Properties

Label 2790.2.a.c
Level $2790$
Weight $2$
Character orbit 2790.a
Self dual yes
Analytic conductor $22.278$
Analytic rank $0$
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: \(0\)
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

\(f(q)\) \(=\) \( q - q^{2} + q^{4} - q^{5} - q^{8} + O(q^{10}) \) \( q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} + 4q^{11} + 6q^{13} + q^{16} - 2q^{17} + 4q^{19} - q^{20} - 4q^{22} + 8q^{23} + q^{25} - 6q^{26} - 6q^{29} - q^{31} - q^{32} + 2q^{34} - 2q^{37} - 4q^{38} + q^{40} - 10q^{41} - 4q^{43} + 4q^{44} - 8q^{46} - 7q^{49} - q^{50} + 6q^{52} + 10q^{53} - 4q^{55} + 6q^{58} + 12q^{59} - 2q^{61} + q^{62} + q^{64} - 6q^{65} - 4q^{67} - 2q^{68} + 2q^{73} + 2q^{74} + 4q^{76} - q^{80} + 10q^{82} - 4q^{83} + 2q^{85} + 4q^{86} - 4q^{88} + 14q^{89} + 8q^{92} - 4q^{95} + 18q^{97} + 7q^{98} + O(q^{100}) \)

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
−1.00000 0 1.00000 −1.00000 0 0 −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.c 1
3.b odd 2 1 930.2.a.o 1
12.b even 2 1 7440.2.a.j 1
15.d odd 2 1 4650.2.a.h 1
15.e even 4 2 4650.2.d.n 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
930.2.a.o 1 3.b odd 2 1
2790.2.a.c 1 1.a even 1 1 trivial
4650.2.a.h 1 15.d odd 2 1
4650.2.d.n 2 15.e even 4 2
7440.2.a.j 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(2790))\):

\( T_{7} \)
\( T_{11} - 4 \)
\( T_{13} - 6 \)
\( T_{17} + 2 \)
\( T_{19} - 4 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + T \)
$3$ \( T \)
$5$ \( 1 + T \)
$7$ \( T \)
$11$ \( -4 + T \)
$13$ \( -6 + T \)
$17$ \( 2 + T \)
$19$ \( -4 + T \)
$23$ \( -8 + T \)
$29$ \( 6 + T \)
$31$ \( 1 + T \)
$37$ \( 2 + T \)
$41$ \( 10 + T \)
$43$ \( 4 + T \)
$47$ \( T \)
$53$ \( -10 + T \)
$59$ \( -12 + T \)
$61$ \( 2 + T \)
$67$ \( 4 + T \)
$71$ \( T \)
$73$ \( -2 + T \)
$79$ \( T \)
$83$ \( 4 + T \)
$89$ \( -14 + T \)
$97$ \( -18 + T \)
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