Properties

Label 1155.2.l.e
Level $1155$
Weight $2$
Character orbit 1155.l
Analytic conductor $9.223$
Analytic rank $0$
Dimension $40$
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] = [1155,2,Mod(1121,1155)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1155.1121");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1155.l (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: \(9.22272143346\)
Analytic rank: \(0\)
Dimension: \(40\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 40 q - 4 q^{2} - 4 q^{3} + 44 q^{4} - 4 q^{6} - 12 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 40 q - 4 q^{2} - 4 q^{3} + 44 q^{4} - 4 q^{6} - 12 q^{8} - 2 q^{9} - 6 q^{11} + 8 q^{12} + 2 q^{15} + 68 q^{16} + 40 q^{18} - 2 q^{21} - 4 q^{22} - 12 q^{24} - 40 q^{25} + 32 q^{27} - 24 q^{29} - 8 q^{31} + 52 q^{32} - 16 q^{33} + 32 q^{34} + 40 q^{35} - 48 q^{37} + 66 q^{39} - 16 q^{41} + 32 q^{44} + 32 q^{48} - 40 q^{49} + 4 q^{50} - 14 q^{51} - 72 q^{54} + 8 q^{55} - 24 q^{57} - 80 q^{58} + 24 q^{60} + 48 q^{62} + 76 q^{64} + 4 q^{65} - 76 q^{66} - 48 q^{67} - 32 q^{68} - 20 q^{69} - 4 q^{70} + 128 q^{72} + 4 q^{75} - 8 q^{77} - 28 q^{78} + 50 q^{81} - 32 q^{82} - 24 q^{83} - 24 q^{84} - 32 q^{87} - 16 q^{88} + 8 q^{90} - 4 q^{91} - 20 q^{93} - 12 q^{95} + 12 q^{96} + 100 q^{97} + 4 q^{98} - 54 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1121.1 −2.79309 0.351991 1.69591i 5.80135 1.00000i −0.983141 + 4.73682i 1.00000i −10.6175 −2.75221 1.19389i 2.79309i
1121.2 −2.79309 0.351991 + 1.69591i 5.80135 1.00000i −0.983141 4.73682i 1.00000i −10.6175 −2.75221 + 1.19389i 2.79309i
1121.3 −2.55898 −0.371837 1.69167i 4.54836 1.00000i 0.951521 + 4.32893i 1.00000i −6.52118 −2.72347 + 1.25805i 2.55898i
1121.4 −2.55898 −0.371837 + 1.69167i 4.54836 1.00000i 0.951521 4.32893i 1.00000i −6.52118 −2.72347 1.25805i 2.55898i
1121.5 −2.21445 1.64596 0.539264i 2.90381 1.00000i −3.64491 + 1.19418i 1.00000i −2.00144 2.41839 1.77522i 2.21445i
1121.6 −2.21445 1.64596 + 0.539264i 2.90381 1.00000i −3.64491 1.19418i 1.00000i −2.00144 2.41839 + 1.77522i 2.21445i
1121.7 −2.04560 −1.22443 1.22506i 2.18447 1.00000i 2.50470 + 2.50597i 1.00000i −0.377355 −0.00153018 + 3.00000i 2.04560i
1121.8 −2.04560 −1.22443 + 1.22506i 2.18447 1.00000i 2.50470 2.50597i 1.00000i −0.377355 −0.00153018 3.00000i 2.04560i
1121.9 −1.88704 1.57144 0.728399i 1.56093 1.00000i −2.96538 + 1.37452i 1.00000i 0.828540 1.93887 2.28928i 1.88704i
1121.10 −1.88704 1.57144 + 0.728399i 1.56093 1.00000i −2.96538 1.37452i 1.00000i 0.828540 1.93887 + 2.28928i 1.88704i
1121.11 −1.80850 −1.28663 + 1.15956i 1.27068 1.00000i 2.32688 2.09707i 1.00000i 1.31898 0.310844 2.98385i 1.80850i
1121.12 −1.80850 −1.28663 1.15956i 1.27068 1.00000i 2.32688 + 2.09707i 1.00000i 1.31898 0.310844 + 2.98385i 1.80850i
1121.13 −1.71054 −0.134822 1.72680i 0.925948 1.00000i 0.230619 + 2.95375i 1.00000i 1.83721 −2.96365 + 0.465620i 1.71054i
1121.14 −1.71054 −0.134822 + 1.72680i 0.925948 1.00000i 0.230619 2.95375i 1.00000i 1.83721 −2.96365 0.465620i 1.71054i
1121.15 −0.805231 −0.972634 + 1.43317i −1.35160 1.00000i 0.783195 1.15404i 1.00000i 2.69881 −1.10797 2.78790i 0.805231i
1121.16 −0.805231 −0.972634 1.43317i −1.35160 1.00000i 0.783195 + 1.15404i 1.00000i 2.69881 −1.10797 + 2.78790i 0.805231i
1121.17 −0.542651 −1.58724 + 0.693309i −1.70553 1.00000i 0.861316 0.376225i 1.00000i 2.01081 2.03865 2.20089i 0.542651i
1121.18 −0.542651 −1.58724 0.693309i −1.70553 1.00000i 0.861316 + 0.376225i 1.00000i 2.01081 2.03865 + 2.20089i 0.542651i
1121.19 0.164753 1.34733 1.08845i −1.97286 1.00000i 0.221976 0.179324i 1.00000i −0.654539 0.630571 2.93298i 0.164753i
1121.20 0.164753 1.34733 + 1.08845i −1.97286 1.00000i 0.221976 + 0.179324i 1.00000i −0.654539 0.630571 + 2.93298i 0.164753i
See all 40 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1121.40
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
33.d even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1155.2.l.e 40
3.b odd 2 1 1155.2.l.f yes 40
11.b odd 2 1 1155.2.l.f yes 40
33.d even 2 1 inner 1155.2.l.e 40
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1155.2.l.e 40 1.a even 1 1 trivial
1155.2.l.e 40 33.d even 2 1 inner
1155.2.l.f yes 40 3.b odd 2 1
1155.2.l.f yes 40 11.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(1155, [\chi])\):

\( T_{2}^{20} + 2 T_{2}^{19} - 29 T_{2}^{18} - 56 T_{2}^{17} + 347 T_{2}^{16} + 634 T_{2}^{15} - 2237 T_{2}^{14} - 3728 T_{2}^{13} + 8561 T_{2}^{12} + 12178 T_{2}^{11} - 20275 T_{2}^{10} - 21856 T_{2}^{9} + 29705 T_{2}^{8} + 19438 T_{2}^{7} + \cdots - 32 \) Copy content Toggle raw display
\( T_{17}^{20} - 121 T_{17}^{18} + 96 T_{17}^{17} + 5899 T_{17}^{16} - 9008 T_{17}^{15} - 146479 T_{17}^{14} + 328436 T_{17}^{13} + 1897072 T_{17}^{12} - 5804480 T_{17}^{11} - 11041120 T_{17}^{10} + 50229300 T_{17}^{9} + \cdots - 18091520 \) Copy content Toggle raw display