Properties

Label 2790.2.a.bh
Level $2790$
Weight $2$
Character orbit 2790.a
Self dual yes
Analytic conductor $22.278$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

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: \(2\)
Coefficient field: \(\Q(\sqrt{3}) \)
Defining polynomial: \( x^{2} - 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
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 \(\beta = \sqrt{3}\). We also show the integral \(q\)-expansion of the trace form.

\(f(q)\) \(=\) \( q + q^{2} + q^{4} + q^{5} + 2 \beta q^{7} + q^{8}+O(q^{10}) \) Copy content Toggle raw display \( q + q^{2} + q^{4} + q^{5} + 2 \beta q^{7} + q^{8} + q^{10} + ( - \beta + 1) q^{11} + ( - \beta - 3) q^{13} + 2 \beta q^{14} + q^{16} + 4 q^{17} + ( - 2 \beta + 2) q^{19} + q^{20} + ( - \beta + 1) q^{22} + (2 \beta + 4) q^{23} + q^{25} + ( - \beta - 3) q^{26} + 2 \beta q^{28} + (\beta + 1) q^{29} - q^{31} + q^{32} + 4 q^{34} + 2 \beta q^{35} + (\beta - 5) q^{37} + ( - 2 \beta + 2) q^{38} + q^{40} + (2 \beta + 6) q^{41} + (\beta + 5) q^{43} + ( - \beta + 1) q^{44} + (2 \beta + 4) q^{46} - 2 \beta q^{47} + 5 q^{49} + q^{50} + ( - \beta - 3) q^{52} + (\beta + 7) q^{53} + ( - \beta + 1) q^{55} + 2 \beta q^{56} + (\beta + 1) q^{58} + (2 \beta - 2) q^{59} + ( - 7 \beta - 3) q^{61} - q^{62} + q^{64} + ( - \beta - 3) q^{65} + ( - 6 \beta - 2) q^{67} + 4 q^{68} + 2 \beta q^{70} - 8 \beta q^{71} + (6 \beta + 6) q^{73} + (\beta - 5) q^{74} + ( - 2 \beta + 2) q^{76} + (2 \beta - 6) q^{77} + ( - 2 \beta + 14) q^{79} + q^{80} + (2 \beta + 6) q^{82} + ( - \beta + 3) q^{83} + 4 q^{85} + (\beta + 5) q^{86} + ( - \beta + 1) q^{88} + (4 \beta + 6) q^{89} + ( - 6 \beta - 6) q^{91} + (2 \beta + 4) q^{92} - 2 \beta q^{94} + ( - 2 \beta + 2) q^{95} + 4 q^{97} + 5 q^{98} +O(q^{100}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{2} + 2 q^{4} + 2 q^{5} + 2 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{2} + 2 q^{4} + 2 q^{5} + 2 q^{8} + 2 q^{10} + 2 q^{11} - 6 q^{13} + 2 q^{16} + 8 q^{17} + 4 q^{19} + 2 q^{20} + 2 q^{22} + 8 q^{23} + 2 q^{25} - 6 q^{26} + 2 q^{29} - 2 q^{31} + 2 q^{32} + 8 q^{34} - 10 q^{37} + 4 q^{38} + 2 q^{40} + 12 q^{41} + 10 q^{43} + 2 q^{44} + 8 q^{46} + 10 q^{49} + 2 q^{50} - 6 q^{52} + 14 q^{53} + 2 q^{55} + 2 q^{58} - 4 q^{59} - 6 q^{61} - 2 q^{62} + 2 q^{64} - 6 q^{65} - 4 q^{67} + 8 q^{68} + 12 q^{73} - 10 q^{74} + 4 q^{76} - 12 q^{77} + 28 q^{79} + 2 q^{80} + 12 q^{82} + 6 q^{83} + 8 q^{85} + 10 q^{86} + 2 q^{88} + 12 q^{89} - 12 q^{91} + 8 q^{92} + 4 q^{95} + 8 q^{97} + 10 q^{98}+O(q^{100}) \) 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
−1.73205
1.73205
1.00000 0 1.00000 1.00000 0 −3.46410 1.00000 0 1.00000
1.2 1.00000 0 1.00000 1.00000 0 3.46410 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.bh 2
3.b odd 2 1 310.2.a.c 2
12.b even 2 1 2480.2.a.s 2
15.d odd 2 1 1550.2.a.j 2
15.e even 4 2 1550.2.b.h 4
24.f even 2 1 9920.2.a.bl 2
24.h odd 2 1 9920.2.a.bt 2
93.c even 2 1 9610.2.a.j 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
310.2.a.c 2 3.b odd 2 1
1550.2.a.j 2 15.d odd 2 1
1550.2.b.h 4 15.e even 4 2
2480.2.a.s 2 12.b even 2 1
2790.2.a.bh 2 1.a even 1 1 trivial
9610.2.a.j 2 93.c even 2 1
9920.2.a.bl 2 24.f even 2 1
9920.2.a.bt 2 24.h odd 2 1

Hecke kernels

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

\( T_{7}^{2} - 12 \) Copy content Toggle raw display
\( T_{11}^{2} - 2T_{11} - 2 \) Copy content Toggle raw display
\( T_{13}^{2} + 6T_{13} + 6 \) Copy content Toggle raw display
\( T_{17} - 4 \) Copy content Toggle raw display
\( T_{19}^{2} - 4T_{19} - 8 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( (T - 1)^{2} \) Copy content Toggle raw display
$3$ \( T^{2} \) Copy content Toggle raw display
$5$ \( (T - 1)^{2} \) Copy content Toggle raw display
$7$ \( T^{2} - 12 \) Copy content Toggle raw display
$11$ \( T^{2} - 2T - 2 \) Copy content Toggle raw display
$13$ \( T^{2} + 6T + 6 \) Copy content Toggle raw display
$17$ \( (T - 4)^{2} \) Copy content Toggle raw display
$19$ \( T^{2} - 4T - 8 \) Copy content Toggle raw display
$23$ \( T^{2} - 8T + 4 \) Copy content Toggle raw display
$29$ \( T^{2} - 2T - 2 \) Copy content Toggle raw display
$31$ \( (T + 1)^{2} \) Copy content Toggle raw display
$37$ \( T^{2} + 10T + 22 \) Copy content Toggle raw display
$41$ \( T^{2} - 12T + 24 \) Copy content Toggle raw display
$43$ \( T^{2} - 10T + 22 \) Copy content Toggle raw display
$47$ \( T^{2} - 12 \) Copy content Toggle raw display
$53$ \( T^{2} - 14T + 46 \) Copy content Toggle raw display
$59$ \( T^{2} + 4T - 8 \) Copy content Toggle raw display
$61$ \( T^{2} + 6T - 138 \) Copy content Toggle raw display
$67$ \( T^{2} + 4T - 104 \) Copy content Toggle raw display
$71$ \( T^{2} - 192 \) Copy content Toggle raw display
$73$ \( T^{2} - 12T - 72 \) Copy content Toggle raw display
$79$ \( T^{2} - 28T + 184 \) Copy content Toggle raw display
$83$ \( T^{2} - 6T + 6 \) Copy content Toggle raw display
$89$ \( T^{2} - 12T - 12 \) Copy content Toggle raw display
$97$ \( (T - 4)^{2} \) Copy content Toggle raw display
show more
show less