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Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [7935,2,Mod(1,7935)] 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("7935.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7935, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 7935 = 3 \cdot 5 \cdot 23^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7935.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [25,1,-25,31,-25,-1,15] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(63.3612940039\)
Analytic rank: \(0\)
Dimension: \(25\)
Twist minimal: no (minimal twist has level 345)
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.

\(\operatorname{Tr}(f)(q) = \) \( 25 q + q^{2} - 25 q^{3} + 31 q^{4} - 25 q^{5} - q^{6} + 15 q^{7} + 3 q^{8} + 25 q^{9} - q^{10} - 15 q^{11} - 31 q^{12} + 24 q^{13} - 5 q^{14} + 25 q^{15} + 39 q^{16} + 6 q^{17} + q^{18} - 13 q^{19}+ \cdots - 15 q^{99}+O(q^{100}) \) 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 −2.70525 −1.00000 5.31837 −1.00000 2.70525 −1.20644 −8.97700 1.00000 2.70525
1.2 −2.56809 −1.00000 4.59508 −1.00000 2.56809 4.04574 −6.66440 1.00000 2.56809
1.3 −2.52606 −1.00000 4.38100 −1.00000 2.52606 3.87823 −6.01456 1.00000 2.52606
1.4 −2.18378 −1.00000 2.76889 −1.00000 2.18378 0.993609 −1.67909 1.00000 2.18378
1.5 −2.08135 −1.00000 2.33203 −1.00000 2.08135 −4.74881 −0.691076 1.00000 2.08135
1.6 −1.81497 −1.00000 1.29411 −1.00000 1.81497 4.23294 1.28116 1.00000 1.81497
1.7 −1.51687 −1.00000 0.300900 −1.00000 1.51687 3.34169 2.57732 1.00000 1.51687
1.8 −1.42787 −1.00000 0.0388086 −1.00000 1.42787 −1.25355 2.80032 1.00000 1.42787
1.9 −1.21553 −1.00000 −0.522493 −1.00000 1.21553 −3.08881 3.06616 1.00000 1.21553
1.10 −0.688592 −1.00000 −1.52584 −1.00000 0.688592 4.50249 2.42787 1.00000 0.688592
1.11 −0.587229 −1.00000 −1.65516 −1.00000 0.587229 −1.98135 2.14642 1.00000 0.587229
1.12 0.0244504 −1.00000 −1.99940 −1.00000 −0.0244504 −1.12043 −0.0977870 1.00000 −0.0244504
1.13 0.137935 −1.00000 −1.98097 −1.00000 −0.137935 −4.46257 −0.549115 1.00000 −0.137935
1.14 0.185184 −1.00000 −1.96571 −1.00000 −0.185184 4.18574 −0.734387 1.00000 −0.185184
1.15 0.535974 −1.00000 −1.71273 −1.00000 −0.535974 1.69269 −1.98993 1.00000 −0.535974
1.16 0.902689 −1.00000 −1.18515 −1.00000 −0.902689 −0.451264 −2.87520 1.00000 −0.902689
1.17 1.28657 −1.00000 −0.344734 −1.00000 −1.28657 0.187319 −3.01667 1.00000 −1.28657
1.18 1.50246 −1.00000 0.257377 −1.00000 −1.50246 4.80829 −2.61822 1.00000 −1.50246
1.19 1.59695 −1.00000 0.550248 −1.00000 −1.59695 −3.15385 −2.31518 1.00000 −1.59695
1.20 1.79106 −1.00000 1.20789 −1.00000 −1.79106 4.79732 −1.41871 1.00000 −1.79106
See all 25 embeddings
\(n\): e.g. 2-40 or 80-90
Embeddings: e.g. 1-3 or 1.25
Significant digits:
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Atkin-Lehner signs

\( p \) Sign
\(3\) \( +1 \)
\(5\) \( +1 \)
\(23\) \( -1 \)

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 7935.2.a.bt 25
23.b odd 2 1 7935.2.a.bu 25
23.d odd 22 2 345.2.m.d ✓ 50
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
345.2.m.d ✓ 50 23.d odd 22 2
7935.2.a.bt 25 1.a even 1 1 trivial
7935.2.a.bu 25 23.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(7935))\):

\( T_{2}^{25} - T_{2}^{24} - 40 T_{2}^{23} + 38 T_{2}^{22} + 696 T_{2}^{21} - 626 T_{2}^{20} - 6918 T_{2}^{19} + \cdots + 23 \) Copy content Toggle raw display
\( T_{7}^{25} - 15 T_{7}^{24} - 21 T_{7}^{23} + 1318 T_{7}^{22} - 3341 T_{7}^{21} - 46190 T_{7}^{20} + \cdots - 564517888 \) Copy content Toggle raw display
\( T_{11}^{25} + 15 T_{11}^{24} - 80 T_{11}^{23} - 2221 T_{11}^{22} - 1858 T_{11}^{21} + \cdots - 456373351424 \) Copy content Toggle raw display