Properties

Label 4375.2.a.p
Level $4375$
Weight $2$
Character orbit 4375.a
Self dual yes
Analytic conductor $34.935$
Analytic rank $0$
Dimension $28$
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] = [4375,2,Mod(1,4375)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4375, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4375.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4375 = 5^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4375.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: \(34.9345508843\)
Analytic rank: \(0\)
Dimension: \(28\)
Twist minimal: no (minimal twist has level 175)
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.

\(\operatorname{Tr}(f)(q) = \) \( 28 q + 8 q^{2} + 8 q^{3} + 24 q^{4} - 28 q^{7} + 24 q^{8} + 22 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 28 q + 8 q^{2} + 8 q^{3} + 24 q^{4} - 28 q^{7} + 24 q^{8} + 22 q^{9} - 16 q^{11} + 24 q^{12} + 16 q^{13} - 8 q^{14} + 24 q^{16} + 40 q^{17} + 24 q^{18} + 4 q^{19} - 8 q^{21} + 16 q^{22} + 32 q^{23} + 14 q^{24} + 6 q^{26} + 32 q^{27} - 24 q^{28} - 24 q^{29} + 6 q^{31} + 56 q^{32} + 28 q^{33} + 18 q^{36} + 32 q^{37} + 40 q^{38} - 28 q^{39} + 2 q^{41} + 16 q^{43} - 26 q^{44} - 12 q^{46} + 26 q^{47} + 46 q^{48} + 28 q^{49} - 22 q^{51} + 28 q^{52} + 60 q^{53} + 38 q^{54} - 24 q^{56} + 76 q^{57} + 16 q^{58} + 8 q^{59} + 18 q^{61} + 34 q^{62} - 22 q^{63} + 28 q^{64} + 38 q^{66} + 24 q^{67} + 62 q^{68} + 14 q^{69} - 54 q^{71} + 40 q^{72} + 46 q^{73} - 30 q^{74} + 26 q^{76} + 16 q^{77} + 32 q^{78} - 30 q^{79} + 4 q^{81} + 22 q^{82} + 60 q^{83} - 24 q^{84} - 10 q^{86} + 18 q^{87} + 16 q^{88} + 6 q^{89} - 16 q^{91} + 72 q^{92} + 48 q^{93} + 86 q^{94} + 106 q^{96} + 70 q^{97} + 8 q^{98} - 30 q^{99}+O(q^{100}) \) 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 −2.39162 2.75183 3.71983 0 −6.58132 −1.00000 −4.11316 4.57256 0
1.2 −2.25420 −0.437412 3.08142 0 0.986013 −1.00000 −2.43773 −2.80867 0
1.3 −2.22283 0.876253 2.94096 0 −1.94776 −1.00000 −2.09160 −2.23218 0
1.4 −2.15723 −0.859279 2.65366 0 1.85367 −1.00000 −1.41009 −2.26164 0
1.5 −1.59572 2.59518 0.546330 0 −4.14119 −1.00000 2.31965 3.73495 0
1.6 −1.50576 −0.541589 0.267313 0 0.815502 −1.00000 2.60901 −2.70668 0
1.7 −1.14814 2.58276 −0.681763 0 −2.96538 −1.00000 3.07905 3.67063 0
1.8 −1.08354 −2.69351 −0.825936 0 2.91854 −1.00000 3.06202 4.25502 0
1.9 −0.953107 −1.09278 −1.09159 0 1.04154 −1.00000 2.94661 −1.80582 0
1.10 −0.775732 1.73672 −1.39824 0 −1.34723 −1.00000 2.63612 0.0162108 0
1.11 −0.407806 0.904287 −1.83369 0 −0.368774 −1.00000 1.56340 −2.18226 0
1.12 −0.392266 −2.78480 −1.84613 0 1.09238 −1.00000 1.50871 4.75511 0
1.13 0.198876 1.54520 −1.96045 0 0.307303 −1.00000 −0.787638 −0.612360 0
1.14 0.237222 −2.06682 −1.94373 0 −0.490294 −1.00000 −0.935537 1.27174 0
1.15 0.429002 0.963349 −1.81596 0 0.413279 −1.00000 −1.63705 −2.07196 0
1.16 0.840072 −0.242722 −1.29428 0 −0.203904 −1.00000 −2.76743 −2.94109 0
1.17 1.02774 2.86976 −0.943758 0 2.94936 −1.00000 −3.02541 5.23555 0
1.18 1.08158 3.19566 −0.830195 0 3.45635 −1.00000 −3.06107 7.21224 0
1.19 1.18550 −1.73464 −0.594585 0 −2.05642 −1.00000 −3.07589 0.00897058 0
1.20 1.25752 −0.637250 −0.418653 0 −0.801353 −1.00000 −3.04150 −2.59391 0
See all 28 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.28
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(5\) \(-1\)
\(7\) \(1\)

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 4375.2.a.p 28
5.b even 2 1 4375.2.a.o 28
25.d even 5 2 875.2.h.d 56
25.e even 10 2 875.2.h.e 56
25.f odd 20 2 175.2.n.a 56
25.f odd 20 2 875.2.n.c 56
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
175.2.n.a 56 25.f odd 20 2
875.2.h.d 56 25.d even 5 2
875.2.h.e 56 25.e even 10 2
875.2.n.c 56 25.f odd 20 2
4375.2.a.o 28 5.b even 2 1
4375.2.a.p 28 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(4375))\):

\( T_{2}^{28} - 8 T_{2}^{27} - 8 T_{2}^{26} + 216 T_{2}^{25} - 258 T_{2}^{24} - 2408 T_{2}^{23} + 5326 T_{2}^{22} + 14012 T_{2}^{21} - 45273 T_{2}^{20} - 42344 T_{2}^{19} + 220154 T_{2}^{18} + 38276 T_{2}^{17} - 670685 T_{2}^{16} + \cdots + 205 \) Copy content Toggle raw display
\( T_{3}^{28} - 8 T_{3}^{27} - 21 T_{3}^{26} + 312 T_{3}^{25} - 84 T_{3}^{24} - 5166 T_{3}^{23} + 6774 T_{3}^{22} + 47508 T_{3}^{21} - 91708 T_{3}^{20} - 266884 T_{3}^{19} + 650500 T_{3}^{18} + 950622 T_{3}^{17} - 2828120 T_{3}^{16} + \cdots + 11321 \) Copy content Toggle raw display