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Properties

Label 495.3.e.a
Level $495$
Weight $3$
Character orbit 495.e
Analytic conductor $13.488$
Analytic rank $0$
Dimension $24$
Inner twists $2$

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Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [495,3,Mod(386,495)] 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, 0, 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("495.386"); S:= CuspForms(chi, 3); N := Newforms(S);
 
Level: \( N \) \(=\) \( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 495.e (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: \(24\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 40 q^{4} - 32 q^{7} + 40 q^{10} + 48 q^{13} - 24 q^{16} - 120 q^{25} + 128 q^{28} + 96 q^{31} + 112 q^{34} - 320 q^{37} - 120 q^{40} + 208 q^{43} - 288 q^{46} + 296 q^{49} - 192 q^{52} + 96 q^{58}+ \cdots + 576 q^{97}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
386.1 − 3.62558i 0 −9.14484 2.23607i 0 −10.4603 18.6530i 0 8.10705
386.2 − 3.30736i 0 −6.93861 2.23607i 0 5.46027 9.71902i 0 7.39547
386.3 − 3.16787i 0 −6.03539 2.23607i 0 5.72133 6.44784i 0 7.08357
386.4 − 3.01235i 0 −5.07425 − 2.23607i 0 −9.19596 3.23603i 0 −6.73582
386.5 − 2.92562i 0 −4.55924 2.23607i 0 −2.18410 1.63612i 0 6.54188
386.6 − 2.40857i 0 −1.80121 − 2.23607i 0 −4.05010 − 5.29594i 0 −5.38573
386.7 − 2.04741i 0 −0.191888 − 2.23607i 0 4.50616 − 7.79677i 0 −4.57815
386.8 − 1.62284i 0 1.36640 2.23607i 0 7.80360 − 8.70879i 0 3.62877
386.9 − 1.33728i 0 2.21168 2.23607i 0 −6.93830 − 8.30676i 0 2.99025
386.10 − 1.11561i 0 2.75541 2.23607i 0 −12.6993 − 7.53641i 0 2.49458
386.11 − 0.763300i 0 3.41737 − 2.23607i 0 11.6630 − 5.66168i 0 −1.70679
386.12 − 0.0737504i 0 3.99456 2.23607i 0 −5.62618 − 0.589602i 0 0.164911
386.13 0.0737504i 0 3.99456 − 2.23607i 0 −5.62618 0.589602i 0 0.164911
386.14 0.763300i 0 3.41737 2.23607i 0 11.6630 5.66168i 0 −1.70679
386.15 1.11561i 0 2.75541 − 2.23607i 0 −12.6993 7.53641i 0 2.49458
386.16 1.33728i 0 2.21168 − 2.23607i 0 −6.93830 8.30676i 0 2.99025
386.17 1.62284i 0 1.36640 − 2.23607i 0 7.80360 8.70879i 0 3.62877
386.18 2.04741i 0 −0.191888 2.23607i 0 4.50616 7.79677i 0 −4.57815
386.19 2.40857i 0 −1.80121 2.23607i 0 −4.05010 5.29594i 0 −5.38573
386.20 2.92562i 0 −4.55924 − 2.23607i 0 −2.18410 − 1.63612i 0 6.54188
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 386.24
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b 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.e.a ✓ 24
3.b odd 2 1 inner 495.3.e.a ✓ 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
495.3.e.a ✓ 24 1.a even 1 1 trivial
495.3.e.a ✓ 24 3.b odd 2 1 inner

Hecke kernels

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