Properties

Label 155.1.c.a
Level 155
Weight 1
Character orbit 155.c
Self dual yes
Analytic conductor 0.077
Analytic rank 0
Dimension 1
Projective image \(D_{2}\)
CM/RM discs -31, -155, 5
Inner twists 4

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 155 = 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 155.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: yes
Analytic conductor: \(0.0773550769581\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image \(D_{2}\)
Projective field Galois closure of \(\Q(\sqrt{5}, \sqrt{-31})\)
Artin image $D_4$
Artin field Galois closure of 4.2.775.1

$q$-expansion

\(f(q)\) \(=\) \( q + q^{4} - q^{5} - q^{9} + O(q^{10}) \) \( q + q^{4} - q^{5} - q^{9} + q^{16} - 2q^{19} - q^{20} + q^{25} - q^{31} - q^{36} + 2q^{41} + q^{45} + q^{49} + 2q^{59} + q^{64} - 2q^{71} - 2q^{76} - q^{80} + q^{81} + 2q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/155\mathbb{Z}\right)^\times\).

\(n\) \(32\) \(96\)
\(\chi(n)\) \(-1\) \(-1\)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
154.1
0
0 0 1.00000 −1.00000 0 0 0 −1.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 RM by \(\Q(\sqrt{5}) \)
31.b odd 2 1 CM by \(\Q(\sqrt{-31}) \)
155.c odd 2 1 CM by \(\Q(\sqrt{-155}) \)

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 155.1.c.a 1
3.b odd 2 1 1395.1.b.a 1
4.b odd 2 1 2480.1.k.b 1
5.b even 2 1 RM 155.1.c.a 1
5.c odd 4 2 775.1.d.a 1
15.d odd 2 1 1395.1.b.a 1
20.d odd 2 1 2480.1.k.b 1
31.b odd 2 1 CM 155.1.c.a 1
93.c even 2 1 1395.1.b.a 1
124.d even 2 1 2480.1.k.b 1
155.c odd 2 1 CM 155.1.c.a 1
155.f even 4 2 775.1.d.a 1
465.g even 2 1 1395.1.b.a 1
620.e even 2 1 2480.1.k.b 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
155.1.c.a 1 1.a even 1 1 trivial
155.1.c.a 1 5.b even 2 1 RM
155.1.c.a 1 31.b odd 2 1 CM
155.1.c.a 1 155.c odd 2 1 CM
775.1.d.a 1 5.c odd 4 2
775.1.d.a 1 155.f even 4 2
1395.1.b.a 1 3.b odd 2 1
1395.1.b.a 1 15.d odd 2 1
1395.1.b.a 1 93.c even 2 1
1395.1.b.a 1 465.g even 2 1
2480.1.k.b 1 4.b odd 2 1
2480.1.k.b 1 20.d odd 2 1
2480.1.k.b 1 124.d even 2 1
2480.1.k.b 1 620.e even 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2} \) acting on \(S_{1}^{\mathrm{new}}(155, [\chi])\).

Hecke characteristic polynomials

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