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Properties

Label 1890.2.t.b
Level $1890$
Weight $2$
Character orbit 1890.t
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(1151,1890)]
 
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, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1890.1151");
 
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.t (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.

\(\operatorname{Tr}(f)(q) = \) \( 28 q + 14 q^{4} + 28 q^{5} - 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 28 q + 14 q^{4} + 28 q^{5} - 4 q^{7} - 6 q^{14} - 14 q^{16} + 6 q^{17} - 6 q^{19} + 14 q^{20} - 6 q^{22} + 28 q^{25} - 12 q^{26} - 8 q^{28} - 12 q^{31} - 4 q^{35} + 4 q^{37} + 12 q^{38} - 18 q^{41} + 28 q^{43} - 18 q^{46} - 30 q^{47} - 14 q^{49} + 42 q^{53} - 6 q^{56} - 12 q^{58} + 24 q^{59} + 24 q^{61} + 12 q^{62} - 28 q^{64} - 40 q^{67} + 12 q^{68} - 6 q^{70} + 6 q^{73} - 6 q^{76} + 24 q^{77} + 2 q^{79} - 14 q^{80} + 24 q^{82} + 18 q^{83} + 6 q^{85} - 12 q^{88} - 6 q^{89} + 66 q^{91} + 30 q^{92} + 42 q^{94} - 6 q^{95} - 72 q^{97} + 24 q^{98}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1151.1 −0.866025 − 0.500000i 0 0.500000 + 0.866025i 1.00000 0 −0.555567 − 2.58676i − 1.00000i 0 −0.866025 − 0.500000i
1151.2 −0.866025 − 0.500000i 0 0.500000 + 0.866025i 1.00000 0 −2.36047 − 1.19507i − 1.00000i 0 −0.866025 − 0.500000i
1151.3 −0.866025 − 0.500000i 0 0.500000 + 0.866025i 1.00000 0 −0.673503 + 2.55859i − 1.00000i 0 −0.866025 − 0.500000i
1151.4 −0.866025 − 0.500000i 0 0.500000 + 0.866025i 1.00000 0 −1.17997 + 2.36805i − 1.00000i 0 −0.866025 − 0.500000i
1151.5 −0.866025 − 0.500000i 0 0.500000 + 0.866025i 1.00000 0 2.13731 + 1.55945i − 1.00000i 0 −0.866025 − 0.500000i
1151.6 −0.866025 − 0.500000i 0 0.500000 + 0.866025i 1.00000 0 2.64030 + 0.169721i − 1.00000i 0 −0.866025 − 0.500000i
1151.7 −0.866025 − 0.500000i 0 0.500000 + 0.866025i 1.00000 0 −0.142082 − 2.64193i − 1.00000i 0 −0.866025 − 0.500000i
1151.8 0.866025 + 0.500000i 0 0.500000 + 0.866025i 1.00000 0 −1.57438 − 2.12634i 1.00000i 0 0.866025 + 0.500000i
1151.9 0.866025 + 0.500000i 0 0.500000 + 0.866025i 1.00000 0 2.05946 + 1.66090i 1.00000i 0 0.866025 + 0.500000i
1151.10 0.866025 + 0.500000i 0 0.500000 + 0.866025i 1.00000 0 2.53870 − 0.744985i 1.00000i 0 0.866025 + 0.500000i
1151.11 0.866025 + 0.500000i 0 0.500000 + 0.866025i 1.00000 0 −2.11261 − 1.59276i 1.00000i 0 0.866025 + 0.500000i
1151.12 0.866025 + 0.500000i 0 0.500000 + 0.866025i 1.00000 0 −1.82075 + 1.91960i 1.00000i 0 0.866025 + 0.500000i
1151.13 0.866025 + 0.500000i 0 0.500000 + 0.866025i 1.00000 0 1.07313 + 2.41835i 1.00000i 0 0.866025 + 0.500000i
1151.14 0.866025 + 0.500000i 0 0.500000 + 0.866025i 1.00000 0 −2.02958 + 1.69729i 1.00000i 0 0.866025 + 0.500000i
1601.1 −0.866025 + 0.500000i 0 0.500000 − 0.866025i 1.00000 0 −0.555567 + 2.58676i 1.00000i 0 −0.866025 + 0.500000i
1601.2 −0.866025 + 0.500000i 0 0.500000 − 0.866025i 1.00000 0 −2.36047 + 1.19507i 1.00000i 0 −0.866025 + 0.500000i
1601.3 −0.866025 + 0.500000i 0 0.500000 − 0.866025i 1.00000 0 −0.673503 − 2.55859i 1.00000i 0 −0.866025 + 0.500000i
1601.4 −0.866025 + 0.500000i 0 0.500000 − 0.866025i 1.00000 0 −1.17997 − 2.36805i 1.00000i 0 −0.866025 + 0.500000i
1601.5 −0.866025 + 0.500000i 0 0.500000 − 0.866025i 1.00000 0 2.13731 − 1.55945i 1.00000i 0 −0.866025 + 0.500000i
1601.6 −0.866025 + 0.500000i 0 0.500000 − 0.866025i 1.00000 0 2.64030 − 0.169721i 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 1151.14
Significant digits:
Format:

Inner twists

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

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{11}^{28} + 162 T_{11}^{26} + 11301 T_{11}^{24} + 444572 T_{11}^{22} + 10843488 T_{11}^{20} + \cdots + 14197824 \) acting on \(S_{2}^{\mathrm{new}}(1890, [\chi])\). Copy content Toggle raw display