Properties

Label 2790.2.a.u
Level $2790$
Weight $2$
Character orbit 2790.a
Self dual yes
Analytic conductor $22.278$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2790 = 2 \cdot 3^{2} \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2790.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(22.2782621639\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 930)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} + q^{4} - q^{5} + 3 q^{7} + q^{8}+O(q^{10}) \) Copy content Toggle raw display \( q + q^{2} + q^{4} - q^{5} + 3 q^{7} + q^{8} - q^{10} - 3 q^{11} - 2 q^{13} + 3 q^{14} + q^{16} - 8 q^{17} - 7 q^{19} - q^{20} - 3 q^{22} - 7 q^{23} + q^{25} - 2 q^{26} + 3 q^{28} + 8 q^{29} - q^{31} + q^{32} - 8 q^{34} - 3 q^{35} - 4 q^{37} - 7 q^{38} - q^{40} + q^{43} - 3 q^{44} - 7 q^{46} - 6 q^{47} + 2 q^{49} + q^{50} - 2 q^{52} - 5 q^{53} + 3 q^{55} + 3 q^{56} + 8 q^{58} - 6 q^{59} + 2 q^{61} - q^{62} + q^{64} + 2 q^{65} + 10 q^{67} - 8 q^{68} - 3 q^{70} - 9 q^{71} + q^{73} - 4 q^{74} - 7 q^{76} - 9 q^{77} + 13 q^{79} - q^{80} + 16 q^{83} + 8 q^{85} + q^{86} - 3 q^{88} + 3 q^{89} - 6 q^{91} - 7 q^{92} - 6 q^{94} + 7 q^{95} + 6 q^{97} + 2 q^{98}+O(q^{100}) \) 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
1.00000 0 1.00000 −1.00000 0 3.00000 1.00000 0 −1.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3\) \(-1\)
\(5\) \(1\)
\(31\) \(1\)

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 2790.2.a.u 1
3.b odd 2 1 930.2.a.e 1
12.b even 2 1 7440.2.a.x 1
15.d odd 2 1 4650.2.a.bk 1
15.e even 4 2 4650.2.d.ba 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
930.2.a.e 1 3.b odd 2 1
2790.2.a.u 1 1.a even 1 1 trivial
4650.2.a.bk 1 15.d odd 2 1
4650.2.d.ba 2 15.e even 4 2
7440.2.a.x 1 12.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 \(S_{2}^{\mathrm{new}}(\Gamma_0(2790))\):

\( T_{7} - 3 \) Copy content Toggle raw display
\( T_{11} + 3 \) Copy content Toggle raw display
\( T_{13} + 2 \) Copy content Toggle raw display
\( T_{17} + 8 \) Copy content Toggle raw display
\( T_{19} + 7 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T - 1 \) Copy content Toggle raw display
$3$ \( T \) Copy content Toggle raw display
$5$ \( T + 1 \) Copy content Toggle raw display
$7$ \( T - 3 \) Copy content Toggle raw display
$11$ \( T + 3 \) Copy content Toggle raw display
$13$ \( T + 2 \) Copy content Toggle raw display
$17$ \( T + 8 \) Copy content Toggle raw display
$19$ \( T + 7 \) Copy content Toggle raw display
$23$ \( T + 7 \) Copy content Toggle raw display
$29$ \( T - 8 \) Copy content Toggle raw display
$31$ \( T + 1 \) Copy content Toggle raw display
$37$ \( T + 4 \) Copy content Toggle raw display
$41$ \( T \) Copy content Toggle raw display
$43$ \( T - 1 \) Copy content Toggle raw display
$47$ \( T + 6 \) Copy content Toggle raw display
$53$ \( T + 5 \) Copy content Toggle raw display
$59$ \( T + 6 \) Copy content Toggle raw display
$61$ \( T - 2 \) Copy content Toggle raw display
$67$ \( T - 10 \) Copy content Toggle raw display
$71$ \( T + 9 \) Copy content Toggle raw display
$73$ \( T - 1 \) Copy content Toggle raw display
$79$ \( T - 13 \) Copy content Toggle raw display
$83$ \( T - 16 \) Copy content Toggle raw display
$89$ \( T - 3 \) Copy content Toggle raw display
$97$ \( T - 6 \) Copy content Toggle raw display
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