Properties

Label 4527.2.a.o
Level $4527$
Weight $2$
Character orbit 4527.a
Self dual yes
Analytic conductor $36.148$
Analytic rank $0$
Dimension $26$
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] = [4527,2,Mod(1,4527)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4527, 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("4527.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4527 = 3^{2} \cdot 503 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4527.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: \(36.1482769950\)
Analytic rank: \(0\)
Dimension: \(26\)
Twist minimal: no (minimal twist has level 503)
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.

\(\operatorname{Tr}(f)(q) = \) \( 26 q - 4 q^{2} + 36 q^{4} - 9 q^{5} + 11 q^{7} - 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 26 q - 4 q^{2} + 36 q^{4} - 9 q^{5} + 11 q^{7} - 18 q^{8} + 4 q^{10} + 17 q^{11} + 14 q^{13} - q^{14} + 48 q^{16} - 17 q^{17} - 22 q^{19} + 19 q^{20} + 38 q^{22} - 27 q^{23} + 93 q^{25} - q^{26} - 9 q^{28} - 13 q^{29} + 26 q^{31} - 5 q^{32} - 32 q^{34} + 22 q^{35} + 55 q^{37} + 24 q^{38} - 7 q^{40} - 24 q^{41} + 20 q^{43} + 27 q^{44} + 6 q^{46} + 25 q^{47} + 65 q^{49} + 16 q^{50} + 32 q^{52} - 30 q^{53} + 25 q^{55} - 3 q^{56} + 58 q^{58} + 26 q^{59} + 15 q^{61} + 12 q^{62} + 44 q^{64} - 20 q^{65} - 20 q^{67} + 4 q^{68} + 2 q^{70} + 35 q^{71} + 38 q^{73} + 59 q^{74} - 42 q^{76} + 6 q^{77} + 21 q^{79} + 100 q^{80} - 59 q^{82} + 48 q^{83} + 6 q^{85} + 7 q^{86} + 106 q^{88} + 5 q^{89} - 24 q^{91} - 26 q^{92} - 22 q^{94} - 43 q^{95} + 142 q^{97} + 38 q^{98}+O(q^{100}) \) 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 −2.71305 0 5.36063 1.98731 0 2.61319 −9.11755 0 −5.39167
1.2 −2.66972 0 5.12740 −2.58453 0 −2.90918 −8.34929 0 6.89997
1.3 −2.58315 0 4.67265 4.14994 0 −3.36863 −6.90384 0 −10.7199
1.4 −2.45386 0 4.02143 −1.44250 0 0.736665 −4.96031 0 3.53970
1.5 −2.36292 0 3.58340 −0.763844 0 −0.178001 −3.74145 0 1.80490
1.6 −2.34577 0 3.50263 2.04978 0 4.12271 −3.52482 0 −4.80830
1.7 −1.88946 0 1.57004 −3.67682 0 1.62501 0.812389 0 6.94719
1.8 −1.81497 0 1.29413 −2.10638 0 1.73516 1.28114 0 3.82302
1.9 −1.61798 0 0.617860 −3.34245 0 −5.14301 2.23628 0 5.40802
1.10 −1.26316 0 −0.404427 4.34050 0 1.70318 3.03718 0 −5.48274
1.11 −0.738482 0 −1.45464 −3.79116 0 4.03115 2.55119 0 2.79970
1.12 −0.477293 0 −1.77219 0.869095 0 5.04945 1.80044 0 −0.414813
1.13 −0.342177 0 −1.88292 −4.14215 0 −0.810419 1.32864 0 1.41735
1.14 0.328801 0 −1.89189 3.16539 0 −3.22876 −1.27966 0 1.04078
1.15 0.349081 0 −1.87814 −1.36534 0 −0.0430977 −1.35379 0 −0.476616
1.16 0.425199 0 −1.81921 3.04539 0 0.946556 −1.62392 0 1.29490
1.17 0.462244 0 −1.78633 −1.15565 0 −1.19216 −1.75021 0 −0.534193
1.18 1.28997 0 −0.335977 −3.81229 0 4.19464 −3.01334 0 −4.91774
1.19 1.43135 0 0.0487521 −1.62138 0 3.43484 −2.79291 0 −2.32076
1.20 1.44158 0 0.0781455 −1.16845 0 −5.22170 −2.77050 0 −1.68442
See all 26 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.26
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \(-1\)
\(503\) \(1\)

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 4527.2.a.o 26
3.b odd 2 1 503.2.a.f 26
12.b even 2 1 8048.2.a.u 26
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
503.2.a.f 26 3.b odd 2 1
4527.2.a.o 26 1.a even 1 1 trivial
8048.2.a.u 26 12.b even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4527))\):

\( T_{2}^{26} + 4 T_{2}^{25} - 36 T_{2}^{24} - 154 T_{2}^{23} + 554 T_{2}^{22} + 2577 T_{2}^{21} - 4772 T_{2}^{20} - 24652 T_{2}^{19} + 25321 T_{2}^{18} + 149131 T_{2}^{17} - 86017 T_{2}^{16} - 595540 T_{2}^{15} + 189834 T_{2}^{14} + \cdots - 1583 \) Copy content Toggle raw display
\( T_{5}^{26} + 9 T_{5}^{25} - 71 T_{5}^{24} - 873 T_{5}^{23} + 1333 T_{5}^{22} + 35769 T_{5}^{21} + 27305 T_{5}^{20} - 795330 T_{5}^{19} - 1730386 T_{5}^{18} + 10082887 T_{5}^{17} + 35969747 T_{5}^{16} + \cdots + 7351042048 \) Copy content Toggle raw display
\( T_{7}^{26} - 11 T_{7}^{25} - 63 T_{7}^{24} + 1107 T_{7}^{23} + 43 T_{7}^{22} - 44446 T_{7}^{21} + 93217 T_{7}^{20} + 898238 T_{7}^{19} - 3273637 T_{7}^{18} - 9066021 T_{7}^{17} + 53508259 T_{7}^{16} + \cdots + 5803441 \) Copy content Toggle raw display