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Properties

Label 1890.2.bk.b
Level $1890$
Weight $2$
Character orbit 1890.bk
Analytic conductor $15.092$
Analytic rank $0$
Dimension $28$
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] = [1890,2,Mod(341,1890)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1890, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5, 0, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1890.341");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1890.bk (of order \(6\), degree \(2\), 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: \(15.0917259820\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(14\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 630)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 28 q - 28 q^{4} + 14 q^{5} + 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 28 q - 28 q^{4} + 14 q^{5} + 8 q^{7} + 28 q^{16} - 6 q^{17} - 6 q^{19} - 14 q^{20} - 6 q^{22} - 30 q^{23} - 14 q^{25} + 12 q^{26} - 8 q^{28} + 4 q^{35} + 4 q^{37} + 6 q^{38} + 18 q^{41} + 28 q^{43} - 18 q^{46} - 60 q^{47} - 20 q^{49} - 42 q^{53} + 6 q^{58} + 48 q^{59} - 12 q^{62} - 28 q^{64} + 80 q^{67} + 6 q^{68} + 6 q^{70} + 6 q^{73} + 6 q^{76} + 18 q^{77} - 4 q^{79} + 14 q^{80} + 24 q^{82} - 18 q^{83} + 6 q^{85} + 96 q^{86} + 6 q^{88} + 6 q^{89} + 66 q^{91} + 30 q^{92} + 72 q^{97} - 24 q^{98}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
341.1 − 1.00000i 0 −1.00000 0.500000 + 0.866025i 0 2.48469 − 0.909025i 1.00000i 0 0.866025 − 0.500000i
341.2 − 1.00000i 0 −1.00000 0.500000 + 0.866025i 0 1.55779 + 2.13853i 1.00000i 0 0.866025 − 0.500000i
341.3 1.00000i 0 −1.00000 0.500000 + 0.866025i 0 −2.21694 − 1.44401i − 1.00000i 0 −0.866025 + 0.500000i
341.4 1.00000i 0 −1.00000 0.500000 + 0.866025i 0 0.145275 − 2.64176i − 1.00000i 0 −0.866025 + 0.500000i
341.5 1.00000i 0 −1.00000 0.500000 + 0.866025i 0 2.55256 + 0.696025i − 1.00000i 0 −0.866025 + 0.500000i
341.6 − 1.00000i 0 −1.00000 0.500000 + 0.866025i 0 −0.323069 − 2.62595i 1.00000i 0 0.866025 − 0.500000i
341.7 1.00000i 0 −1.00000 0.500000 + 0.866025i 0 −1.17317 + 2.37143i − 1.00000i 0 −0.866025 + 0.500000i
341.8 − 1.00000i 0 −1.00000 0.500000 + 0.866025i 0 −1.91453 + 1.82609i 1.00000i 0 0.866025 − 0.500000i
341.9 1.00000i 0 −1.00000 0.500000 + 0.866025i 0 0.281867 + 2.63069i − 1.00000i 0 −0.866025 + 0.500000i
341.10 1.00000i 0 −1.00000 0.500000 + 0.866025i 0 2.64078 + 0.162142i − 1.00000i 0 −0.866025 + 0.500000i
341.11 − 1.00000i 0 −1.00000 0.500000 + 0.866025i 0 2.57280 − 0.617016i 1.00000i 0 0.866025 − 0.500000i
341.12 − 1.00000i 0 −1.00000 0.500000 + 0.866025i 0 0.408654 + 2.61400i 1.00000i 0 0.866025 − 0.500000i
341.13 1.00000i 0 −1.00000 0.500000 + 0.866025i 0 −1.96242 − 1.77452i − 1.00000i 0 −0.866025 + 0.500000i
341.14 − 1.00000i 0 −1.00000 0.500000 + 0.866025i 0 −1.05428 − 2.42662i 1.00000i 0 0.866025 − 0.500000i
521.1 1.00000i 0 −1.00000 0.500000 − 0.866025i 0 2.48469 + 0.909025i − 1.00000i 0 0.866025 + 0.500000i
521.2 1.00000i 0 −1.00000 0.500000 − 0.866025i 0 1.55779 − 2.13853i − 1.00000i 0 0.866025 + 0.500000i
521.3 − 1.00000i 0 −1.00000 0.500000 − 0.866025i 0 −2.21694 + 1.44401i 1.00000i 0 −0.866025 − 0.500000i
521.4 − 1.00000i 0 −1.00000 0.500000 − 0.866025i 0 0.145275 + 2.64176i 1.00000i 0 −0.866025 − 0.500000i
521.5 − 1.00000i 0 −1.00000 0.500000 − 0.866025i 0 2.55256 − 0.696025i 1.00000i 0 −0.866025 − 0.500000i
521.6 1.00000i 0 −1.00000 0.500000 − 0.866025i 0 −0.323069 + 2.62595i − 1.00000i 0 0.866025 + 0.500000i
See all 28 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 341.14
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
63.i even 6 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1890.2.bk.b 28
3.b odd 2 1 630.2.bk.b yes 28
7.d odd 6 1 1890.2.t.b 28
9.c even 3 1 630.2.t.b ✓ 28
9.d odd 6 1 1890.2.t.b 28
21.g even 6 1 630.2.t.b ✓ 28
63.i even 6 1 inner 1890.2.bk.b 28
63.t odd 6 1 630.2.bk.b yes 28
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
630.2.t.b ✓ 28 9.c even 3 1
630.2.t.b ✓ 28 21.g even 6 1
630.2.bk.b yes 28 3.b odd 2 1
630.2.bk.b yes 28 63.t odd 6 1
1890.2.t.b 28 7.d odd 6 1
1890.2.t.b 28 9.d odd 6 1
1890.2.bk.b 28 1.a even 1 1 trivial
1890.2.bk.b 28 63.i even 6 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{11}^{28} - 81 T_{11}^{26} + 4191 T_{11}^{24} + 618 T_{11}^{23} - 131338 T_{11}^{22} - 41034 T_{11}^{21} + \cdots + 14197824 \) acting on \(S_{2}^{\mathrm{new}}(1890, [\chi])\). Copy content Toggle raw display