Properties

Label 2790.2.a.bi
Level $2790$
Weight $2$
Character orbit 2790.a
Self dual yes
Analytic conductor $22.278$
Analytic rank $1$
Dimension $3$
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: \(3\)
Coefficient field: 3.3.148.1
Defining polynomial: \( x^{3} - x^{2} - 3x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 310)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of a basis \(1,\beta_1,\beta_2\) for the coefficient ring described below. We also show the integral \(q\)-expansion of the trace form.

\(f(q)\) \(=\) \( q - q^{2} + q^{4} - q^{5} + ( - \beta_{2} + \beta_1) q^{7} - q^{8}+O(q^{10}) \) Copy content Toggle raw display \( q - q^{2} + q^{4} - q^{5} + ( - \beta_{2} + \beta_1) q^{7} - q^{8} + q^{10} + ( - \beta_{2} - 2 \beta_1 + 1) q^{11} + (\beta_1 - 3) q^{13} + (\beta_{2} - \beta_1) q^{14} + q^{16} + (\beta_{2} - \beta_1) q^{17} + (2 \beta_{2} + 2) q^{19} - q^{20} + (\beta_{2} + 2 \beta_1 - 1) q^{22} + (\beta_{2} + \beta_1) q^{23} + q^{25} + ( - \beta_1 + 3) q^{26} + ( - \beta_{2} + \beta_1) q^{28} + (3 \beta_{2} + 2 \beta_1 - 1) q^{29} + q^{31} - q^{32} + ( - \beta_{2} + \beta_1) q^{34} + (\beta_{2} - \beta_1) q^{35} + (2 \beta_{2} - \beta_1 - 3) q^{37} + ( - 2 \beta_{2} - 2) q^{38} + q^{40} + ( - 3 \beta_{2} - \beta_1 + 2) q^{41} + (2 \beta_{2} - 3 \beta_1 - 3) q^{43} + ( - \beta_{2} - 2 \beta_1 + 1) q^{44} + ( - \beta_{2} - \beta_1) q^{46} + (\beta_{2} + 3 \beta_1 - 8) q^{47} + ( - 4 \beta_1 + 5) q^{49} - q^{50} + (\beta_1 - 3) q^{52} + ( - 2 \beta_{2} + \beta_1 + 7) q^{53} + (\beta_{2} + 2 \beta_1 - 1) q^{55} + (\beta_{2} - \beta_1) q^{56} + ( - 3 \beta_{2} - 2 \beta_1 + 1) q^{58} + ( - 2 \beta_1 - 6) q^{59} + ( - \beta_{2} - 2 \beta_1 - 5) q^{61} - q^{62} + q^{64} + ( - \beta_1 + 3) q^{65} + ( - 4 \beta_{2} - 2 \beta_1 - 2) q^{67} + (\beta_{2} - \beta_1) q^{68} + ( - \beta_{2} + \beta_1) q^{70} + (2 \beta_{2} + 2 \beta_1 - 4) q^{71} + ( - 3 \beta_{2} + \beta_1 - 6) q^{73} + ( - 2 \beta_{2} + \beta_1 + 3) q^{74} + (2 \beta_{2} + 2) q^{76} - 4 \beta_{2} q^{77} + (6 \beta_1 - 2) q^{79} - q^{80} + (3 \beta_{2} + \beta_1 - 2) q^{82} + ( - 2 \beta_{2} + \beta_1 - 3) q^{83} + ( - \beta_{2} + \beta_1) q^{85} + ( - 2 \beta_{2} + 3 \beta_1 + 3) q^{86} + (\beta_{2} + 2 \beta_1 - 1) q^{88} + ( - 2 \beta_{2} + 2 \beta_1 - 6) q^{89} + (4 \beta_{2} - 4 \beta_1 + 4) q^{91} + (\beta_{2} + \beta_1) q^{92} + ( - \beta_{2} - 3 \beta_1 + 8) q^{94} + ( - 2 \beta_{2} - 2) q^{95} + ( - \beta_{2} + 3 \beta_1 - 4) q^{97} + (4 \beta_1 - 5) q^{98}+O(q^{100}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 3 q^{2} + 3 q^{4} - 3 q^{5} - 3 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - 3 q^{2} + 3 q^{4} - 3 q^{5} - 3 q^{8} + 3 q^{10} - 8 q^{13} + 3 q^{16} + 8 q^{19} - 3 q^{20} + 2 q^{23} + 3 q^{25} + 8 q^{26} + 2 q^{29} + 3 q^{31} - 3 q^{32} - 8 q^{37} - 8 q^{38} + 3 q^{40} + 2 q^{41} - 10 q^{43} - 2 q^{46} - 20 q^{47} + 11 q^{49} - 3 q^{50} - 8 q^{52} + 20 q^{53} - 2 q^{58} - 20 q^{59} - 18 q^{61} - 3 q^{62} + 3 q^{64} + 8 q^{65} - 12 q^{67} - 8 q^{71} - 20 q^{73} + 8 q^{74} + 8 q^{76} - 4 q^{77} - 3 q^{80} - 2 q^{82} - 10 q^{83} + 10 q^{86} - 18 q^{89} + 12 q^{91} + 2 q^{92} + 20 q^{94} - 8 q^{95} - 10 q^{97} - 11 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Basis of coefficient ring in terms of a root \(\nu\) of \( x^{3} - x^{2} - 3x + 1 \) : Copy content Toggle raw display

