Properties

Label 2527.1.m.d
Level $2527$
Weight $1$
Character orbit 2527.m
Analytic conductor $1.261$
Analytic rank $0$
Dimension $4$
Projective image $A_{4}$
CM/RM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2527,1,Mod(790,2527)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2527, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 4]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2527.790");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2527 = 7 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2527.m (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: \(1.26113728692\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 133)
Projective image: \(A_{4}\)
Projective field: Galois closure of 4.0.17689.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 

The \(q\)-expansion and trace form are shown below.

\(f(q)\) \(=\) \( q + \zeta_{12}^{2} q^{2} + \zeta_{12}^{5} q^{3} + \zeta_{12}^{5} q^{5} - \zeta_{12} q^{6} + \zeta_{12}^{3} q^{7} + q^{8} +O(q^{10}) \) Copy content Toggle raw display \( q + \zeta_{12}^{2} q^{2} + \zeta_{12}^{5} q^{3} + \zeta_{12}^{5} q^{5} - \zeta_{12} q^{6} + \zeta_{12}^{3} q^{7} + q^{8} - \zeta_{12} q^{10} + \zeta_{12} q^{13} + \zeta_{12}^{5} q^{14} - \zeta_{12}^{4} q^{15} + \zeta_{12}^{2} q^{16} - \zeta_{12}^{5} q^{17} - \zeta_{12}^{2} q^{21} + \zeta_{12}^{4} q^{23} + \zeta_{12}^{5} q^{24} + \zeta_{12}^{3} q^{26} - \zeta_{12}^{3} q^{27} + \zeta_{12}^{4} q^{29} + q^{30} + \zeta_{12} q^{34} - \zeta_{12}^{2} q^{35} - q^{39} + \zeta_{12}^{5} q^{40} + \zeta_{12}^{5} q^{41} - \zeta_{12}^{4} q^{42} - \zeta_{12}^{2} q^{43} - q^{46} - \zeta_{12} q^{47} - \zeta_{12} q^{48} - q^{49} + \zeta_{12}^{4} q^{51} + \zeta_{12}^{4} q^{53} - \zeta_{12}^{5} q^{54} + \zeta_{12}^{3} q^{56} - q^{58} - \zeta_{12}^{5} q^{59} + \zeta_{12} q^{61} + q^{64} - q^{65} - \zeta_{12}^{4} q^{67} - \zeta_{12}^{3} q^{69} - \zeta_{12}^{4} q^{70} - \zeta_{12}^{2} q^{71} + \zeta_{12}^{5} q^{73} - \zeta_{12}^{2} q^{78} + \zeta_{12}^{2} q^{79} - \zeta_{12} q^{80} + \zeta_{12}^{2} q^{81} - \zeta_{12} q^{82} + \zeta_{12}^{4} q^{85} - \zeta_{12}^{4} q^{86} - \zeta_{12}^{3} q^{87} - \zeta_{12} q^{89} + \zeta_{12}^{4} q^{91} - \zeta_{12}^{3} q^{94} + \zeta_{12}^{5} q^{97} - \zeta_{12}^{2} q^{98} +O(q^{100}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} + 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} + 4 q^{8} + 2 q^{15} + 2 q^{16} - 2 q^{21} - 2 q^{23} - 2 q^{29} + 4 q^{30} - 2 q^{35} - 4 q^{39} + 2 q^{42} - 2 q^{43} - 4 q^{46} - 4 q^{49} - 2 q^{51} - 2 q^{53} - 4 q^{58} + 4 q^{64} - 4 q^{65} + 2 q^{67} + 2 q^{70} - 2 q^{71} - 2 q^{78} + 2 q^{79} + 2 q^{81} - 2 q^{85} + 2 q^{86} - 2 q^{91} - 2 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2527\mathbb{Z}\right)^\times\).

