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Properties

Label 855.2.b.d
Level $855$
Weight $2$
Character orbit 855.b
Analytic conductor $6.827$
Analytic rank $0$
Dimension $24$
Inner twists $8$

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Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [855,2,Mod(854,855)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(855, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 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("855.854"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 855.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [24,0,0,-56,0,0,0,0,0,0,0,0,0,0,0,8,0,0,32,0,0,0,0,0,-8,0,0,0, 0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(29)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.82720937282\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 56 q^{4} + 8 q^{16} + 32 q^{19} - 8 q^{25} - 104 q^{49} - 16 q^{55} - 16 q^{61} - 72 q^{64} - 112 q^{76} + 128 q^{85}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
854.1 − 2.62034i 0 −4.86620 −2.20595 − 0.365789i 0 − 3.50917i 7.51042i 0 −0.958493 + 5.78034i
854.2 − 2.62034i 0 −4.86620 −2.20595 + 0.365789i 0 3.50917i 7.51042i 0 0.958493 + 5.78034i
854.3 − 2.62034i 0 −4.86620 2.20595 − 0.365789i 0 3.50917i 7.51042i 0 −0.958493 − 5.78034i
854.4 − 2.62034i 0 −4.86620 2.20595 + 0.365789i 0 − 3.50917i 7.51042i 0 0.958493 − 5.78034i
854.5 − 1.94660i 0 −1.78924 −1.33763 − 1.79186i 0 1.78523i − 0.410257i 0 −3.48803 + 2.60382i
854.6 − 1.94660i 0 −1.78924 −1.33763 + 1.79186i 0 − 1.78523i − 0.410257i 0 3.48803 + 2.60382i
854.7 − 1.94660i 0 −1.78924 1.33763 − 1.79186i 0 − 1.78523i − 0.410257i 0 −3.48803 − 2.60382i
854.8 − 1.94660i 0 −1.78924 1.33763 + 1.79186i 0 1.78523i − 0.410257i 0 3.48803 − 2.60382i
854.9 − 1.53119i 0 −0.344558 −0.586990 − 2.15765i 0 − 4.30101i − 2.53480i 0 −3.30378 + 0.898797i
854.10 − 1.53119i 0 −0.344558 −0.586990 + 2.15765i 0 4.30101i − 2.53480i 0 3.30378 + 0.898797i
854.11 − 1.53119i 0 −0.344558 0.586990 − 2.15765i 0 4.30101i − 2.53480i 0 −3.30378 − 0.898797i
854.12 − 1.53119i 0 −0.344558 0.586990 + 2.15765i 0 − 4.30101i − 2.53480i 0 3.30378 − 0.898797i
854.13 1.53119i 0 −0.344558 −0.586990 − 2.15765i 0 − 4.30101i 2.53480i 0 3.30378 − 0.898797i
854.14 1.53119i 0 −0.344558 −0.586990 + 2.15765i 0 4.30101i 2.53480i 0 −3.30378 − 0.898797i
854.15 1.53119i 0 −0.344558 0.586990 − 2.15765i 0 4.30101i 2.53480i 0 3.30378 + 0.898797i
854.16 1.53119i 0 −0.344558 0.586990 + 2.15765i 0 − 4.30101i 2.53480i 0 −3.30378 + 0.898797i
854.17 1.94660i 0 −1.78924 −1.33763 − 1.79186i 0 1.78523i 0.410257i 0 3.48803 − 2.60382i
854.18 1.94660i 0 −1.78924 −1.33763 + 1.79186i 0 − 1.78523i 0.410257i 0 −3.48803 − 2.60382i
854.19 1.94660i 0 −1.78924 1.33763 − 1.79186i 0 − 1.78523i 0.410257i 0 3.48803 + 2.60382i
854.20 1.94660i 0 −1.78924 1.33763 + 1.79186i 0 1.78523i 0.410257i 0 −3.48803 + 2.60382i
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 854.24
Significant digits:
Format:

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
19.b odd 2 1 inner
57.d even 2 1 inner
95.d odd 2 1 inner
285.b even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 855.2.b.d ✓ 24
3.b odd 2 1 inner 855.2.b.d ✓ 24
5.b even 2 1 inner 855.2.b.d ✓ 24
15.d odd 2 1 inner 855.2.b.d ✓ 24
19.b odd 2 1 inner 855.2.b.d ✓ 24
57.d even 2 1 inner 855.2.b.d ✓ 24
95.d odd 2 1 inner 855.2.b.d ✓ 24
285.b even 2 1 inner 855.2.b.d ✓ 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
855.2.b.d ✓ 24 1.a even 1 1 trivial
855.2.b.d ✓ 24 3.b odd 2 1 inner
855.2.b.d ✓ 24 5.b even 2 1 inner
855.2.b.d ✓ 24 15.d odd 2 1 inner
855.2.b.d ✓ 24 19.b odd 2 1 inner
855.2.b.d ✓ 24 57.d even 2 1 inner
855.2.b.d ✓ 24 95.d odd 2 1 inner
855.2.b.d ✓ 24 285.b even 2 1 inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(855, [\chi])\):

\( T_{2}^{6} + 13T_{2}^{4} + 51T_{2}^{2} + 61 \) Copy content Toggle raw display
\( T_{29}^{6} - 214T_{29}^{4} + 14476T_{29}^{2} - 307806 \) Copy content Toggle raw display