↑

Properties

Label 925.2.t.c
Level $925$
Weight $2$
Character orbit 925.t
Analytic conductor $7.386$
Analytic rank $0$
Dimension $96$
Inner twists $4$

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] = [925,2,Mod(82,925)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([3, 1])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("925.82"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 925 = 5^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 925.t (of order \(12\), degree \(4\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [96] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.38616218697\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(24\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 96 q - 40 q^{4} + 32 q^{14} - 4 q^{16} + 24 q^{19} + 36 q^{21} - 52 q^{24} + 16 q^{26} - 12 q^{29} + 4 q^{31} + 60 q^{34} - 100 q^{39} - 48 q^{41} - 48 q^{44} + 24 q^{46} + 120 q^{49} - 84 q^{51} - 104 q^{54}+ \cdots + 24 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
82.1 −1.26558 − 2.19204i −2.03116 + 0.544247i −2.20337 + 3.81634i 0 3.76360 + 3.76360i −3.58267 + 0.959973i 6.09181 1.23132 − 0.710902i 0
82.2 −1.25039 − 2.16574i −0.129293 + 0.0346441i −2.12696 + 3.68400i 0 0.236698 + 0.236698i 0.0116185 − 0.00311317i 5.63657 −2.58256 + 1.49104i 0
82.3 −1.09158 − 1.89068i 2.60860 − 0.698972i −1.38311 + 2.39562i 0 −4.16904 − 4.16904i −4.16388 + 1.11571i 1.67281 3.71815 − 2.14668i 0
82.4 −0.996919 − 1.72671i −0.688157 + 0.184391i −0.987696 + 1.71074i 0 1.00443 + 1.00443i 3.07412 − 0.823709i −0.0490658 −2.15852 + 1.24622i 0
82.5 −0.857546 − 1.48531i −2.60553 + 0.698150i −0.470771 + 0.815400i 0 3.27133 + 3.27133i 2.22512 − 0.596218i −1.81535 3.70330 − 2.13810i 0
82.6 −0.841034 − 1.45671i 1.29860 − 0.347958i −0.414678 + 0.718243i 0 −1.59904 − 1.59904i −2.06442 + 0.553160i −1.96910 −1.03280 + 0.596286i 0
82.7 −0.712489 − 1.23407i 1.96615 − 0.526828i −0.0152826 + 0.0264702i 0 −2.05100 − 2.05100i 3.97336 − 1.06466i −2.80640 0.990112 − 0.571641i 0
82.8 −0.606650 − 1.05075i −1.53719 + 0.411889i 0.263951 − 0.457177i 0 1.36533 + 1.36533i −4.47739 + 1.19971i −3.06710 −0.404773 + 0.233696i 0
82.9 −0.547441 − 0.948196i 3.12797 − 0.838136i 0.400617 − 0.693888i 0 −2.50709 − 2.50709i 2.21890 − 0.594554i −3.06702 6.48363 − 3.74333i 0
82.10 −0.242909 − 0.420731i −2.51234 + 0.673179i 0.881990 − 1.52765i 0 0.893496 + 0.893496i 1.03380 − 0.277006i −1.82861 3.26059 − 1.88250i 0
82.11 −0.197235 − 0.341622i 0.759377 − 0.203474i 0.922196 − 1.59729i 0 −0.219287 − 0.219287i −4.19733 + 1.12467i −1.51650 −2.06282 + 1.19097i 0
82.12 −0.0207406 − 0.0359237i −0.348443 + 0.0933650i 0.999140 − 1.73056i 0 0.0105809 + 0.0105809i −1.08642 + 0.291106i −0.165853 −2.48538 + 1.43494i 0
82.13 0.0207406 + 0.0359237i 0.348443 − 0.0933650i 0.999140 − 1.73056i 0 0.0105809 + 0.0105809i 1.08642 − 0.291106i 0.165853 −2.48538 + 1.43494i 0
82.14 0.197235 + 0.341622i −0.759377 + 0.203474i 0.922196 − 1.59729i 0 −0.219287 − 0.219287i 4.19733 − 1.12467i 1.51650 −2.06282 + 1.19097i 0
82.15 0.242909 + 0.420731i 2.51234 − 0.673179i 0.881990 − 1.52765i 0 0.893496 + 0.893496i −1.03380 + 0.277006i 1.82861 3.26059 − 1.88250i 0
82.16 0.547441 + 0.948196i −3.12797 + 0.838136i 0.400617 − 0.693888i 0 −2.50709 − 2.50709i −2.21890 + 0.594554i 3.06702 6.48363 − 3.74333i 0
82.17 0.606650 + 1.05075i 1.53719 − 0.411889i 0.263951 − 0.457177i 0 1.36533 + 1.36533i 4.47739 − 1.19971i 3.06710 −0.404773 + 0.233696i 0
82.18 0.712489 + 1.23407i −1.96615 + 0.526828i −0.0152826 + 0.0264702i 0 −2.05100 − 2.05100i −3.97336 + 1.06466i 2.80640 0.990112 − 0.571641i 0
82.19 0.841034 + 1.45671i −1.29860 + 0.347958i −0.414678 + 0.718243i 0 −1.59904 − 1.59904i 2.06442 − 0.553160i 1.96910 −1.03280 + 0.596286i 0
82.20 0.857546 + 1.48531i 2.60553 − 0.698150i −0.470771 + 0.815400i 0 3.27133 + 3.27133i −2.22512 + 0.596218i 1.81535 3.70330 − 2.13810i 0
See all 96 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 82.24
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner
185.p even 12 1 inner
185.u even 12 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 925.2.t.c ✓ 96
5.b even 2 1 inner 925.2.t.c ✓ 96
5.c odd 4 2 925.2.y.c yes 96
37.g odd 12 1 925.2.y.c yes 96
185.p even 12 1 inner 925.2.t.c ✓ 96
185.q odd 12 1 925.2.y.c yes 96
185.u even 12 1 inner 925.2.t.c ✓ 96
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
925.2.t.c ✓ 96 1.a even 1 1 trivial
925.2.t.c ✓ 96 5.b even 2 1 inner
925.2.t.c ✓ 96 185.p even 12 1 inner
925.2.t.c ✓ 96 185.u even 12 1 inner
925.2.y.c yes 96 5.c odd 4 2
925.2.y.c yes 96 37.g odd 12 1
925.2.y.c yes 96 185.q odd 12 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{96} + 68 T_{2}^{94} + 2469 T_{2}^{92} + 61956 T_{2}^{90} + 1192136 T_{2}^{88} + 18582652 T_{2}^{86} + \cdots + 14641 \) acting on \(S_{2}^{\mathrm{new}}(925, [\chi])\). Copy content Toggle raw display