Properties

Label 175.3.v.a
Level $175$
Weight $3$
Character orbit 175.v
Analytic conductor $4.768$
Analytic rank $0$
Dimension $304$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [175,3,Mod(31,175)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(175, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([12, 5]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("175.31");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 175.v (of order \(30\), degree \(8\), 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: \(304\)
Relative dimension: \(38\) over \(\Q(\zeta_{30})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{30}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 304 q - 3 q^{2} - 9 q^{3} + 69 q^{4} - 15 q^{5} - 18 q^{7} - 46 q^{8} - 105 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 304 q - 3 q^{2} - 9 q^{3} + 69 q^{4} - 15 q^{5} - 18 q^{7} - 46 q^{8} - 105 q^{9} - 15 q^{10} - 18 q^{11} - 33 q^{12} + 36 q^{14} - 80 q^{15} + 133 q^{16} - 63 q^{17} - 74 q^{18} - 9 q^{19} - 3 q^{21} - 12 q^{22} + 99 q^{23} - 66 q^{24} - 35 q^{25} - 48 q^{26} - 12 q^{28} + 48 q^{29} - 265 q^{30} + 171 q^{31} + 44 q^{32} + 252 q^{33} - 110 q^{35} + 620 q^{36} - 49 q^{37} - 210 q^{38} - 91 q^{39} - 15 q^{40} + 368 q^{42} + 444 q^{43} + 21 q^{44} - 315 q^{45} - 39 q^{46} - 219 q^{47} + 154 q^{49} - 90 q^{50} + 148 q^{51} + 138 q^{52} + 69 q^{53} - 249 q^{54} - 430 q^{56} - 1272 q^{57} - 103 q^{58} + 351 q^{59} + 35 q^{60} - 99 q^{61} + 199 q^{63} - 946 q^{64} - 35 q^{65} - 651 q^{66} - 227 q^{67} - 1842 q^{68} - 975 q^{70} - 362 q^{71} + 36 q^{72} + 33 q^{73} + 246 q^{74} + 135 q^{75} + 291 q^{77} + 202 q^{78} + 97 q^{79} + 1080 q^{80} - 103 q^{81} + 2268 q^{82} - 1209 q^{84} + 1590 q^{85} - 195 q^{86} - 153 q^{87} + 1026 q^{88} + 666 q^{89} + 538 q^{91} + 1858 q^{92} - 814 q^{93} - 489 q^{94} - 75 q^{95} + 1485 q^{96} - 868 q^{98} - 180 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
31.1 −2.49483 + 2.77079i −4.88519 + 0.513454i −1.03498 9.84720i 0.0370158 4.99986i 10.7650 14.8168i −6.93002 + 0.987337i 17.8011 + 12.9332i 14.7981 3.14543i 13.7612 + 12.5764i
31.2 −2.46635 + 2.73916i 3.90575 0.410511i −1.00199 9.53333i −4.87433 + 1.11397i −8.50848 + 11.7109i −5.89171 3.77992i 16.6567 + 12.1018i 6.28303 1.33550i 8.97045 16.0990i
31.3 −2.40308 + 2.66889i −0.888631 + 0.0933988i −0.930071 8.84903i 2.13906 + 4.51934i 1.88618 2.59610i −0.0558604 + 6.99978i 14.2303 + 10.3389i −8.02239 + 1.70521i −17.2020 5.15141i
31.4 −2.23580 + 2.48310i −0.901848 + 0.0947881i −0.748904 7.12534i −4.52006 2.13753i 1.78098 2.45131i 6.60425 2.32031i 8.55454 + 6.21524i −7.99898 + 1.70024i 15.4136 6.44471i
31.5 −2.10006 + 2.33235i 3.01791 0.317195i −0.611504 5.81807i 3.10424 3.91965i −5.59798 + 7.70496i −5.63331 + 4.15521i 4.69763 + 3.41303i 0.203842 0.0433280i 2.62292 + 15.4717i
31.6 −2.06481 + 2.29321i 4.51294 0.474329i −0.577233 5.49201i 3.92442 + 3.09821i −8.23064 + 11.3285i 5.63678 4.15051i 3.80029 + 2.76107i 11.3383 2.41003i −15.2080 + 2.60227i
