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Properties

Label 1890.2.bl.b
Level $1890$
Weight $2$
Character orbit 1890.bl
Analytic conductor $15.092$
Analytic rank $0$
Dimension $32$
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(251,1890)]
 
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([1, 0, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1890.251");
 
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.bl (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: \(32\)
Relative dimension: \(16\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 32 q + 16 q^{4} + 16 q^{5} - 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 32 q + 16 q^{4} + 16 q^{5} - 2 q^{7} - 6 q^{11} - 6 q^{13} - 16 q^{16} + 12 q^{17} - 16 q^{20} - 36 q^{23} - 16 q^{25} - 4 q^{28} - 6 q^{29} + 48 q^{31} - 4 q^{35} + 8 q^{37} - 6 q^{41} - 4 q^{43} - 12 q^{46} - 6 q^{47} - 28 q^{49} - 6 q^{52} - 6 q^{56} + 6 q^{61} - 32 q^{64} - 6 q^{65} + 28 q^{67} + 6 q^{68} - 6 q^{70} + 36 q^{74} + 6 q^{77} + 10 q^{79} - 32 q^{80} - 6 q^{83} + 6 q^{85} - 24 q^{86} + 60 q^{89} - 24 q^{91} - 36 q^{92} + 42 q^{94} + 90 q^{97}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
251.1 −0.866025 − 0.500000i 0 0.500000 + 0.866025i 0.500000 + 0.866025i 0 −2.63140 + 0.275220i − 1.00000i 0 − 1.00000i
251.2 −0.866025 − 0.500000i 0 0.500000 + 0.866025i 0.500000 + 0.866025i 0 1.00174 + 2.44878i − 1.00000i 0 − 1.00000i
251.3 −0.866025 − 0.500000i 0 0.500000 + 0.866025i 0.500000 + 0.866025i 0 −0.474749 − 2.60281i − 1.00000i 0 − 1.00000i
251.4 −0.866025 − 0.500000i 0 0.500000 + 0.866025i 0.500000 + 0.866025i 0 −1.54699 + 2.14635i − 1.00000i 0 − 1.00000i
251.5 −0.866025 − 0.500000i 0 0.500000 + 0.866025i 0.500000 + 0.866025i 0 1.15259 + 2.38150i − 1.00000i 0 − 1.00000i
251.6 −0.866025 − 0.500000i 0 0.500000 + 0.866025i 0.500000 + 0.866025i 0 −2.13969 − 1.55619i − 1.00000i 0 − 1.00000i
251.7 −0.866025 − 0.500000i 0 0.500000 + 0.866025i 0.500000 + 0.866025i 0 2.32919 − 1.25494i − 1.00000i 0 − 1.00000i
251.8 −0.866025 − 0.500000i 0 0.500000 + 0.866025i 0.500000 + 0.866025i 0 0.943282 − 2.47189i − 1.00000i 0 − 1.00000i
251.9 0.866025 + 0.500000i 0 0.500000 + 0.866025i 0.500000 + 0.866025i 0 2.64304 − 0.119814i 1.00000i 0 1.00000i
251.10 0.866025 + 0.500000i 0 0.500000 + 0.866025i 0.500000 + 0.866025i 0 1.22724 + 2.34390i 1.00000i 0 1.00000i
251.11 0.866025 + 0.500000i 0 0.500000 + 0.866025i 0.500000 + 0.866025i 0 2.55222 + 0.697255i 1.00000i 0 1.00000i
251.12 0.866025 + 0.500000i 0 0.500000 + 0.866025i 0.500000 + 0.866025i 0 −2.23931 − 1.40907i 1.00000i 0 1.00000i
251.13 0.866025 + 0.500000i 0 0.500000 + 0.866025i 0.500000 + 0.866025i 0 0.0425252 − 2.64541i 1.00000i 0 1.00000i
251.14 0.866025 + 0.500000i 0 0.500000 + 0.866025i 0.500000 + 0.866025i 0 −2.17621 − 1.50470i 1.00000i 0 1.00000i
251.15 0.866025 + 0.500000i 0 0.500000 + 0.866025i 0.500000 + 0.866025i 0 −1.01084 + 2.44504i 1.00000i 0 1.00000i
251.16 0.866025 + 0.500000i 0 0.500000 + 0.866025i 0.500000 + 0.866025i 0 −0.672634 + 2.55882i 1.00000i 0 1.00000i
881.1 −0.866025 + 0.500000i 0 0.500000 − 0.866025i 0.500000 − 0.866025i 0 −2.63140 − 0.275220i 1.00000i 0 1.00000i
881.2 −0.866025 + 0.500000i 0 0.500000 − 0.866025i 0.500000 − 0.866025i 0 1.00174 − 2.44878i 1.00000i 0 1.00000i
881.3 −0.866025 + 0.500000i 0 0.500000 − 0.866025i 0.500000 − 0.866025i 0 −0.474749 + 2.60281i 1.00000i 0 1.00000i
881.4 −0.866025 + 0.500000i 0 0.500000 − 0.866025i 0.500000 − 0.866025i 0 −1.54699 − 2.14635i 1.00000i 0 1.00000i
See all 32 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 251.16
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
63.o 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.bl.b 32
3.b odd 2 1 630.2.bl.a ✓ 32
7.b odd 2 1 1890.2.bl.a 32
9.c even 3 1 630.2.bl.b yes 32
9.d odd 6 1 1890.2.bl.a 32
21.c even 2 1 630.2.bl.b yes 32
63.l odd 6 1 630.2.bl.a ✓ 32
63.o even 6 1 inner 1890.2.bl.b 32
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
630.2.bl.a ✓ 32 3.b odd 2 1
630.2.bl.a ✓ 32 63.l odd 6 1
630.2.bl.b yes 32 9.c even 3 1
630.2.bl.b yes 32 21.c even 2 1
1890.2.bl.a 32 7.b odd 2 1
1890.2.bl.a 32 9.d odd 6 1
1890.2.bl.b 32 1.a even 1 1 trivial
1890.2.bl.b 32 63.o even 6 1 inner