Properties

Label 275.3.u.a
Level $275$
Weight $3$
Character orbit 275.u
Analytic conductor $7.493$
Analytic rank $0$
Dimension $232$
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [275,3,Mod(61,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.61"); S:= CuspForms(chi, 3); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8, 9])) N = Newforms(chi, 3, names="a")
 
Level: \( N \) \(=\) \( 275 = 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 275.u (of order \(10\), degree \(4\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.49320726991\)
Analytic rank: \(0\)
Dimension: \(232\)
Relative dimension: \(58\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 232 q - 5 q^{2} + 2 q^{3} + 111 q^{4} - 9 q^{5} + 10 q^{7} + 15 q^{8} - 148 q^{9} - 20 q^{10} + 7 q^{11} - 2 q^{12} - 5 q^{13} - 22 q^{14} + 60 q^{15} - 185 q^{16} + 35 q^{18} - 5 q^{19} - 61 q^{20} + 95 q^{22}+ \cdots + 202 q^{99}+O(q^{100}) \) 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.

Copy content comment:embeddings in the coefficient field
 
Copy content gp:mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
61.1 −2.30644 + 3.17454i −3.27493 + 2.37937i −3.52197 − 10.8395i −4.98365 + 0.404023i − 15.8843i −0.340947 − 0.469273i 27.6061 + 8.96975i 2.28258 − 7.02506i 10.2119 − 16.7526i
61.2 −2.20374 + 3.03319i 4.44415 − 3.22886i −3.10769 − 9.56448i 4.97579 + 0.491490i 20.5955i 3.92691 + 5.40493i 21.5965 + 7.01712i 6.54374 − 20.1396i −12.4561 + 14.0094i
61.3 −2.18883 + 3.01267i 2.26392 − 1.64484i −3.04912 − 9.38423i −2.90736 − 4.06783i 10.4207i −4.06250 − 5.59155i 20.7792 + 6.75156i −0.361290 + 1.11194i 18.6188 + 0.144897i
61.4 −2.12433 + 2.92389i 0.409335 − 0.297399i −2.80029 − 8.61841i 3.19065 + 3.84964i 1.82863i −6.75175 − 9.29298i 17.3991 + 5.65330i −2.70204 + 8.31604i −18.0339 + 1.15119i
61.5 −2.08948 + 2.87593i −2.52852 + 1.83708i −2.66895 − 8.21418i 3.93872 + 3.08002i − 11.1104i 5.64288 + 7.76676i 15.6767 + 5.09366i 0.237414 − 0.730687i −17.0878 + 4.89182i
61.6 −1.97812 + 2.72264i −0.0462941 + 0.0336346i −2.26378 − 6.96719i 3.46277 − 3.60683i − 0.192576i 1.37391 + 1.89102i 10.6446 + 3.45862i −2.78014 + 8.55639i 2.97036 + 16.5626i
61.7 −1.87627 + 2.58246i 1.53548 − 1.11559i −1.91265 − 5.88654i −1.80641 + 4.66228i 6.05846i 1.79273 + 2.46748i 6.64696 + 2.15973i −1.66800 + 5.13358i −8.65084 − 13.4127i
61.8 −1.86741 + 2.57027i −3.21632 + 2.33679i −1.88299 − 5.79525i 2.92560 − 4.05474i − 12.6305i −5.61458 − 7.72781i 6.32553 + 2.05529i 2.10295 − 6.47220i 4.95848 + 15.0914i
61.9 −1.77004 + 2.43624i 2.68389 − 1.94996i −1.56619 − 4.82025i −4.02729 − 2.96326i 9.99010i 6.40589 + 8.81695i 3.05962 + 0.994132i 0.619761 − 1.90743i 14.3477 − 4.56640i
61.10 −1.75205 + 2.41149i −0.937739 + 0.681307i −1.50954 − 4.64589i −4.75402 + 1.54896i − 3.45504i 2.08711 + 2.87266i 2.50880 + 0.815160i −2.36598 + 7.28173i 4.59397 − 14.1781i
61.11 −1.64054 + 2.25800i 4.80005 − 3.48744i −1.17116 − 3.60445i −3.66584 + 3.40024i 16.5598i −4.02810 − 5.54421i −0.557593 − 0.181173i 8.09710 − 24.9203i −1.66382 − 13.8557i
61.12 −1.60338 + 2.20687i −4.07618 + 2.96151i −1.06336 − 3.27269i −1.89878 − 4.62543i − 13.7440i 2.71447 + 3.73615i −1.44996 − 0.471120i 5.06348 − 15.5838i 13.2522 + 3.22599i
61.13 −1.43683 + 1.97763i −4.38933 + 3.18904i −0.610466 − 1.87882i 3.26594 + 3.78597i − 13.2626i 0.383349 + 0.527634i −4.70663 − 1.52928i 6.31514 − 19.4360i −12.1799 + 1.01902i
61.14 −1.43211 + 1.97113i 2.74974 − 1.99781i −0.598342 − 1.84151i 3.99783 − 3.00289i 8.28117i −0.276211 − 0.380172i −4.78206 − 1.55379i 0.788713 − 2.42741i 0.193748 + 12.1807i
61.15 −1.26916 + 1.74685i −0.660273 + 0.479716i −0.204641 − 0.629819i −4.69525 − 1.71890i − 1.76223i −5.89433 − 8.11284i −6.85424 − 2.22708i −2.57532 + 7.92602i 8.96167 − 6.02031i
61.16 −1.26903 + 1.74667i 2.00828 − 1.45910i −0.204352 − 0.628931i 1.87538 + 4.63497i 5.35943i −3.82737 − 5.26792i −6.85547 − 2.22748i −0.876949 + 2.69897i −10.4757 − 2.60625i
61.17 −1.25126 + 1.72221i −2.33045 + 1.69317i −0.164298 − 0.505658i −2.21449 + 4.48286i − 6.13214i −1.20304 − 1.65584i −7.02191 − 2.28156i −0.216977 + 0.667786i −4.94954 − 9.42306i
61.18 −1.10716 + 1.52387i 3.03390 − 2.20426i 0.139676 + 0.429879i 0.916543 − 4.91528i 7.06375i −4.15343 − 5.71671i −7.97542 − 2.59137i 1.56465 − 4.81550i 6.47551 + 6.83869i
61.19 −1.09027 + 1.50063i −0.635108 + 0.461433i 0.172865 + 0.532023i 4.88244 − 1.07788i − 1.45615i 3.09497 + 4.25986i −8.04324 − 2.61341i −2.59071 + 7.97339i −3.70569 + 8.50193i
61.20 −1.02962 + 1.41715i −1.72993 + 1.25687i 0.287868 + 0.885968i −1.61579 − 4.73172i − 3.74567i 5.71841 + 7.87072i −8.21579 − 2.66947i −1.36821 + 4.21093i 8.36922 + 2.58206i
See next 80 embeddings (of 232 total)
\(n\): e.g. 2-40 or 80-90
Embeddings: e.g. 1-3 or 61.58
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
275.u odd 10 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 275.3.u.a ✓ 232
11.d odd 10 1 275.3.w.a yes 232
25.d even 5 1 275.3.w.a yes 232
275.u odd 10 1 inner 275.3.u.a ✓ 232
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
275.3.u.a ✓ 232 1.a even 1 1 trivial
275.3.u.a ✓ 232 275.u odd 10 1 inner
275.3.w.a yes 232 11.d odd 10 1
275.3.w.a yes 232 25.d even 5 1

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(275, [\chi])\).