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Properties

Label 1875.4.a.k
Level $1875$
Weight $4$
Character orbit 1875.a
Self dual yes
Analytic conductor $110.629$
Analytic rank $0$
Dimension $24$
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] = [1875,4,Mod(1,1875)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1875, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1875.1"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Level: \( N \) \(=\) \( 1875 = 3 \cdot 5^{4} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1875.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [24,-1,-72] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(110.628581261\)
Analytic rank: \(0\)
Dimension: \(24\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - q^{2} - 72 q^{3} + 133 q^{4} + 3 q^{6} - 62 q^{7} - 27 q^{8} + 216 q^{9} + 96 q^{11} - 399 q^{12} - 156 q^{13} + 92 q^{14} + 845 q^{16} + 46 q^{17} - 9 q^{18} + 182 q^{19} + 186 q^{21} - 158 q^{22}+ \cdots + 864 q^{99}+O(q^{100}) \) 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 −5.63525 −3.00000 23.7560 0 16.9058 12.9594 −88.7893 9.00000 0
1.2 −5.42895 −3.00000 21.4736 0 16.2869 −15.6883 −73.1473 9.00000 0
1.3 −5.20860 −3.00000 19.1295 0 15.6258 −35.1109 −57.9692 9.00000 0
1.4 −4.82486 −3.00000 15.2792 0 14.4746 −14.5960 −35.1213 9.00000 0
1.5 −3.88504 −3.00000 7.09353 0 11.6551 27.2564 3.52166 9.00000 0
1.6 −3.33280 −3.00000 3.10756 0 9.99840 −15.5967 16.3055 9.00000 0
1.7 −2.99872 −3.00000 0.992297 0 8.99615 35.4081 21.0141 9.00000 0
1.8 −2.99444 −3.00000 0.966662 0 8.98332 20.0639 21.0609 9.00000 0
1.9 −2.67175 −3.00000 −0.861747 0 8.01525 −25.7294 23.6764 9.00000 0
1.10 −1.22991 −3.00000 −6.48731 0 3.68974 −22.2749 17.8181 9.00000 0
1.11 −0.896911 −3.00000 −7.19555 0 2.69073 −28.1780 13.6291 9.00000 0
1.12 −0.234134 −3.00000 −7.94518 0 0.702403 2.94104 3.73331 9.00000 0
1.13 0.382314 −3.00000 −7.85384 0 −1.14694 13.0193 −6.06115 9.00000 0
1.14 0.487528 −3.00000 −7.76232 0 −1.46258 9.19148 −7.68457 9.00000 0
1.15 0.848785 −3.00000 −7.27956 0 −2.54636 −4.78585 −12.9691 9.00000 0
1.16 2.12561 −3.00000 −3.48177 0 −6.37684 −8.29876 −24.4058 9.00000 0
1.17 3.24482 −3.00000 2.52885 0 −9.73446 −6.19089 −17.7529 9.00000 0
1.18 3.31176 −3.00000 2.96774 0 −9.93527 −17.0520 −16.6656 9.00000 0
1.19 3.80799 −3.00000 6.50079 0 −11.4240 18.9068 −5.70897 9.00000 0
1.20 3.84470 −3.00000 6.78175 0 −11.5341 25.3925 −4.68382 9.00000 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.24
Significant digits:
Format:

Atkin-Lehner signs

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

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 1875.4.a.k ✓ 24
5.b even 2 1 1875.4.a.l yes 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1875.4.a.k ✓ 24 1.a even 1 1 trivial
1875.4.a.l yes 24 5.b even 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{24} + T_{2}^{23} - 162 T_{2}^{22} - 148 T_{2}^{21} + 11359 T_{2}^{20} + 9556 T_{2}^{19} + \cdots + 2143086336 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1875))\). Copy content Toggle raw display