\(\beta_{1}\)\(=\) \( \nu^{2} - 2 \) Copy content Toggle raw display
\(\beta_{2}\)\(=\) \( -\nu^{2} + 2\nu + 2 \) Copy content Toggle raw display
\(\nu\)\(=\) \( ( \beta_{2} + \beta_1 ) / 2 \) Copy content Toggle raw display
\(\nu^{2}\)\(=\) \( \beta _1 + 2 \) 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
0.311108
2.17009
−1.48119
−1.00000 0 1.00000 −1.00000 0 −4.42864 −1.00000 0 1.00000
1.2 −1.00000 0 1.00000 −1.00000 0 1.07838 −1.00000 0 1.00000
1.3 −1.00000 0 1.00000 −1.00000 0 3.35026 −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.bi 3
3.b odd 2 1 310.2.a.e 3
12.b even 2 1 2480.2.a.u 3
15.d odd 2 1 1550.2.a.k 3
15.e even 4 2 1550.2.b.j 6
24.f even 2 1 9920.2.a.bx 3
24.h odd 2 1 9920.2.a.bw 3
93.c even 2 1 9610.2.a.u 3
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
310.2.a.e 3 3.b odd 2 1
1550.2.a.k 3 15.d odd 2 1
1550.2.b.j 6 15.e even 4 2
2480.2.a.u 3 12.b even 2 1
2790.2.a.bi 3 1.a even 1 1 trivial
9610.2.a.u 3 93.c even 2 1
9920.2.a.bw 3 24.h odd 2 1
9920.2.a.bx 3 24.f even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(2790))\):

\( T_{7}^{3} - 16T_{7} + 16 \) Copy content Toggle raw display
\( T_{11}^{3} - 28T_{11} + 52 \) Copy content Toggle raw display
\( T_{13}^{3} + 8T_{13}^{2} + 16T_{13} + 4 \) Copy content Toggle raw display
\( T_{17}^{3} - 16T_{17} - 16 \) Copy content Toggle raw display
\( T_{19}^{3} - 8T_{19}^{2} - 16T_{19} + 160 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( (T + 1)^{3} \) Copy content Toggle raw display
$3$ \( T^{3} \) Copy content Toggle raw display
$5$ \( (T + 1)^{3} \) Copy content Toggle raw display
$7$ \( T^{3} - 16T + 16 \) Copy content Toggle raw display
$11$ \( T^{3} - 28T + 52 \) Copy content Toggle raw display
$13$ \( T^{3} + 8 T^{2} + 16 T + 4 \) Copy content Toggle raw display
$17$ \( T^{3} - 16T - 16 \) Copy content Toggle raw display
$19$ \( T^{3} - 8 T^{2} - 16 T + 160 \) Copy content Toggle raw display
$23$ \( T^{3} - 2 T^{2} - 12 T + 8 \) Copy content Toggle raw display
$29$ \( T^{3} - 2 T^{2} - 96 T + 260 \) Copy content Toggle raw display
$31$ \( (T - 1)^{3} \) Copy content Toggle raw display
$37$ \( T^{3} + 8 T^{2} - 24 T - 92 \) Copy content Toggle raw display
$41$ \( T^{3} - 2 T^{2} - 84 T - 232 \) Copy content Toggle raw display
$43$ \( T^{3} + 10 T^{2} - 60 T - 604 \) Copy content Toggle raw display
$47$ \( T^{3} + 20 T^{2} + 80 T - 208 \) Copy content Toggle raw display
$53$ \( T^{3} - 20 T^{2} + 88 T - 4 \) Copy content Toggle raw display
$59$ \( T^{3} + 20 T^{2} + 112 T + 160 \) Copy content Toggle raw display
$61$ \( T^{3} + 18 T^{2} + 80 T + 100 \) Copy content Toggle raw display
$67$ \( T^{3} + 12 T^{2} - 112 T - 1184 \) Copy content Toggle raw display
$71$ \( T^{3} + 8 T^{2} - 32 T - 128 \) Copy content Toggle raw display
$73$ \( T^{3} + 20 T^{2} + 40 T - 464 \) Copy content Toggle raw display
$79$ \( T^{3} - 192T - 160 \) Copy content Toggle raw display
$83$ \( T^{3} + 10 T^{2} - 12 T - 124 \) Copy content Toggle raw display
$89$ \( T^{3} + 18 T^{2} + 44 T - 40 \) Copy content Toggle raw display
$97$ \( T^{3} + 10 T^{2} - 28 T - 8 \) Copy content Toggle raw display
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