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Properties

Label 9065.2.a.w
Level $9065$
Weight $2$
Character orbit 9065.a
Self dual yes
Analytic conductor $72.384$
Analytic rank $1$
Dimension $21$
CM no
Inner twists $1$

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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] = [9065,2,Mod(1,9065)] 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("9065.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9065, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 9065 = 5 \cdot 7^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9065.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [21,-3,1,13,-21,6,0,-9,12,3,-5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(72.3843894323\)
Analytic rank: \(1\)
Dimension: \(21\)
Twist minimal: no (minimal twist has level 1295)
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.

\(\operatorname{Tr}(f)(q) = \) \( 21 q - 3 q^{2} + q^{3} + 13 q^{4} - 21 q^{5} + 6 q^{6} - 9 q^{8} + 12 q^{9} + 3 q^{10} - 5 q^{11} + 4 q^{12} - q^{13} - q^{15} + q^{16} - 2 q^{17} - 11 q^{18} + 12 q^{19} - 13 q^{20} - 10 q^{22} - 20 q^{23}+ \cdots - 7 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −2.59422 2.52455 4.73000 −1.00000 −6.54925 0 −7.08224 3.37336 2.59422
1.2 −2.52298 −2.20843 4.36545 −1.00000 5.57183 0 −5.96798 1.87716 2.52298
1.3 −2.33780 −1.79577 3.46531 −1.00000 4.19814 0 −3.42560 0.224772 2.33780
1.4 −2.10060 −0.249801 2.41254 −1.00000 0.524733 0 −0.866579 −2.93760 2.10060
1.5 −1.69924 1.96177 0.887425 −1.00000 −3.33353 0 1.89053 0.848558 1.69924
1.6 −1.30753 2.06355 −0.290371 −1.00000 −2.69815 0 2.99472 1.25823 1.30753
1.7 −1.19691 −0.187938 −0.567401 −1.00000 0.224945 0 3.07295 −2.96468 1.19691
1.8 −1.15401 −1.86626 −0.668271 −1.00000 2.15368 0 3.07920 0.482939 1.15401
1.9 −0.920498 0.0591591 −1.15268 −1.00000 −0.0544558 0 2.90204 −2.99650 0.920498
1.10 −0.660099 −3.19813 −1.56427 −1.00000 2.11109 0 2.35277 7.22806 0.660099
1.11 0.139129 3.07995 −1.98064 −1.00000 0.428509 0 −0.553821 6.48611 −0.139129
1.12 0.228803 −0.669752 −1.94765 −1.00000 −0.153241 0 −0.903235 −2.55143 −0.228803
1.13 0.479405 1.37025 −1.77017 −1.00000 0.656906 0 −1.80744 −1.12241 −0.479405
1.14 0.684392 1.13018 −1.53161 −1.00000 0.773487 0 −2.41700 −1.72269 −0.684392
1.15 0.872576 −2.26649 −1.23861 −1.00000 −1.97769 0 −2.82593 2.13699 −0.872576
1.16 0.961439 −2.34496 −1.07563 −1.00000 −2.25454 0 −2.95704 2.49886 −0.961439
1.17 1.57614 3.08549 0.484230 −1.00000 4.86317 0 −2.38907 6.52024 −1.57614
1.18 1.90284 0.799527 1.62079 −1.00000 1.52137 0 −0.721581 −2.36076 −1.90284
1.19 2.00155 −1.66611 2.00621 −1.00000 −3.33480 0 0.0124273 −0.224087 −2.00155
1.20 2.23673 −0.0152947 3.00296 −1.00000 −0.0342102 0 2.24336 −2.99977 −2.23673
See all 21 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.21
Significant digits:
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Atkin-Lehner signs

\( p \) Sign
\(5\) \( +1 \)
\(7\) \( +1 \)
\(37\) \( +1 \)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 9065.2.a.w 21
7.b odd 2 1 9065.2.a.v 21
7.c even 3 2 1295.2.j.b ✓ 42
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1295.2.j.b ✓ 42 7.c even 3 2
9065.2.a.v 21 7.b odd 2 1
9065.2.a.w 21 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(9065))\):

\( T_{2}^{21} + 3 T_{2}^{20} - 23 T_{2}^{19} - 71 T_{2}^{18} + 217 T_{2}^{17} + 696 T_{2}^{16} - 1085 T_{2}^{15} + \cdots - 17 \) Copy content Toggle raw display
\( T_{3}^{21} - T_{3}^{20} - 37 T_{3}^{19} + 33 T_{3}^{18} + 569 T_{3}^{17} - 450 T_{3}^{16} - 4746 T_{3}^{15} + \cdots + 1 \) Copy content Toggle raw display
\( T_{11}^{21} + 5 T_{11}^{20} - 105 T_{11}^{19} - 557 T_{11}^{18} + 4212 T_{11}^{17} + 24857 T_{11}^{16} + \cdots + 20206416 \) Copy content Toggle raw display