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Properties

Label 1875.4.a.n
Level $1875$
Weight $4$
Character orbit 1875.a
Self dual yes
Analytic conductor $110.629$
Analytic rank $0$
Dimension $32$
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 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);
 
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")
 
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 = [32,8,96] 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: \(32\)
Twist minimal: no (minimal twist has level 75)
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.

\(\operatorname{Tr}(f)(q) = \) \( 32 q + 8 q^{2} + 96 q^{3} + 144 q^{4} + 24 q^{6} + 56 q^{7} + 96 q^{8} + 288 q^{9} + 28 q^{11} + 432 q^{12} + 208 q^{13} + 66 q^{14} + 740 q^{16} + 272 q^{17} + 72 q^{18} + 316 q^{19} + 168 q^{21} + 564 q^{22}+ \cdots + 252 q^{99}+O(q^{100}) \) 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 −5.53400 3.00000 22.6251 0 −16.6020 25.0469 −80.9353 9.00000 0
1.2 −5.19838 3.00000 19.0232 0 −15.5951 2.85806 −57.3028 9.00000 0
1.3 −4.79737 3.00000 15.0148 0 −14.3921 4.05683 −33.6524 9.00000 0
1.4 −4.38642 3.00000 11.2407 0 −13.1593 −28.2575 −14.2151 9.00000 0
1.5 −4.22975 3.00000 9.89076 0 −12.6892 16.6083 −7.99742 9.00000 0
1.6 −4.09436 3.00000 8.76378 0 −12.2831 −3.23603 −3.12717 9.00000 0
1.7 −3.75359 3.00000 6.08945 0 −11.2608 −23.9377 7.17142 9.00000 0
1.8 −3.13541 3.00000 1.83080 0 −9.40623 36.1544 19.3430 9.00000 0
1.9 −2.52100 3.00000 −1.64455 0 −7.56301 −17.6747 24.3139 9.00000 0
1.10 −2.22454 3.00000 −3.05143 0 −6.67362 13.2560 24.5843 9.00000 0
1.11 −1.86274 3.00000 −4.53019 0 −5.58823 −5.91042 23.3405 9.00000 0
1.12 −1.70598 3.00000 −5.08962 0 −5.11795 −2.02294 22.3307 9.00000 0
1.13 −1.04611 3.00000 −6.90564 0 −3.13834 −25.7467 15.5930 9.00000 0
1.14 −0.655280 3.00000 −7.57061 0 −1.96584 35.0184 10.2031 9.00000 0
1.15 −0.627264 3.00000 −7.60654 0 −1.88179 −11.1579 9.78943 9.00000 0
1.16 −0.617344 3.00000 −7.61889 0 −1.85203 24.8866 9.64222 9.00000 0
1.17 1.01336 3.00000 −6.97309 0 3.04009 13.5310 −15.1732 9.00000 0
1.18 1.27670 3.00000 −6.37004 0 3.83010 −32.4814 −18.3462 9.00000 0
1.19 1.52908 3.00000 −5.66192 0 4.58724 −11.0201 −20.8901 9.00000 0
1.20 1.96152 3.00000 −4.15244 0 5.88456 −24.0186 −23.8373 9.00000 0
See all 32 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.32
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.n 32
5.b even 2 1 1875.4.a.m 32
25.f odd 20 2 75.4.i.a ✓ 64
75.l even 20 2 225.4.m.c 64
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
75.4.i.a ✓ 64 25.f odd 20 2
225.4.m.c 64 75.l even 20 2
1875.4.a.m 32 5.b even 2 1
1875.4.a.n 32 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{32} - 8 T_{2}^{31} - 168 T_{2}^{30} + 1440 T_{2}^{29} + 12295 T_{2}^{28} - 115354 T_{2}^{27} + \cdots + 25165447561216 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1875))\). Copy content Toggle raw display