Properties

Label 1122.2.a.c
Level $1122$
Weight $2$
Character orbit 1122.a
Self dual yes
Analytic conductor $8.959$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1122 = 2 \cdot 3 \cdot 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1122.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(8.95921510679\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{2} - q^{3} + q^{4} + 2 q^{5} + q^{6} + 4 q^{7} - q^{8} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - q^{2} - q^{3} + q^{4} + 2 q^{5} + q^{6} + 4 q^{7} - q^{8} + q^{9} - 2 q^{10} + q^{11} - q^{12} + 6 q^{13} - 4 q^{14} - 2 q^{15} + q^{16} - q^{17} - q^{18} + 4 q^{19} + 2 q^{20} - 4 q^{21} - q^{22} + q^{24} - q^{25} - 6 q^{26} - q^{27} + 4 q^{28} + 2 q^{29} + 2 q^{30} - q^{32} - q^{33} + q^{34} + 8 q^{35} + q^{36} - 10 q^{37} - 4 q^{38} - 6 q^{39} - 2 q^{40} - 10 q^{41} + 4 q^{42} - 4 q^{43} + q^{44} + 2 q^{45} + 4 q^{47} - q^{48} + 9 q^{49} + q^{50} + q^{51} + 6 q^{52} - 2 q^{53} + q^{54} + 2 q^{55} - 4 q^{56} - 4 q^{57} - 2 q^{58} - 2 q^{60} + 2 q^{61} + 4 q^{63} + q^{64} + 12 q^{65} + q^{66} + 12 q^{67} - q^{68} - 8 q^{70} - q^{72} - 10 q^{73} + 10 q^{74} + q^{75} + 4 q^{76} + 4 q^{77} + 6 q^{78} + 4 q^{79} + 2 q^{80} + q^{81} + 10 q^{82} - 12 q^{83} - 4 q^{84} - 2 q^{85} + 4 q^{86} - 2 q^{87} - q^{88} - 14 q^{89} - 2 q^{90} + 24 q^{91} - 4 q^{94} + 8 q^{95} + q^{96} + 18 q^{97} - 9 q^{98} + q^{99}+O(q^{100}) \) 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
−1.00000 −1.00000 1.00000 2.00000 1.00000 4.00000 −1.00000 1.00000 −2.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(3\) \(1\)
\(11\) \(-1\)
\(17\) \(1\)

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 1122.2.a.c 1
3.b odd 2 1 3366.2.a.m 1
4.b odd 2 1 8976.2.a.ba 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1122.2.a.c 1 1.a even 1 1 trivial
3366.2.a.m 1 3.b odd 2 1
8976.2.a.ba 1 4.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1122))\):

\( T_{5} - 2 \) Copy content Toggle raw display
\( T_{7} - 4 \) Copy content Toggle raw display
\( T_{13} - 6 \) Copy content Toggle raw display
\( T_{19} - 4 \) Copy content Toggle raw display

Hecke characteristic polynomials

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