↑

Properties

Label 925.2.f.e
Level $925$
Weight $2$
Character orbit 925.f
Analytic conductor $7.386$
Analytic rank $0$
Dimension $28$
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [925,2,Mod(43,925)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(925, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("925.43");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 925 = 5^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 925.f (of order \(4\), degree \(2\), 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: \(7.38616218697\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(14\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 28 q - 36 q^{4} - 20 q^{14} + 12 q^{16} - 4 q^{19} + 4 q^{24} - 8 q^{26} - 12 q^{29} - 12 q^{31} + 12 q^{39} + 36 q^{51} - 16 q^{54} - 8 q^{56} - 4 q^{59} + 48 q^{61} + 92 q^{64} + 88 q^{66} + 28 q^{69}+ \cdots + 240 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
43.1 − 2.54912i 0.0578304 − 0.0578304i −4.49802 0 −0.147417 − 0.147417i 2.62099 − 2.62099i 6.36776i 2.99331i 0
43.2 − 2.32678i −1.90626 + 1.90626i −3.41392 0 4.43546 + 4.43546i −1.66625 + 1.66625i 3.28988i − 4.26769i 0
43.3 − 2.21947i 0.837300 − 0.837300i −2.92604 0 −1.85836 − 1.85836i −2.71073 + 2.71073i 2.05533i 1.59786i 0
43.4 − 1.95162i 2.31819 − 2.31819i −1.80883 0 −4.52423 − 4.52423i 2.88408 − 2.88408i − 0.373100i − 7.74804i 0
43.5 − 1.11789i −1.84398 + 1.84398i 0.750316 0 2.06138 + 2.06138i 3.21238 − 3.21238i − 3.07456i − 3.80055i 0
43.6 − 1.03074i 0.234013 − 0.234013i 0.937573 0 −0.241206 − 0.241206i −0.639240 + 0.639240i − 3.02788i 2.89048i 0
43.7 − 0.202680i −1.35377 + 1.35377i 1.95892 0 0.274381 + 0.274381i −1.72047 + 1.72047i − 0.802393i − 0.665378i 0
43.8 0.202680i 1.35377 − 1.35377i 1.95892 0 0.274381 + 0.274381i 1.72047 − 1.72047i 0.802393i − 0.665378i 0
43.9 1.03074i −0.234013 + 0.234013i 0.937573 0 −0.241206 − 0.241206i 0.639240 − 0.639240i 3.02788i 2.89048i 0
43.10 1.11789i 1.84398 − 1.84398i 0.750316 0 2.06138 + 2.06138i −3.21238 + 3.21238i 3.07456i − 3.80055i 0
43.11 1.95162i −2.31819 + 2.31819i −1.80883 0 −4.52423 − 4.52423i −2.88408 + 2.88408i 0.373100i − 7.74804i 0
43.12 2.21947i −0.837300 + 0.837300i −2.92604 0 −1.85836 − 1.85836i 2.71073 − 2.71073i − 2.05533i 1.59786i 0
43.13 2.32678i 1.90626 − 1.90626i −3.41392 0 4.43546 + 4.43546i 1.66625 − 1.66625i − 3.28988i − 4.26769i 0
43.14 2.54912i −0.0578304 + 0.0578304i −4.49802 0 −0.147417 − 0.147417i −2.62099 + 2.62099i − 6.36776i 2.99331i 0
882.1 − 2.54912i −0.0578304 − 0.0578304i −4.49802 0 −0.147417 + 0.147417i −2.62099 − 2.62099i 6.36776i − 2.99331i 0
882.2 − 2.32678i 1.90626 + 1.90626i −3.41392 0 4.43546 − 4.43546i 1.66625 + 1.66625i 3.28988i 4.26769i 0
882.3 − 2.21947i −0.837300 − 0.837300i −2.92604 0 −1.85836 + 1.85836i 2.71073 + 2.71073i 2.05533i − 1.59786i 0
882.4 − 1.95162i −2.31819 − 2.31819i −1.80883 0 −4.52423 + 4.52423i −2.88408 − 2.88408i − 0.373100i 7.74804i 0
882.5 − 1.11789i 1.84398 + 1.84398i 0.750316 0 2.06138 − 2.06138i −3.21238 − 3.21238i − 3.07456i 3.80055i 0
882.6 − 1.03074i −0.234013 − 0.234013i 0.937573 0 −0.241206 + 0.241206i 0.639240 + 0.639240i − 3.02788i − 2.89048i 0
See all 28 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 43.14
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner
185.f even 4 1 inner
185.k even 4 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 925.2.f.e ✓ 28
5.b even 2 1 inner 925.2.f.e ✓ 28
5.c odd 4 2 925.2.k.e yes 28
37.d odd 4 1 925.2.k.e yes 28
185.f even 4 1 inner 925.2.f.e ✓ 28
185.j odd 4 1 925.2.k.e yes 28
185.k even 4 1 inner 925.2.f.e ✓ 28
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
925.2.f.e ✓ 28 1.a even 1 1 trivial
925.2.f.e ✓ 28 5.b even 2 1 inner
925.2.f.e ✓ 28 185.f even 4 1 inner
925.2.f.e ✓ 28 185.k even 4 1 inner
925.2.k.e yes 28 5.c odd 4 2
925.2.k.e yes 28 37.d odd 4 1
925.2.k.e yes 28 185.j odd 4 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(925, [\chi])\):

\( T_{2}^{14} + 23T_{2}^{12} + 208T_{2}^{10} + 932T_{2}^{8} + 2135T_{2}^{6} + 2317T_{2}^{4} + 968T_{2}^{2} + 36 \) Copy content Toggle raw display
\( T_{3}^{28} + 230T_{3}^{24} + 17221T_{3}^{20} + 501936T_{3}^{16} + 4718812T_{3}^{12} + 7510232T_{3}^{8} + 89744T_{3}^{4} + 4 \) Copy content Toggle raw display