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Properties

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

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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(193,925)] 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("925.193"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 1])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 925 = 5^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 925.y (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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
193.1 −2.19204 + 1.26558i −0.544247 − 2.03116i 2.20337 − 3.81634i 0 3.76360 + 3.76360i 0.959973 + 3.58267i 6.09181i −1.23132 + 0.710902i 0
193.2 −2.16574 + 1.25039i −0.0346441 − 0.129293i 2.12696 − 3.68400i 0 0.236698 + 0.236698i −0.00311317 − 0.0116185i 5.63657i 2.58256 − 1.49104i 0
193.3 −1.89068 + 1.09158i 0.698972 + 2.60860i 1.38311 − 2.39562i 0 −4.16904 − 4.16904i 1.11571 + 4.16388i 1.67281i −3.71815 + 2.14668i 0
193.4 −1.72671 + 0.996919i −0.184391 − 0.688157i 0.987696 − 1.71074i 0 1.00443 + 1.00443i −0.823709 − 3.07412i − 0.0490658i 2.15852 − 1.24622i 0
193.5 −1.48531 + 0.857546i −0.698150 − 2.60553i 0.470771 − 0.815400i 0 3.27133 + 3.27133i −0.596218 − 2.22512i − 1.81535i −3.70330 + 2.13810i 0
193.6 −1.45671 + 0.841034i 0.347958 + 1.29860i 0.414678 − 0.718243i 0 −1.59904 − 1.59904i 0.553160 + 2.06442i − 1.96910i 1.03280 − 0.596286i 0
193.7 −1.23407 + 0.712489i 0.526828 + 1.96615i 0.0152826 − 0.0264702i 0 −2.05100 − 2.05100i −1.06466 − 3.97336i − 2.80640i −0.990112 + 0.571641i 0
193.8 −1.05075 + 0.606650i −0.411889 − 1.53719i −0.263951 + 0.457177i 0 1.36533 + 1.36533i 1.19971 + 4.47739i − 3.06710i 0.404773 − 0.233696i 0
193.9 −0.948196 + 0.547441i 0.838136 + 3.12797i −0.400617 + 0.693888i 0 −2.50709 − 2.50709i −0.594554 − 2.21890i − 3.06702i −6.48363 + 3.74333i 0
193.10 −0.420731 + 0.242909i −0.673179 − 2.51234i −0.881990 + 1.52765i 0 0.893496 + 0.893496i −0.277006 − 1.03380i − 1.82861i −3.26059 + 1.88250i 0
193.11 −0.341622 + 0.197235i 0.203474 + 0.759377i −0.922196 + 1.59729i 0 −0.219287 − 0.219287i 1.12467 + 4.19733i − 1.51650i 2.06282 − 1.19097i 0
193.12 −0.0359237 + 0.0207406i −0.0933650 − 0.348443i −0.999140 + 1.73056i 0 0.0105809 + 0.0105809i 0.291106 + 1.08642i − 0.165853i 2.48538 − 1.43494i 0
193.13 0.0359237 − 0.0207406i 0.0933650 + 0.348443i −0.999140 + 1.73056i 0 0.0105809 + 0.0105809i −0.291106 − 1.08642i 0.165853i 2.48538 − 1.43494i 0
193.14 0.341622 − 0.197235i −0.203474 − 0.759377i −0.922196 + 1.59729i 0 −0.219287 − 0.219287i −1.12467 − 4.19733i 1.51650i 2.06282 − 1.19097i 0
193.15 0.420731 − 0.242909i 0.673179 + 2.51234i −0.881990 + 1.52765i 0 0.893496 + 0.893496i 0.277006 + 1.03380i 1.82861i −3.26059 + 1.88250i 0
193.16 0.948196 − 0.547441i −0.838136 − 3.12797i −0.400617 + 0.693888i 0 −2.50709 − 2.50709i 0.594554 + 2.21890i 3.06702i −6.48363 + 3.74333i 0
193.17 1.05075 − 0.606650i 0.411889 + 1.53719i −0.263951 + 0.457177i 0 1.36533 + 1.36533i −1.19971 − 4.47739i 3.06710i 0.404773 − 0.233696i 0
193.18 1.23407 − 0.712489i −0.526828 − 1.96615i 0.0152826 − 0.0264702i 0 −2.05100 − 2.05100i 1.06466 + 3.97336i 2.80640i −0.990112 + 0.571641i 0
193.19 1.45671 − 0.841034i −0.347958 − 1.29860i 0.414678 − 0.718243i 0 −1.59904 − 1.59904i −0.553160 − 2.06442i 1.96910i 1.03280 − 0.596286i 0
193.20 1.48531 − 0.857546i 0.698150 + 2.60553i 0.470771 − 0.815400i 0 3.27133 + 3.27133i 0.596218 + 2.22512i 1.81535i −3.70330 + 2.13810i 0
See all 96 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 193.24
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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.y.c yes 96
5.b even 2 1 inner 925.2.y.c yes 96
5.c odd 4 2 925.2.t.c ✓ 96
37.g odd 12 1 925.2.t.c ✓ 96
185.p even 12 1 inner 925.2.y.c yes 96
185.q odd 12 1 925.2.t.c ✓ 96
185.u even 12 1 inner 925.2.y.c yes 96
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
925.2.t.c ✓ 96 5.c odd 4 2
925.2.t.c ✓ 96 37.g odd 12 1
925.2.t.c ✓ 96 185.q odd 12 1
925.2.y.c yes 96 1.a even 1 1 trivial
925.2.y.c yes 96 5.b even 2 1 inner
925.2.y.c yes 96 185.p even 12 1 inner
925.2.y.c yes 96 185.u even 12 1 inner

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