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Properties

Label 4805.2.a.bd
Level $4805$
Weight $2$
Character orbit 4805.a
Self dual yes
Analytic conductor $38.368$
Analytic rank $0$
Dimension $48$
Inner twists $2$

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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] = [4805,2,Mod(1,4805)] 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("4805.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4805, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 4805 = 5 \cdot 31^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4805.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [48,16,0,64,48,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(38.3681181712\)
Analytic rank: \(0\)
Dimension: \(48\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 48 q + 16 q^{2} + 64 q^{4} + 48 q^{5} + 48 q^{7} + 48 q^{8} + 48 q^{9} + 16 q^{10} + 16 q^{14} + 96 q^{16} + 64 q^{18} + 48 q^{19} + 64 q^{20} + 48 q^{25} + 112 q^{28} + 112 q^{32} + 64 q^{33} + 48 q^{35}+ \cdots + 80 q^{97}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −2.59059 −0.417119 4.71114 1.00000 1.08058 3.94746 −7.02344 −2.82601 −2.59059
1.2 −2.59059 0.417119 4.71114 1.00000 −1.08058 3.94746 −7.02344 −2.82601 −2.59059
1.3 −2.52501 −0.770138 4.37569 1.00000 1.94461 −0.982955 −5.99865 −2.40689 −2.52501
1.4 −2.52501 0.770138 4.37569 1.00000 −1.94461 −0.982955 −5.99865 −2.40689 −2.52501
1.5 −2.20431 −0.249222 2.85898 1.00000 0.549363 −1.77100 −1.89346 −2.93789 −2.20431
1.6 −2.20431 0.249222 2.85898 1.00000 −0.549363 −1.77100 −1.89346 −2.93789 −2.20431
1.7 −2.07191 −3.26613 2.29283 1.00000 6.76715 4.59172 −0.606714 7.66762 −2.07191
1.8 −2.07191 3.26613 2.29283 1.00000 −6.76715 4.59172 −0.606714 7.66762 −2.07191
1.9 −1.51649 −1.73391 0.299748 1.00000 2.62945 3.08104 2.57842 0.00642818 −1.51649
1.10 −1.51649 1.73391 0.299748 1.00000 −2.62945 3.08104 2.57842 0.00642818 −1.51649
1.11 −1.45482 −2.53218 0.116490 1.00000 3.68385 −0.554427 2.74016 3.41192 −1.45482
1.12 −1.45482 2.53218 0.116490 1.00000 −3.68385 −0.554427 2.74016 3.41192 −1.45482
1.13 −1.21372 −0.902032 −0.526895 1.00000 1.09481 5.17931 3.06693 −2.18634 −1.21372
1.14 −1.21372 0.902032 −0.526895 1.00000 −1.09481 5.17931 3.06693 −2.18634 −1.21372
1.15 −0.905885 −1.83878 −1.17937 1.00000 1.66573 −3.86870 2.88015 0.381122 −0.905885
1.16 −0.905885 1.83878 −1.17937 1.00000 −1.66573 −3.86870 2.88015 0.381122 −0.905885
1.17 −0.754060 −2.98611 −1.43139 1.00000 2.25171 −0.705491 2.58748 5.91687 −0.754060
1.18 −0.754060 2.98611 −1.43139 1.00000 −2.25171 −0.705491 2.58748 5.91687 −0.754060
1.19 −0.0352503 −2.73916 −1.99876 1.00000 0.0965564 3.11573 0.140958 4.50302 −0.0352503
1.20 −0.0352503 2.73916 −1.99876 1.00000 −0.0965564 3.11573 0.140958 4.50302 −0.0352503
See all 48 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.48
Significant digits:
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Atkin-Lehner signs

\( p \) Sign
\(5\) \( -1 \)
\(31\) \( +1 \)

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
31.b odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 4805.2.a.bd ✓ 48
31.b odd 2 1 inner 4805.2.a.bd ✓ 48
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4805.2.a.bd ✓ 48 1.a even 1 1 trivial
4805.2.a.bd ✓ 48 31.b odd 2 1 inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4805))\):

\( T_{2}^{24} - 8 T_{2}^{23} - 8 T_{2}^{22} + 216 T_{2}^{21} - 268 T_{2}^{20} - 2328 T_{2}^{19} + 5336 T_{2}^{18} + \cdots - 2 \) Copy content Toggle raw display
\( T_{3}^{48} - 96 T_{3}^{46} + 4272 T_{3}^{44} - 117000 T_{3}^{42} + 2208336 T_{3}^{40} - 30482944 T_{3}^{38} + \cdots + 51076 \) Copy content Toggle raw display