Properties

Label 1875.4.a.l
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 / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1875,4,Mod(1,1875)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
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")
 
//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

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
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 dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + q^{2} + 72 q^{3} + 133 q^{4} + 3 q^{6} + 62 q^{7} + 27 q^{8} + 216 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q + q^{2} + 72 q^{3} + 133 q^{4} + 3 q^{6} + 62 q^{7} + 27 q^{8} + 216 q^{9} + 96 q^{11} + 399 q^{12} + 156 q^{13} + 92 q^{14} + 845 q^{16} - 46 q^{17} + 9 q^{18} + 182 q^{19} + 186 q^{21} + 158 q^{22} - 286 q^{23} + 81 q^{24} + 478 q^{26} + 648 q^{27} + 701 q^{28} + 1144 q^{29} + 64 q^{31} + 1212 q^{32} + 288 q^{33} + 961 q^{34} + 1197 q^{36} + 762 q^{37} + 474 q^{38} + 468 q^{39} + 1074 q^{41} + 276 q^{42} + 460 q^{43} + 319 q^{44} + 459 q^{46} - 960 q^{47} + 2535 q^{48} + 2680 q^{49} - 138 q^{51} + 2969 q^{52} + 914 q^{53} + 27 q^{54} + 1680 q^{56} + 546 q^{57} + 208 q^{58} + 208 q^{59} + 3520 q^{61} + 334 q^{62} + 558 q^{63} + 5747 q^{64} + 474 q^{66} + 154 q^{67} - 5727 q^{68} - 858 q^{69} - 252 q^{71} + 243 q^{72} + 4414 q^{73} + 5637 q^{74} + 627 q^{76} + 2344 q^{77} + 1434 q^{78} + 1110 q^{79} + 1944 q^{81} + 3714 q^{82} - 1488 q^{83} + 2103 q^{84} + 3036 q^{86} + 3432 q^{87} + 3947 q^{88} + 3402 q^{89} + 3504 q^{91} - 11163 q^{92} + 192 q^{93} + 3408 q^{94} + 3636 q^{96} + 534 q^{97} + 2244 q^{98} + 864 q^{99}+O(q^{100}) \) 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.

comment: embeddings in the coefficient field
 
gp: mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −5.46877 3.00000 21.9074 0 −16.4063 −12.3964 −76.0564 9.00000 0
1.2 −5.18816 3.00000 18.9170 0 −15.5645 32.8379 −56.6394 9.00000 0
1.3 −5.02516 3.00000 17.2522 0 −15.0755 −20.3527 −46.4938 9.00000 0
1.4 −4.60577 3.00000 13.2131 0 −13.8173 33.5484 −24.0102 9.00000 0
1.5 −3.84470 3.00000 6.78175 0 −11.5341 −25.3925 4.68382 9.00000 0
1.6 −3.80799 3.00000 6.50079 0 −11.4240 −18.9068 5.70897 9.00000 0
1.7 −3.31176 3.00000 2.96774 0 −9.93527 17.0520 16.6656 9.00000 0
1.8 −3.24482 3.00000 2.52885 0 −9.73446 6.19089 17.7529 9.00000 0
1.9 −2.12561 3.00000 −3.48177 0 −6.37684 8.29876 24.4058 9.00000 0
1.10 −0.848785 3.00000 −7.27956 0 −2.54636 4.78585 12.9691 9.00000 0
1.11 −0.487528 3.00000 −7.76232 0 −1.46258 −9.19148 7.68457 9.00000 0
1.12 −0.382314 3.00000 −7.85384 0 −1.14694 −13.0193 6.06115 9.00000 0
1.13 0.234134 3.00000 −7.94518 0 0.702403 −2.94104 −3.73331 9.00000 0
1.14 0.896911 3.00000 −7.19555 0 2.69073 28.1780 −13.6291 9.00000 0
1.15 1.22991 3.00000 −6.48731 0 3.68974 22.2749 −17.8181 9.00000 0
1.16 2.67175 3.00000 −0.861747 0 8.01525 25.7294 −23.6764 9.00000 0
1.17 2.99444 3.00000 0.966662 0 8.98332 −20.0639 −21.0609 9.00000 0
1.18 2.99872 3.00000 0.992297 0 8.99615 −35.4081 −21.0141 9.00000 0
1.19 3.33280 3.00000 3.10756 0 9.99840 15.5967 −16.3055 9.00000 0
1.20 3.88504 3.00000 7.09353 0 11.6551 −27.2564 −3.52166 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.l yes 24
5.b even 2 1 1875.4.a.k 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1875.4.a.k 24 5.b even 2 1
1875.4.a.l yes 24 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{24} - T_{2}^{23} - 162 T_{2}^{22} + 148 T_{2}^{21} + 11359 T_{2}^{20} - 9556 T_{2}^{19} - 452004 T_{2}^{18} + 354292 T_{2}^{17} + 11247807 T_{2}^{16} - 8329949 T_{2}^{15} - 181797882 T_{2}^{14} + \cdots + 2143086336 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1875))\). Copy content Toggle raw display