\(n\) \(1445\) \(1807\)
\(\chi(n)\) \(-1\) \(\zeta_{12}^{4}\)

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   \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
790.1
0.866025 0.500000i
−0.866025 + 0.500000i
0.866025 + 0.500000i
−0.866025 0.500000i
0.500000 0.866025i −0.866025 0.500000i 0 −0.866025 0.500000i −0.866025 + 0.500000i 1.00000i 1.00000 0 −0.866025 + 0.500000i
790.2 0.500000 0.866025i 0.866025 + 0.500000i 0 0.866025 + 0.500000i 0.866025 0.500000i 1.00000i 1.00000 0 0.866025 0.500000i
1014.1 0.500000 + 0.866025i −0.866025 + 0.500000i 0 −0.866025 + 0.500000i −0.866025 0.500000i 1.00000i 1.00000 0 −0.866025 0.500000i
1014.2 0.500000 + 0.866025i 0.866025 0.500000i 0 0.866025 0.500000i 0.866025 + 0.500000i 1.00000i 1.00000 0 0.866025 + 0.500000i
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
7.b odd 2 1 inner
19.c even 3 1 inner
133.m odd 6 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2527.1.m.d 4
7.b odd 2 1 inner 2527.1.m.d 4
19.b odd 2 1 133.1.m.a 4
19.c even 3 1 2527.1.d.b 2
19.c even 3 1 inner 2527.1.m.d 4
19.d odd 6 1 133.1.m.a 4
19.d odd 6 1 2527.1.d.e 2
19.e even 9 6 2527.1.y.d 12
19.f odd 18 6 2527.1.y.e 12
57.d even 2 1 1197.1.ci.c 4
57.f even 6 1 1197.1.ci.c 4
76.d even 2 1 2128.1.cy.a 4
76.f even 6 1 2128.1.cy.a 4
95.d odd 2 1 3325.1.bc.a 4
95.g even 4 1 3325.1.bi.a 4
95.g even 4 1 3325.1.bi.b 4
95.h odd 6 1 3325.1.bc.a 4
95.l even 12 1 3325.1.bi.a 4
95.l even 12 1 3325.1.bi.b 4
133.c even 2 1 133.1.m.a 4
133.i even 6 1 931.1.k.a 4
133.j odd 6 1 931.1.k.a 4
133.m odd 6 1 2527.1.d.b 2
133.m odd 6 1 inner 2527.1.m.d 4
133.n odd 6 1 931.1.t.a 4
133.o even 6 1 931.1.k.a 4
133.o even 6 1 931.1.t.a 4
133.p even 6 1 133.1.m.a 4
133.p even 6 1 2527.1.d.e 2
133.r odd 6 1 931.1.k.a 4
133.r odd 6 1 931.1.t.a 4
133.s even 6 1 931.1.t.a 4
133.y odd 18 6 2527.1.y.d 12
133.ba even 18 6 2527.1.y.e 12
399.h odd 2 1 1197.1.ci.c 4
399.q odd 6 1 1197.1.ci.c 4
532.b odd 2 1 2128.1.cy.a 4
532.bf odd 6 1 2128.1.cy.a 4
665.g even 2 1 3325.1.bc.a 4
665.n odd 4 1 3325.1.bi.a 4
665.n odd 4 1 3325.1.bi.b 4
665.ba even 6 1 3325.1.bc.a 4
665.ch odd 12 1 3325.1.bi.a 4
665.ch odd 12 1 3325.1.bi.b 4
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
133.1.m.a 4 19.b odd 2 1
133.1.m.a 4 19.d odd 6 1
133.1.m.a 4 133.c even 2 1
133.1.m.a 4 133.p even 6 1
931.1.k.a 4 133.i even 6 1
931.1.k.a 4 133.j odd 6 1
931.1.k.a 4 133.o even 6 1
931.1.k.a 4 133.r odd 6 1
931.1.t.a 4 133.n odd 6 1
931.1.t.a 4 133.o even 6 1
931.1.t.a 4 133.r odd 6 1
931.1.t.a 4 133.s even 6 1
1197.1.ci.c 4 57.d even 2 1
1197.1.ci.c 4 57.f even 6 1
