Properties

Label 2151.1.d.a
Level $2151$
Weight $1$
Character orbit 2151.d
Self dual yes
Analytic conductor $1.073$
Analytic rank $0$
Dimension $1$
Projective image $D_{3}$
CM discriminant -239
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2151 = 3^{2} \cdot 239 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2151.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: yes
Analytic conductor: \(1.07348884217\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 239)
Projective image \(D_{3}\)
Projective field Galois closure of 3.1.239.1
Artin image $D_6$
Artin field Galois closure of 6.0.1542267.1

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} + q^{5} - q^{8} + O(q^{10}) \) \( q + q^{2} + q^{5} - q^{8} + q^{10} + q^{11} - q^{16} + q^{17} + q^{22} + q^{29} - q^{31} + q^{34} - q^{40} + q^{49} + q^{55} + q^{58} - q^{61} - q^{62} + q^{64} - q^{67} - 2q^{71} - q^{80} + q^{83} + q^{85} - q^{88} + q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2151\mathbb{Z}\right)^\times\).

\(n\) \(479\) \(1441\)
\(\chi(n)\) \(1\) \(-1\)

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.

Label \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
955.1
0
1.00000 0 0 1.00000 0 0 −1.00000 0 1.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
239.b odd 2 1 CM by \(\Q(\sqrt{-239}) \)

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2151.1.d.a 1
3.b odd 2 1 239.1.b.a 1
12.b even 2 1 3824.1.h.a 1
239.b odd 2 1 CM 2151.1.d.a 1
717.b even 2 1 239.1.b.a 1
2868.e odd 2 1 3824.1.h.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
239.1.b.a 1 3.b odd 2 1
239.1.b.a 1 717.b even 2 1
2151.1.d.a 1 1.a even 1 1 trivial
2151.1.d.a 1 239.b odd 2 1 CM
3824.1.h.a 1 12.b even 2 1
3824.1.h.a 1 2868.e odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{1}^{\mathrm{new}}(2151, [\chi])\):

\( T_{2} - 1 \)
\( T_{5} - 1 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -1 + T \)
$3$ \( T \)
$5$ \( -1 + T \)
$7$ \( T \)
$11$ \( -1 + T \)
$13$ \( T \)
$17$ \( -1 + T \)
$19$ \( T \)
$23$ \( T \)
$29$ \( -1 + T \)
$31$ \( 1 + T \)
$37$ \( T \)
$41$ \( T \)
$43$ \( T \)
$47$ \( T \)
$53$ \( T \)
$59$ \( T \)
$61$ \( 1 + T \)
$67$ \( 1 + T \)
$71$ \( 2 + T \)
$73$ \( T \)
$79$ \( T \)
$83$ \( -1 + T \)
$89$ \( T \)
$97$ \( T \)
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