Properties

Label 1755.2.c.c
Level $1755$
Weight $2$
Character orbit 1755.c
Analytic conductor $14.014$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1755,2,Mod(1054,1755)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1755, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1755.1054");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1755 = 3^{3} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1755.c (of order \(2\), degree \(1\), minimal)

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: no
Analytic conductor: \(14.0137455547\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 22 q^{4}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q - 22 q^{4} + 2 q^{10} + 18 q^{11} - 24 q^{14} + 10 q^{16} + 4 q^{19} - 18 q^{20} + 14 q^{25} + 6 q^{26} - 32 q^{29} + 42 q^{34} - 8 q^{35} - 14 q^{40} + 94 q^{41} - 56 q^{44} - 26 q^{46} - 50 q^{49} - 20 q^{50} + 14 q^{55} + 108 q^{56} - 68 q^{59} - 26 q^{61} - 12 q^{64} + 2 q^{65} - 26 q^{70} + 54 q^{71} - 48 q^{74} + 54 q^{76} + 6 q^{79} + 2 q^{80} - 8 q^{85} + 72 q^{86} - 140 q^{89} - 2 q^{91} - 16 q^{94} + 8 q^{95}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1054.1 2.74548i 0 −5.53764 2.17097 + 0.535606i 0 3.22219i 9.71252i 0 1.47049 5.96036i
1054.2 2.41139i 0 −3.81481 −2.23354 0.106317i 0 3.03216i 4.37623i 0 −0.256373 + 5.38594i
1054.3 2.16130i 0 −2.67123 −0.878285 2.05636i 0 3.06336i 1.45074i 0 −4.44442 + 1.89824i
1054.4 2.15187i 0 −2.63053 −1.22772 + 1.86888i 0 1.91033i 1.35682i 0 4.02158 + 2.64188i
1054.5 2.02678i 0 −2.10785 2.15690 + 0.589721i 0 3.38762i 0.218585i 0 1.19524 4.37157i
1054.6 1.61293i 0 −0.601541 1.84270 1.26667i 0 2.78276i 2.25562i 0 −2.04305 2.97214i
1054.7 1.55410i 0 −0.415232 0.130512 + 2.23226i 0 3.05332i 2.46289i 0 3.46915 0.202829i
1054.8 1.26785i 0 0.392563 1.19142 1.89222i 0 1.78234i 3.03340i 0 −2.39905 1.51054i
1054.9 0.872948i 0 1.23796 1.62865 1.53215i 0 4.38491i 2.82657i 0 −1.33749 1.42173i
1054.10 0.819591i 0 1.32827 −2.12060 + 0.709260i 0 0.824970i 2.72782i 0 0.581303 + 1.73803i
1054.11 0.347415i 0 1.87930 −2.15064 + 0.612168i 0 0.968821i 1.34773i 0 0.212676 + 0.747163i
1054.12 0.243423i 0 1.94075 −0.510383 + 2.17704i 0 4.88099i 0.959268i 0 0.529942 + 0.124239i
1054.13 0.243423i 0 1.94075 −0.510383 2.17704i 0 4.88099i 0.959268i 0 0.529942 0.124239i
1054.14 0.347415i 0 1.87930 −2.15064 0.612168i 0 0.968821i 1.34773i 0 0.212676 0.747163i
1054.15 0.819591i 0 1.32827 −2.12060 0.709260i 0 0.824970i 2.72782i 0 0.581303 1.73803i
1054.16 0.872948i 0 1.23796 1.62865 + 1.53215i 0 4.38491i 2.82657i 0 −1.33749 + 1.42173i
1054.17 1.26785i 0 0.392563 1.19142 + 1.89222i 0 1.78234i 3.03340i 0 −2.39905 + 1.51054i
1054.18 1.55410i 0 −0.415232 0.130512 2.23226i 0 3.05332i 2.46289i 0 3.46915 + 0.202829i
1054.19 1.61293i 0 −0.601541 1.84270 + 1.26667i 0 2.78276i 2.25562i 0 −2.04305 + 2.97214i
1054.20 2.02678i 0 −2.10785 2.15690 0.589721i 0 3.38762i 0.218585i 0 1.19524 + 4.37157i
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1054.24
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1755.2.c.c yes 24
3.b odd 2 1 1755.2.c.b 24
5.b even 2 1 inner 1755.2.c.c yes 24
5.c odd 4 1 8775.2.a.cl 12
5.c odd 4 1 8775.2.a.cm 12
15.d odd 2 1 1755.2.c.b 24
15.e even 4 1 8775.2.a.ck 12
15.e even 4 1 8775.2.a.cn 12
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1755.2.c.b 24 3.b odd 2 1
1755.2.c.b 24 15.d odd 2 1
1755.2.c.c yes 24 1.a even 1 1 trivial
1755.2.c.c yes 24 5.b even 2 1 inner
8775.2.a.ck 12 15.e even 4 1
8775.2.a.cl 12 5.c odd 4 1
8775.2.a.cm 12 5.c odd 4 1
8775.2.a.cn 12 15.e even 4 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(1755, [\chi])\):

\( T_{2}^{24} + 35 T_{2}^{22} + 529 T_{2}^{20} + 4534 T_{2}^{18} + 24322 T_{2}^{16} + 85014 T_{2}^{14} + 195433 T_{2}^{12} + 291375 T_{2}^{10} + 271189 T_{2}^{8} + 146744 T_{2}^{6} + 40572 T_{2}^{4} + 4372 T_{2}^{2} + \cdots + 144 \) Copy content Toggle raw display
\( T_{11}^{12} - 9 T_{11}^{11} - 36 T_{11}^{10} + 550 T_{11}^{9} - 646 T_{11}^{8} - 8896 T_{11}^{7} + 30071 T_{11}^{6} + 7763 T_{11}^{5} - 163498 T_{11}^{4} + 217476 T_{11}^{3} - 13872 T_{11}^{2} - 89152 T_{11} + 12544 \) Copy content Toggle raw display