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Properties

Label 435.3.t.a
Level $435$
Weight $3$
Character orbit 435.t
Analytic conductor $11.853$
Analytic rank $0$
Dimension $232$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [435,3,Mod(278,435)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(435, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3, 3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("435.278");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 435 = 3 \cdot 5 \cdot 29 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 435.t (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: \(11.8528914997\)
Analytic rank: \(0\)
Dimension: \(232\)
Relative dimension: \(116\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 232 q - 4 q^{3} + 448 q^{4} - 8 q^{7} - 32 q^{9} - 20 q^{10} - 56 q^{12} + 8 q^{13} + 22 q^{15} + 816 q^{16} - 32 q^{21} - 32 q^{22} - 8 q^{25} + 80 q^{27} - 32 q^{28} - 104 q^{30} + 8 q^{31} - 12 q^{33}+ \cdots - 180 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
278.1 −3.95364 −0.942097 − 2.84824i 11.6313 −1.48769 − 4.77355i 3.72471 + 11.2609i −3.33539 + 3.33539i −30.1712 −7.22491 + 5.36663i 5.88179 + 18.8729i
278.2 −3.88587 −0.310934 + 2.98384i 11.1000 4.98666 + 0.365024i 1.20825 − 11.5948i 4.48665 − 4.48665i −27.5895 −8.80664 − 1.85556i −19.3775 − 1.41844i
278.3 −3.84641 −2.97021 + 0.421723i 10.7949 −2.15430 + 4.51209i 11.4246 − 1.62212i −2.01617 + 2.01617i −26.1358 8.64430 − 2.50521i 8.28633 − 17.3553i
278.4 −3.73128 2.13163 + 2.11096i 9.92244 −4.98623 + 0.370846i −7.95371 − 7.87658i −8.54295 + 8.54295i −22.0983 0.0877024 + 8.99957i 18.6050 − 1.38373i
278.5 −3.69633 2.83997 + 0.966733i 9.66287 4.62600 − 1.89741i −10.4975 − 3.57337i −2.45888 + 2.45888i −20.9318 7.13085 + 5.49098i −17.0992 + 7.01345i
278.6 −3.62901 −0.785209 + 2.89542i 9.16969 −4.40007 − 2.37473i 2.84953 − 10.5075i 5.16860 − 5.16860i −18.7609 −7.76689 − 4.54702i 15.9679 + 8.61793i
278.7 −3.60043 2.68965 − 1.32883i 8.96309 0.718788 + 4.94806i −9.68389 + 4.78435i −2.02154 + 2.02154i −17.8692 5.46843 − 7.14816i −2.58795 − 17.8152i
278.8 −3.55971 −1.57699 − 2.55208i 8.67156 3.64447 + 3.42313i 5.61363 + 9.08467i 8.45974 − 8.45974i −16.6294 −4.02622 + 8.04920i −12.9733 − 12.1854i
278.9 −3.51607 1.75635 − 2.43212i 8.36273 3.82461 − 3.22061i −6.17546 + 8.55151i 3.02496 − 3.02496i −15.3397 −2.83045 − 8.54334i −13.4476 + 11.3239i
278.10 −3.48411 −2.55611 + 1.57045i 8.13902 1.46538 − 4.78045i 8.90576 − 5.47161i −4.60769 + 4.60769i −14.4208 4.06739 − 8.02847i −5.10553 + 16.6556i
278.11 −3.38483 1.02035 − 2.82115i 7.45706 −4.68208 + 1.75447i −3.45372 + 9.54910i 4.93897 − 4.93897i −11.7016 −6.91776 − 5.75713i 15.8480 − 5.93857i
278.12 −3.35734 −2.73564 − 1.23136i 7.27175 4.99772 + 0.150858i 9.18449 + 4.13411i −3.27150 + 3.27150i −10.9844 5.96749 + 6.73714i −16.7791 − 0.506482i
278.13 −3.33447 2.96349 + 0.466589i 7.11866 −0.694281 − 4.95156i −9.88167 − 1.55582i 6.53846 − 6.53846i −10.3991 8.56459 + 2.76546i 2.31506 + 16.5108i
278.14 −3.21045 −2.87961 − 0.841353i 6.30701 −4.45336 − 2.27323i 9.24484 + 2.70112i 5.48202 − 5.48202i −7.40653 7.58425 + 4.84553i 14.2973 + 7.29810i
278.15 −3.15592 1.95115 + 2.27882i 5.95983 1.06207 + 4.88590i −6.15766 − 7.19177i 2.48694 − 2.48694i −6.18505 −1.38604 + 8.89263i −3.35180 − 15.4195i
278.16 −3.08915 −0.883603 − 2.86692i 5.54285 −4.06793 + 2.90723i 2.72958 + 8.85636i −7.76116 + 7.76116i −4.76611 −7.43849 + 5.06644i 12.5664 − 8.98086i
278.17 −3.08252 −0.424294 + 2.96984i 5.50194 −3.69568 + 3.36778i 1.30790 − 9.15461i −0.0291339 + 0.0291339i −4.62976 −8.63995 − 2.52017i 11.3920 − 10.3813i
278.18 −2.97576 1.62141 + 2.52409i 4.85516 −1.69404 − 4.70428i −4.82493 − 7.51109i 0.982362 − 0.982362i −2.54476 −3.74206 + 8.18517i 5.04106 + 13.9988i
278.19 −2.94209 −1.13113 + 2.77859i 4.65590 3.38503 + 3.67989i 3.32788 − 8.17486i −9.18492 + 9.18492i −1.92973 −6.44110 − 6.28587i −9.95906 − 10.8266i
278.20 −2.88498 2.57538 − 1.53865i 4.32312 −3.63148 − 3.43691i −7.42992 + 4.43896i −6.13316 + 6.13316i −0.932202 4.26514 − 7.92519i 10.4768 + 9.91542i
See next 80 embeddings (of 232 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 278.116
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
145.e even 4 1 inner
435.t odd 4 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 435.3.t.a yes 232
3.b odd 2 1 inner 435.3.t.a yes 232
5.c odd 4 1 435.3.i.a ✓ 232
15.e even 4 1 435.3.i.a ✓ 232
29.c odd 4 1 435.3.i.a ✓ 232
87.f even 4 1 435.3.i.a ✓ 232
145.e even 4 1 inner 435.3.t.a yes 232
435.t odd 4 1 inner 435.3.t.a yes 232
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
435.3.i.a ✓ 232 5.c odd 4 1
435.3.i.a ✓ 232 15.e even 4 1
435.3.i.a ✓ 232 29.c odd 4 1
435.3.i.a ✓ 232 87.f even 4 1
435.3.t.a yes 232 1.a even 1 1 trivial
435.3.t.a yes 232 3.b odd 2 1 inner
435.3.t.a yes 232 145.e even 4 1 inner
435.3.t.a yes 232 435.t odd 4 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(435, [\chi])\).