Properties

Label 1849.4.a.a
Level 1849
Weight 4
Character orbit 1849.a
Self dual yes
Analytic conductor 109.095
Analytic rank 0
Dimension 1
CM discriminant -43
Inner twists 2

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 1849 = 43^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1849.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(109.094531601\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $N(\mathrm{U}(1))$

$q$-expansion

\(f(q)\) \(=\) \( q - 8q^{4} - 27q^{9} + O(q^{10}) \) \( q - 8q^{4} - 27q^{9} + 32q^{11} - 90q^{13} + 64q^{16} - 130q^{17} - 140q^{23} - 125q^{25} + 108q^{31} + 216q^{36} + 22q^{41} - 256q^{44} + 500q^{47} - 343q^{49} + 720q^{52} - 130q^{53} - 904q^{59} - 512q^{64} - 360q^{67} + 1040q^{68} - 1116q^{79} + 729q^{81} - 680q^{83} + 1120q^{92} + 290q^{97} - 864q^{99} + O(q^{100}) \)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1
0
0 0 −8.00000 0 0 0 0 −27.0000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(43\) \(1\)

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
43.b odd 2 1 CM by \(\Q(\sqrt{-43}) \)

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1849.4.a.a 1
43.b odd 2 1 CM 1849.4.a.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1849.4.a.a 1 1.a even 1 1 trivial
1849.4.a.a 1 43.b odd 2 1 CM

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2} \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1849))\).

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + 8 T^{2} \)
$3$ \( 1 + 27 T^{2} \)
$5$ \( 1 + 125 T^{2} \)
$7$ \( 1 + 343 T^{2} \)
$11$ \( 1 - 32 T + 1331 T^{2} \)
$13$ \( 1 + 90 T + 2197 T^{2} \)
$17$ \( 1 + 130 T + 4913 T^{2} \)
$19$ \( 1 + 6859 T^{2} \)
$23$ \( 1 + 140 T + 12167 T^{2} \)
$29$ \( 1 + 24389 T^{2} \)
$31$ \( 1 - 108 T + 29791 T^{2} \)
$37$ \( 1 + 50653 T^{2} \)
$41$ \( 1 - 22 T + 68921 T^{2} \)
$43$ 1
$47$ \( 1 - 500 T + 103823 T^{2} \)
$53$ \( 1 + 130 T + 148877 T^{2} \)
$59$ \( 1 + 904 T + 205379 T^{2} \)
$61$ \( 1 + 226981 T^{2} \)
$67$ \( 1 + 360 T + 300763 T^{2} \)
$71$ \( 1 + 357911 T^{2} \)
$73$ \( 1 + 389017 T^{2} \)
$79$ \( 1 + 1116 T + 493039 T^{2} \)
$83$ \( 1 + 680 T + 571787 T^{2} \)
$89$ \( 1 + 704969 T^{2} \)
$97$ \( 1 - 290 T + 912673 T^{2} \)
show more
show less