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Properties

Label 495.3.g.a
Level $495$
Weight $3$
Character orbit 495.g
Analytic conductor $13.488$
Analytic rank $0$
Dimension $40$
Inner twists $4$

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Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [495,3,Mod(89,495)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(495, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0])) N = Newforms(chi, 3, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("495.89"); S:= CuspForms(chi, 3); N := Newforms(S);
 
Level: \( N \) \(=\) \( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 495.g (of order \(2\), degree \(1\), 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: \(13.4877730858\)
Analytic rank: \(0\)
Dimension: \(40\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 40 q + 72 q^{4} + 8 q^{10} + 184 q^{16} - 80 q^{19} + 32 q^{25} - 16 q^{31} - 160 q^{34} - 136 q^{40} + 560 q^{46} - 104 q^{49} - 96 q^{61} + 264 q^{64} - 872 q^{70} - 176 q^{76} - 672 q^{79} + 16 q^{85}+ \cdots + 400 q^{94}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
89.1 −3.68531 0 9.58148 0.638085 + 4.95912i 0 − 5.17232i −20.5695 0 −2.35154 − 18.2759i
89.2 −3.68531 0 9.58148 0.638085 − 4.95912i 0 5.17232i −20.5695 0 −2.35154 + 18.2759i
89.3 −3.53246 0 8.47824 4.02218 + 2.97020i 0 − 11.9775i −15.8192 0 −14.2082 − 10.4921i
89.4 −3.53246 0 8.47824 4.02218 − 2.97020i 0 11.9775i −15.8192 0 −14.2082 + 10.4921i
89.5 −3.50330 0 8.27308 −4.54045 − 2.09387i 0 − 0.502290i −14.9699 0 15.9066 + 7.33543i
89.6 −3.50330 0 8.27308 −4.54045 + 2.09387i 0 0.502290i −14.9699 0 15.9066 − 7.33543i
89.7 −2.54676 0 2.48600 4.87674 + 1.10334i 0 0.521381i 3.85580 0 −12.4199 − 2.80995i
89.8 −2.54676 0 2.48600 4.87674 − 1.10334i 0 − 0.521381i 3.85580 0 −12.4199 + 2.80995i
89.9 −2.18425 0 0.770929 −4.16841 + 2.76122i 0 12.4121i 7.05308 0 9.10484 − 6.03118i
89.10 −2.18425 0 0.770929 −4.16841 − 2.76122i 0 − 12.4121i 7.05308 0 9.10484 + 6.03118i
89.11 −2.09140 0 0.373951 −3.17303 + 3.86418i 0 − 2.11730i 7.58352 0 6.63607 − 8.08155i
89.12 −2.09140 0 0.373951 −3.17303 − 3.86418i 0 2.11730i 7.58352 0 6.63607 + 8.08155i
89.13 −1.57464 0 −1.52052 −1.98419 + 4.58944i 0 − 4.21179i 8.69281 0 3.12438 − 7.22671i
89.14 −1.57464 0 −1.52052 −1.98419 − 4.58944i 0 4.21179i 8.69281 0 3.12438 + 7.22671i
89.15 −0.881621 0 −3.22275 4.45405 − 2.27188i 0 − 4.31988i 6.36772 0 −3.92678 + 2.00293i
89.16 −0.881621 0 −3.22275 4.45405 + 2.27188i 0 4.31988i 6.36772 0 −3.92678 − 2.00293i
89.17 −0.835939 0 −3.30121 1.17408 + 4.86020i 0 − 10.8251i 6.10336 0 −0.981462 − 4.06283i
89.18 −0.835939 0 −3.30121 1.17408 − 4.86020i 0 10.8251i 6.10336 0 −0.981462 + 4.06283i
89.19 −0.284215 0 −3.91922 −3.92667 − 3.09536i 0 − 5.75646i 2.25076 0 1.11602 + 0.879748i
89.20 −0.284215 0 −3.91922 −3.92667 + 3.09536i 0 5.75646i 2.25076 0 1.11602 − 0.879748i
See all 40 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 89.40
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
5.b even 2 1 inner
15.d odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 495.3.g.a ✓ 40
3.b odd 2 1 inner 495.3.g.a ✓ 40
5.b even 2 1 inner 495.3.g.a ✓ 40
15.d odd 2 1 inner 495.3.g.a ✓ 40
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
495.3.g.a ✓ 40 1.a even 1 1 trivial
495.3.g.a ✓ 40 3.b odd 2 1 inner
495.3.g.a ✓ 40 5.b even 2 1 inner
495.3.g.a ✓ 40 15.d odd 2 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(495, [\chi])\).