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Properties

Label 175.3.m.a
Level $175$
Weight $3$
Character orbit 175.m
Analytic conductor $4.768$
Analytic rank $0$
Dimension $152$
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] = [175,3,Mod(34,175)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(175, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([7, 5]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("175.34");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 175.m (of order \(10\), degree \(4\), 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: \(4.76840462631\)
Analytic rank: \(0\)
Dimension: \(152\)
Relative dimension: \(38\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 152 q - 10 q^{2} + 66 q^{4} - 40 q^{8} - 108 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 152 q - 10 q^{2} + 66 q^{4} - 40 q^{8} - 108 q^{9} + 24 q^{11} - 21 q^{14} + 60 q^{15} - 150 q^{16} - 50 q^{22} - 180 q^{23} + 20 q^{25} - 45 q^{28} + 24 q^{29} + 170 q^{30} - 155 q^{35} + 136 q^{36} - 10 q^{37} + 250 q^{39} - 305 q^{42} + 202 q^{44} - 342 q^{46} - 178 q^{49} + 260 q^{50} - 220 q^{51} - 60 q^{53} + 78 q^{56} + 50 q^{58} + 100 q^{60} + 190 q^{63} + 424 q^{64} - 220 q^{65} + 710 q^{67} + 270 q^{70} - 236 q^{71} + 690 q^{72} + 28 q^{74} + 360 q^{77} + 80 q^{78} + 374 q^{79} - 688 q^{81} - 370 q^{84} + 490 q^{85} - 522 q^{86} - 2620 q^{88} - 170 q^{91} + 440 q^{92} - 880 q^{95} + 65 q^{98} - 36 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
34.1 −2.26014 + 3.11082i −0.985854 − 3.03415i −3.33289 − 10.2576i −3.51649 + 3.55447i 11.6669 + 3.79079i −3.03756 − 6.30660i 24.8143 + 8.06265i −0.952992 + 0.692389i −3.10954 − 18.9728i
34.2 −2.26014 + 3.11082i 0.985854 + 3.03415i −3.33289 − 10.2576i 3.51649 − 3.55447i −11.6669 − 3.79079i 3.03756 − 6.30660i 24.8143 + 8.06265i −0.952992 + 0.692389i 3.10954 + 18.9728i
34.3 −2.06967 + 2.84866i −1.26709 − 3.89971i −2.59524 − 7.98733i 4.17349 − 2.75354i 13.7314 + 4.46160i −2.51263 + 6.53351i 14.7293 + 4.78583i −6.32106 + 4.59252i −0.793875 + 17.5878i
34.4 −2.06967 + 2.84866i 1.26709 + 3.89971i −2.59524 − 7.98733i −4.17349 + 2.75354i −13.7314 − 4.46160i 2.51263 + 6.53351i 14.7293 + 4.78583i −6.32106 + 4.59252i 0.793875 − 17.5878i
34.5 −1.78460 + 2.45629i −0.0535701 − 0.164872i −1.61251 − 4.96278i −3.05061 − 3.96153i 0.500574 + 0.162646i −5.95081 + 3.68617i 3.51754 + 1.14292i 7.25684 − 5.27240i 15.1748 − 0.423443i
34.6 −1.78460 + 2.45629i 0.0535701 + 0.164872i −1.61251 − 4.96278i 3.05061 + 3.96153i −0.500574 − 0.162646i 5.95081 + 3.68617i 3.51754 + 1.14292i 7.25684 − 5.27240i −15.1748 + 0.423443i
34.7 −1.49002 + 2.05083i −0.655975 − 2.01888i −0.749698 − 2.30733i 4.60718 + 1.94266i 5.11781 + 1.66288i −1.53522 − 6.82958i −3.79458 − 1.23293i 3.63557 − 2.64139i −10.8488 + 6.55396i
34.8 −1.49002 + 2.05083i 0.655975 + 2.01888i −0.749698 − 2.30733i −4.60718 − 1.94266i −5.11781 − 1.66288i 1.53522 − 6.82958i −3.79458 − 1.23293i 3.63557 − 2.64139i 10.8488 − 6.55396i
