Properties

Label 1520.2.a.h
Level $1520$
Weight $2$
Character orbit 1520.a
Self dual yes
Analytic conductor $12.137$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1520 = 2^{4} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1520.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(12.1372611072\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 760)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 2 q^{3} + q^{5} - 4 q^{7} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + 2 q^{3} + q^{5} - 4 q^{7} + q^{9} - 4 q^{11} - 4 q^{13} + 2 q^{15} - 2 q^{17} + q^{19} - 8 q^{21} + q^{25} - 4 q^{27} + 2 q^{29} - 8 q^{31} - 8 q^{33} - 4 q^{35} + 4 q^{37} - 8 q^{39} + 6 q^{41} + q^{45} - 12 q^{47} + 9 q^{49} - 4 q^{51} - 8 q^{53} - 4 q^{55} + 2 q^{57} + 2 q^{61} - 4 q^{63} - 4 q^{65} + 14 q^{67} - 8 q^{71} + 6 q^{73} + 2 q^{75} + 16 q^{77} + 4 q^{79} - 11 q^{81} - 4 q^{83} - 2 q^{85} + 4 q^{87} + 14 q^{89} + 16 q^{91} - 16 q^{93} + q^{95} - 12 q^{97} - 4 q^{99}+O(q^{100}) \) 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 2.00000 0 1.00000 0 −4.00000 0 1.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(5\) \(-1\)
\(19\) \(-1\)

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 1520.2.a.h 1
4.b odd 2 1 760.2.a.b 1
5.b even 2 1 7600.2.a.f 1
8.b even 2 1 6080.2.a.c 1
8.d odd 2 1 6080.2.a.u 1
12.b even 2 1 6840.2.a.l 1
20.d odd 2 1 3800.2.a.f 1
20.e even 4 2 3800.2.d.e 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
760.2.a.b 1 4.b odd 2 1
1520.2.a.h 1 1.a even 1 1 trivial
3800.2.a.f 1 20.d odd 2 1
3800.2.d.e 2 20.e even 4 2
6080.2.a.c 1 8.b even 2 1
6080.2.a.u 1 8.d odd 2 1
6840.2.a.l 1 12.b even 2 1
7600.2.a.f 1 5.b even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1520))\):

\( T_{3} - 2 \) Copy content Toggle raw display
\( T_{7} + 4 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \) Copy content Toggle raw display
$3$ \( T - 2 \) Copy content Toggle raw display
$5$ \( T - 1 \) Copy content Toggle raw display
$7$ \( T + 4 \) Copy content Toggle raw display
$11$ \( T + 4 \) Copy content Toggle raw display
$13$ \( T + 4 \) Copy content Toggle raw display
$17$ \( T + 2 \) Copy content Toggle raw display
$19$ \( T - 1 \) Copy content Toggle raw display
$23$ \( T \) Copy content Toggle raw display
$29$ \( T - 2 \) Copy content Toggle raw display
$31$ \( T + 8 \) Copy content Toggle raw display
$37$ \( T - 4 \) Copy content Toggle raw display
$41$ \( T - 6 \) Copy content Toggle raw display
$43$ \( T \) Copy content Toggle raw display
$47$ \( T + 12 \) Copy content Toggle raw display
$53$ \( T + 8 \) Copy content Toggle raw display
$59$ \( T \) Copy content Toggle raw display
$61$ \( T - 2 \) Copy content Toggle raw display
$67$ \( T - 14 \) Copy content Toggle raw display
$71$ \( T + 8 \) Copy content Toggle raw display
$73$ \( T - 6 \) Copy content Toggle raw display
$79$ \( T - 4 \) Copy content Toggle raw display
$83$ \( T + 4 \) Copy content Toggle raw display
$89$ \( T - 14 \) Copy content Toggle raw display
$97$ \( T + 12 \) Copy content Toggle raw display
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