31.7 −1.91067 + 2.12201i −3.47027 + 0.364740i −0.434170 4.13085i −1.55857 + 4.75088i 5.85656 8.06086i −2.25597 6.62651i 0.354846 + 0.257811i 3.10641 0.660287i −7.10353 12.3847i
31.8 −1.70001 + 1.88805i 0.145330 0.0152748i −0.256596 2.44134i 4.49189 2.19612i −0.218223 + 0.300358i −2.33140 6.60035i −3.17604 2.30753i −8.78244 + 1.86677i −3.48986 + 12.2144i
31.9 −1.65998 + 1.84360i −4.90771 + 0.515821i −0.225195 2.14259i 4.96258 0.610552i 7.19574 9.90409i 6.87919 + 1.29487i −3.70416 2.69123i 15.0162 3.19179i −7.11219 + 10.1625i
31.10 −1.40049 + 1.55540i −0.438533 + 0.0460917i −0.0397882 0.378560i −0.744880 4.94420i 0.542470 0.746646i 4.32167 + 5.50665i −6.12855 4.45265i −8.61314 + 1.83078i 8.73342 + 5.76572i
31.11 −1.38496 + 1.53816i 3.56615 0.374817i −0.0296908 0.282489i −3.08750 + 3.93286i −4.36245 + 6.00440i 2.60110 + 6.49879i −6.22236 4.52081i 3.77359 0.802101i −1.77329 10.1959i
31.12 −1.12383 + 1.24813i −4.12211 + 0.433251i 0.123257 + 1.17272i −4.98024 0.444119i 4.09177 5.63185i −5.21929 + 4.66465i −7.03730 5.11290i 8.00074 1.70061i 6.15124 5.71689i
31.13 −0.967647 + 1.07468i 2.37369 0.249485i 0.199516 + 1.89826i −4.47801 2.22428i −2.02877 + 2.79237i −6.34778 2.95054i −6.91285 5.02248i −3.23118 + 0.686808i 6.72353 2.66011i
31.14 −0.907746 + 1.00815i 5.11223 0.537317i 0.225742 + 2.14779i −1.47546 4.77734i −4.09891 + 5.64167i 4.76870 5.12440i −6.76029 4.91164i 17.0429 3.62257i 6.15565 + 2.84912i
31.15 −0.805329 + 0.894408i 0.182928 0.0192266i 0.266702 + 2.53750i 2.29201 + 4.44372i −0.130121 + 0.179096i −6.99969 + 0.0657773i −6.37910 4.63469i −8.77024 + 1.86417i −5.82033 1.52867i
31.16 −0.492153 + 0.546592i −3.83732 + 0.403319i 0.361566 + 3.44007i −1.97600 + 4.59298i 1.66810 2.29594i 6.41025 + 2.81223i −4.43843 3.22471i 5.75904 1.22412i −1.53799 3.34051i
31.17 −0.259618 + 0.288335i −3.00636 + 0.315981i 0.402378 + 3.82837i 1.63247 4.72600i 0.689396 0.948872i −0.900309 6.94186i −2.46389 1.79012i 0.135019 0.0286991i 0.938850 + 1.69765i
31.18 −0.229715 + 0.255125i 0.760744 0.0799574i 0.405794 + 3.86088i 4.46427 + 2.25174i −0.154355 + 0.212452i 6.90683 1.13829i −2.18918 1.59053i −8.23099 + 1.74955i −1.59998 + 0.621685i
31.19 −0.202397 + 0.224785i 4.72650 0.496775i 0.408550 + 3.88710i 4.80168 1.39423i −0.844963 + 1.16299i −2.30801 + 6.60856i −1.93529 1.40607i 13.2896 2.82480i −0.658444 + 1.36154i
31.20 0.192889 0.214225i −2.42365 + 0.254736i 0.409428 + 3.89544i 1.90879 4.62131i −0.412925 + 0.568343i −2.66665 + 6.47217i 1.84633 + 1.34144i −2.99412 + 0.636419i −0.621814 1.30031i
See next 80 embeddings (of 304 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 31.38
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
7.d odd 6 1 inner
25.d even 5 1 inner
175.v odd 30 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 175.3.v.a 304
7.d odd 6 1 inner 175.3.v.a 304
25.d even 5 1 inner 175.3.v.a 304
175.v odd 30 1 inner 175.3.v.a 304
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
175.3.v.a 304 1.a even 1 1 trivial
175.3.v.a 304 7.d odd 6 1 inner
175.3.v.a 304 25.d even 5 1 inner
175.3.v.a 304 175.v odd 30 1 inner

Hecke kernels

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