34.9 −1.43842 + 1.97982i −1.33368 − 4.10463i −0.614560 − 1.89142i −3.78572 + 3.26624i 10.0448 + 3.26376i 6.02718 + 3.55993i −4.68100 − 1.52095i −7.78815 + 5.65842i −1.02110 − 12.1933i
34.10 −1.43842 + 1.97982i 1.33368 + 4.10463i −0.614560 − 1.89142i 3.78572 − 3.26624i −10.0448 − 3.26376i −6.02718 + 3.55993i −4.68100 − 1.52095i −7.78815 + 5.65842i 1.02110 + 12.1933i
34.11 −1.31330 + 1.80760i −1.70798 − 5.25662i −0.306598 − 0.943611i −0.416113 − 4.98265i 11.7449 + 3.81617i 1.51101 − 6.83497i −6.39152 − 2.07673i −17.4337 + 12.6663i 9.55313 + 5.79155i
34.12 −1.31330 + 1.80760i 1.70798 + 5.25662i −0.306598 − 0.943611i 0.416113 + 4.98265i −11.7449 − 3.81617i −1.51101 − 6.83497i −6.39152 − 2.07673i −17.4337 + 12.6663i −9.55313 − 5.79155i
34.13 −0.914682 + 1.25895i −0.0609050 − 0.187446i 0.487752 + 1.50115i −2.63899 + 4.24685i 0.291695 + 0.0947773i −6.99522 − 0.258529i −8.25595 − 2.68252i 7.24973 − 5.26723i −2.93275 − 7.20687i
34.14 −0.914682 + 1.25895i 0.0609050 + 0.187446i 0.487752 + 1.50115i 2.63899 − 4.24685i −0.291695 − 0.0947773i 6.99522 − 0.258529i −8.25595 − 2.68252i 7.24973 − 5.26723i 2.93275 + 7.20687i
34.15 −0.568993 + 0.783152i −1.48834 − 4.58065i 0.946494 + 2.91301i 3.93550 + 3.08412i 4.43420 + 1.44076i −5.46639 + 4.37248i −6.50248 − 2.11278i −11.4861 + 8.34511i −4.65461 + 1.32725i
34.16 −0.568993 + 0.783152i 1.48834 + 4.58065i 0.946494 + 2.91301i −3.93550 − 3.08412i −4.43420 − 1.44076i 5.46639 + 4.37248i −6.50248 − 2.11278i −11.4861 + 8.34511i 4.65461 − 1.32725i
34.17 −0.405562 + 0.558208i −0.878315 − 2.70318i 1.08895 + 3.35145i −4.39662 − 2.38112i 1.86515 + 0.606023i 1.23529 + 6.89014i −4.93729 − 1.60422i 0.745425 − 0.541583i 3.11226 − 1.48854i
34.18 −0.405562 + 0.558208i 0.878315 + 2.70318i 1.08895 + 3.35145i 4.39662 + 2.38112i −1.86515 − 0.606023i −1.23529 + 6.89014i −4.93729 − 1.60422i 0.745425 − 0.541583i −3.11226 + 1.48854i
34.19 −0.0322264 + 0.0443558i −0.766900 − 2.36028i 1.23514 + 3.80137i 0.478540 − 4.97705i 0.129406 + 0.0420467i −6.59180 − 2.35547i −0.416990 − 0.135488i 2.29838 − 1.66987i 0.205339 + 0.181618i
34.20 −0.0322264 + 0.0443558i 0.766900 + 2.36028i 1.23514 + 3.80137i −0.478540 + 4.97705i −0.129406 − 0.0420467i 6.59180 − 2.35547i −0.416990 − 0.135488i 2.29838 − 1.66987i −0.205339 − 0.181618i
See next 80 embeddings (of 152 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 34.38
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
7.b odd 2 1 inner
25.e even 10 1 inner
175.m odd 10 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 175.3.m.a ✓ 152
7.b odd 2 1 inner 175.3.m.a ✓ 152
25.e even 10 1 inner 175.3.m.a ✓ 152
175.m odd 10 1 inner 175.3.m.a ✓ 152
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
175.3.m.a ✓ 152 1.a even 1 1 trivial
175.3.m.a ✓ 152 7.b odd 2 1 inner
175.3.m.a ✓ 152 25.e even 10 1 inner
175.3.m.a ✓ 152 175.m odd 10 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(175, [\chi])\).