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Properties

Label 1175.2.c.h
Level $1175$
Weight $2$
Character orbit 1175.c
Analytic conductor $9.382$
Analytic rank $0$
Dimension $26$
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] = [1175,2,Mod(424,1175)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1175, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("1175.424");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1175 = 5^{2} \cdot 47 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1175.c (of order \(2\), degree \(1\), not 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: \(9.38242223750\)
Analytic rank: \(0\)
Dimension: \(26\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 26 q - 40 q^{4} + 10 q^{6} - 54 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 26 q - 40 q^{4} + 10 q^{6} - 54 q^{9} + 18 q^{11} + 8 q^{14} + 68 q^{16} - 32 q^{19} + 52 q^{21} + 16 q^{24} + 6 q^{26} - 20 q^{29} + 30 q^{31} - 2 q^{34} + 114 q^{36} + 4 q^{39} + 48 q^{41} + 12 q^{44} + 100 q^{46} - 78 q^{49} + 18 q^{51} + 68 q^{54} - 18 q^{56} + 50 q^{59} + 44 q^{61} - 106 q^{64} + 4 q^{66} - 10 q^{69} - 12 q^{71} + 98 q^{74} + 126 q^{76} - 74 q^{79} + 98 q^{81} + 4 q^{84} + 6 q^{86} - 64 q^{89} + 24 q^{91} - 22 q^{96} - 72 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
424.1 − 2.74421i − 2.93795i −5.53069 0 −8.06236 3.68590i 9.68894i −5.63156 0
424.2 − 2.70217i 1.87663i −5.30175 0 5.07098 − 0.754185i 8.92190i −0.521743 0
424.3 − 2.63214i 2.36135i −4.92818 0 6.21541 2.69509i 7.70738i −2.57596 0
424.4 − 2.43775i 0.173250i −3.94261 0 0.422339 − 2.26378i 4.73559i 2.96998 0
424.5 − 2.30741i − 2.74069i −3.32413 0 −6.32389 − 4.14817i 3.05531i −4.51138 0
424.6 − 2.09045i 0.807628i −2.36999 0 1.68831 − 0.424369i 0.773439i 2.34774 0
424.7 − 1.63744i 3.34240i −0.681219 0 5.47299 − 0.857318i − 2.15943i −8.17165 0
424.8 − 1.51512i 3.07956i −0.295574 0 4.66590 − 2.65977i − 2.58240i −6.48372 0
424.9 − 1.41853i − 3.19052i −0.0122215 0 −4.52584 4.71614i − 2.81972i −7.17942 0
424.10 − 0.719439i − 2.00949i 1.48241 0 −1.44570 3.86564i − 2.50538i −1.03803 0
424.11 − 0.684957i 1.97644i 1.53083 0 1.35378 4.30619i − 2.41847i −0.906331 0
424.12 − 0.649794i 1.04162i 1.57777 0 0.676842 − 4.46925i − 2.32481i 1.91502 0
424.13 − 0.452387i − 0.461453i 1.79535 0 −0.208755 1.59927i − 1.71697i 2.78706 0
424.14 0.452387i 0.461453i 1.79535 0 −0.208755 − 1.59927i 1.71697i 2.78706 0
424.15 0.649794i − 1.04162i 1.57777 0 0.676842 4.46925i 2.32481i 1.91502 0
424.16 0.684957i − 1.97644i 1.53083 0 1.35378 − 4.30619i 2.41847i −0.906331 0
424.17 0.719439i 2.00949i 1.48241 0 −1.44570 − 3.86564i 2.50538i −1.03803 0
424.18 1.41853i 3.19052i −0.0122215 0 −4.52584 − 4.71614i 2.81972i −7.17942 0
424.19 1.51512i − 3.07956i −0.295574 0 4.66590 2.65977i 2.58240i −6.48372 0
424.20 1.63744i − 3.34240i −0.681219 0 5.47299 0.857318i 2.15943i −8.17165 0
See all 26 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 424.26
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 1175.2.c.h 26
5.b even 2 1 inner 1175.2.c.h 26
5.c odd 4 1 1175.2.a.k ✓ 13
5.c odd 4 1 1175.2.a.l yes 13
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1175.2.a.k ✓ 13 5.c odd 4 1
1175.2.a.l yes 13 5.c odd 4 1
1175.2.c.h 26 1.a even 1 1 trivial
1175.2.c.h 26 5.b even 2 1 inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(1175, [\chi])\):

\( T_{2}^{26} + 46 T_{2}^{24} + 929 T_{2}^{22} + 10833 T_{2}^{20} + 80720 T_{2}^{18} + 401903 T_{2}^{16} + \cdots + 13689 \) Copy content Toggle raw display
\( T_{11}^{13} - 9 T_{11}^{12} - 66 T_{11}^{11} + 781 T_{11}^{10} + 612 T_{11}^{9} - 22396 T_{11}^{8} + \cdots - 162816 \) Copy content Toggle raw display