Properties

Label 1444.2.a.b
Level $1444$
Weight $2$
Character orbit 1444.a
Self dual yes
Analytic conductor $11.530$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1444 = 2^{2} \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1444.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(11.5303980519\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 76)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{3} - q^{5} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - q^{3} - q^{5} - 2 q^{9} - 4 q^{11} - q^{13} + q^{15} + 3 q^{17} + 5 q^{23} - 4 q^{25} + 5 q^{27} + 7 q^{29} + 4 q^{31} + 4 q^{33} + 10 q^{37} + q^{39} - 5 q^{41} - 5 q^{43} + 2 q^{45} - 7 q^{47} - 7 q^{49} - 3 q^{51} + 11 q^{53} + 4 q^{55} + 3 q^{59} + 11 q^{61} + q^{65} - 3 q^{67} - 5 q^{69} + 11 q^{71} + 15 q^{73} + 4 q^{75} - 13 q^{79} + q^{81} - 3 q^{85} - 7 q^{87} + 3 q^{89} - 4 q^{93} - 5 q^{97} + 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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 −1.00000 0 −1.00000 0 0 0 −2.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(19\) \(1\)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1444.2.a.b 1
4.b odd 2 1 5776.2.a.k 1
19.b odd 2 1 1444.2.a.c 1
19.c even 3 2 76.2.e.a 2
19.d odd 6 2 1444.2.e.b 2
57.h odd 6 2 684.2.k.b 2
76.d even 2 1 5776.2.a.f 1
76.g odd 6 2 304.2.i.a 2
95.i even 6 2 1900.2.i.a 2
95.m odd 12 4 1900.2.s.a 4
152.k odd 6 2 1216.2.i.g 2
152.p even 6 2 1216.2.i.c 2
228.m even 6 2 2736.2.s.g 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
76.2.e.a 2 19.c even 3 2
304.2.i.a 2 76.g odd 6 2
684.2.k.b 2 57.h odd 6 2
1216.2.i.c 2 152.p even 6 2
1216.2.i.g 2 152.k odd 6 2
1444.2.a.b 1 1.a even 1 1 trivial
1444.2.a.c 1 19.b odd 2 1
1444.2.e.b 2 19.d odd 6 2
1900.2.i.a 2 95.i even 6 2
1900.2.s.a 4 95.m odd 12 4
2736.2.s.g 2 228.m even 6 2
5776.2.a.f 1 76.d even 2 1
5776.2.a.k 1 4.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3} + 1 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1444))\). Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \) Copy content Toggle raw display
$3$ \( T + 1 \) Copy content Toggle raw display
$5$ \( T + 1 \) Copy content Toggle raw display
$7$ \( T \) Copy content Toggle raw display
$11$ \( T + 4 \) Copy content Toggle raw display
$13$ \( T + 1 \) Copy content Toggle raw display
$17$ \( T - 3 \) Copy content Toggle raw display
$19$ \( T \) Copy content Toggle raw display
$23$ \( T - 5 \) Copy content Toggle raw display
$29$ \( T - 7 \) Copy content Toggle raw display
$31$ \( T - 4 \) Copy content Toggle raw display
$37$ \( T - 10 \) Copy content Toggle raw display
$41$ \( T + 5 \) Copy content Toggle raw display
$43$ \( T + 5 \) Copy content Toggle raw display
$47$ \( T + 7 \) Copy content Toggle raw display
$53$ \( T - 11 \) Copy content Toggle raw display
$59$ \( T - 3 \) Copy content Toggle raw display
$61$ \( T - 11 \) Copy content Toggle raw display
$67$ \( T + 3 \) Copy content Toggle raw display
$71$ \( T - 11 \) Copy content Toggle raw display
$73$ \( T - 15 \) Copy content Toggle raw display
$79$ \( T + 13 \) Copy content Toggle raw display
$83$ \( T \) Copy content Toggle raw display
$89$ \( T - 3 \) Copy content Toggle raw display
$97$ \( T + 5 \) Copy content Toggle raw display
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