0.685266 + 3.00235i −0.00851313 + 0.0106751i 0.695947 − 3.04914i −0.965799 − 4.23144i −1.96917 + 1.76703i 0.631514 − 2.76684i −5.84159 − 2.81316i 0.980852 + 4.29739i
120.14 −1.12739 + 0.542922i 0.534232 − 2.34063i −0.270739 + 0.339496i −0.192389 + 0.842913i 0.668489 + 2.92884i 2.56882 − 0.633388i 0.677792 − 2.96960i −2.49022 − 1.19922i −0.240738 − 1.05474i
120.15 −0.673989 + 0.324576i 0.377036 − 1.65190i −0.898068 + 1.12614i −0.915531 + 4.01120i 0.282050 + 1.23574i −2.46973 − 0.948900i 0.572693 − 2.50913i 0.116275 + 0.0559949i −0.684882 − 3.00067i
120.16 −0.594110 + 0.286108i 0.427979 − 1.87510i −0.975871 + 1.22370i −0.0308663 + 0.135234i 0.282214 + 1.23646i −2.18951 + 1.48527i 0.523129 − 2.29198i −0.629919 − 0.303353i −0.0203536 − 0.0891751i
120.17 −0.537156 + 0.258681i −0.382965 + 1.67788i −1.02536 + 1.28576i 0.472733 − 2.07118i −0.228323 − 1.00035i −0.280380 + 2.63085i 0.483510 − 2.11840i 0.0342871 + 0.0165118i 0.281843 + 1.23483i
120.18 −0.165953 + 0.0799190i −0.539573 + 2.36403i −1.22583 + 1.53714i −0.385039 + 1.68696i −0.0993864 − 0.435440i −2.64115 − 0.155956i 0.162558 − 0.712213i −2.59457 − 1.24948i −0.0709220 − 0.310729i
120.19 −0.133811 + 0.0644401i −0.0351422 + 0.153968i −1.23323 + 1.54642i −0.364104 + 1.59524i −0.00521929 − 0.0228672i 0.812254 − 2.51798i 0.131466 − 0.575988i 2.68044 + 1.29083i −0.0540764 − 0.236924i
120.20 0.209208 − 0.100749i −0.167779 + 0.735090i −1.21336 + 1.52151i −0.201636 + 0.883426i 0.0389590 + 0.170691i 1.33538 + 2.28403i −0.203895 + 0.893322i 2.19070 + 1.05499i 0.0468207 + 0.205135i
See next 80 embeddings (of 234 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 120.39
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
49.e even 7 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 833.2.k.c ✓ 234
49.e even 7 1 inner 833.2.k.c ✓ 234
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
833.2.k.c ✓ 234 1.a even 1 1 trivial
833.2.k.c ✓ 234 49.e even 7 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{234} - T_{2}^{233} + 59 T_{2}^{232} - 43 T_{2}^{231} + 1896 T_{2}^{230} - 1058 T_{2}^{229} + \cdots + 42\!\cdots\!61 \) acting on \(S_{2}^{\mathrm{new}}(833, [\chi])\). Copy content Toggle raw display