1197.1.ci.c 4 399.h odd 2 1
1197.1.ci.c 4 399.q odd 6 1
2128.1.cy.a 4 76.d even 2 1
2128.1.cy.a 4 76.f even 6 1
2128.1.cy.a 4 532.b odd 2 1
2128.1.cy.a 4 532.bf odd 6 1
2527.1.d.b 2 19.c even 3 1
2527.1.d.b 2 133.m odd 6 1
2527.1.d.e 2 19.d odd 6 1
2527.1.d.e 2 133.p even 6 1
2527.1.m.d 4 1.a even 1 1 trivial
2527.1.m.d 4 7.b odd 2 1 inner
2527.1.m.d 4 19.c even 3 1 inner
2527.1.m.d 4 133.m odd 6 1 inner
2527.1.y.d 12 19.e even 9 6
2527.1.y.d 12 133.y odd 18 6
2527.1.y.e 12 19.f odd 18 6
2527.1.y.e 12 133.ba even 18 6
3325.1.bc.a 4 95.d odd 2 1
3325.1.bc.a 4 95.h odd 6 1
3325.1.bc.a 4 665.g even 2 1
3325.1.bc.a 4 665.ba even 6 1
3325.1.bi.a 4 95.g even 4 1
3325.1.bi.a 4 95.l even 12 1
3325.1.bi.a 4 665.n odd 4 1
3325.1.bi.a 4 665.ch odd 12 1
3325.1.bi.b 4 95.g even 4 1
3325.1.bi.b 4 95.l even 12 1
3325.1.bi.b 4 665.n odd 4 1
3325.1.bi.b 4 665.ch odd 12 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{2} - T_{2} + 1 \) acting on \(S_{1}^{\mathrm{new}}(2527, [\chi])\). Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( (T^{2} - T + 1)^{2} \) Copy content Toggle raw display
$3$ \( T^{4} - T^{2} + 1 \) Copy content Toggle raw display
$5$ \( T^{4} - T^{2} + 1 \) Copy content Toggle raw display
$7$ \( (T^{2} + 1)^{2} \) Copy content Toggle raw display
$11$ \( T^{4} \) Copy content Toggle raw display
$13$ \( T^{4} - T^{2} + 1 \) Copy content Toggle raw display
$17$ \( T^{4} - T^{2} + 1 \) Copy content Toggle raw display
$19$ \( T^{4} \) Copy content Toggle raw display
$23$ \( (T^{2} + T + 1)^{2} \) Copy content Toggle raw display
$29$ \( (T^{2} + T + 1)^{2} \) Copy content Toggle raw display
$31$ \( T^{4} \) Copy content Toggle raw display
$37$ \( T^{4} \) Copy content Toggle raw display
$41$ \( T^{4} - T^{2} + 1 \) Copy content Toggle raw display
$43$ \( (T^{2} + T + 1)^{2} \) Copy content Toggle raw display
$47$ \( T^{4} - T^{2} + 1 \) Copy content Toggle raw display
$53$ \( (T^{2} + T + 1)^{2} \) Copy content Toggle raw display
$59$ \( T^{4} - T^{2} + 1 \) Copy content Toggle raw display
$61$ \( T^{4} - T^{2} + 1 \) Copy content Toggle raw display
$67$ \( (T^{2} - T + 1)^{2} \) Copy content Toggle raw display
$71$ \( (T^{2} + T + 1)^{2} \) Copy content Toggle raw display
$73$ \( T^{4} - T^{2} + 1 \) Copy content Toggle raw display
$79$ \( (T^{2} - T + 1)^{2} \) Copy content Toggle raw display
$83$ \( T^{4} \) Copy content Toggle raw display
$89$ \( T^{4} - T^{2} + 1 \) Copy content Toggle raw display
$97$ \( T^{4} - T^{2} + 1 \) Copy content Toggle raw display
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