Properties

Label 1122.2.a.n
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

\(f(q)\) \(=\) \( q + q^{2} + q^{3} + q^{4} + 4q^{5} + q^{6} - 2q^{7} + q^{8} + q^{9} + O(q^{10}) \) \( q + q^{2} + q^{3} + q^{4} + 4q^{5} + q^{6} - 2q^{7} + q^{8} + q^{9} + 4q^{10} + q^{11} + q^{12} - 2q^{14} + 4q^{15} + q^{16} - q^{17} + q^{18} + 4q^{20} - 2q^{21} + q^{22} - 6q^{23} + q^{24} + 11q^{25} + q^{27} - 2q^{28} - 2q^{29} + 4q^{30} + 4q^{31} + q^{32} + q^{33} - q^{34} - 8q^{35} + q^{36} + 2q^{37} + 4q^{40} - 6q^{41} - 2q^{42} - 4q^{43} + q^{44} + 4q^{45} - 6q^{46} - 6q^{47} + q^{48} - 3q^{49} + 11q^{50} - q^{51} + 8q^{53} + q^{54} + 4q^{55} - 2q^{56} - 2q^{58} + 8q^{59} + 4q^{60} - 8q^{61} + 4q^{62} - 2q^{63} + q^{64} + q^{66} - 4q^{67} - q^{68} - 6q^{69} - 8q^{70} - 6q^{71} + q^{72} + 10q^{73} + 2q^{74} + 11q^{75} - 2q^{77} - 6q^{79} + 4q^{80} + q^{81} - 6q^{82} - 4q^{83} - 2q^{84} - 4q^{85} - 4q^{86} - 2q^{87} + q^{88} - 14q^{89} + 4q^{90} - 6q^{92} + 4q^{93} - 6q^{94} + q^{96} + 14q^{97} - 3q^{98} + q^{99} + O(q^{100}) \)

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 1.00000 1.00000 4.00000 1.00000 −2.00000 1.00000 1.00000 4.00000
\(n\): 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.n 1
3.b odd 2 1 3366.2.a.a 1
4.b odd 2 1 8976.2.a.s 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1122.2.a.n 1 1.a even 1 1 trivial
3366.2.a.a 1 3.b odd 2 1
8976.2.a.s 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(1122))\):

\( T_{5} - 4 \)
\( T_{7} + 2 \)
\( T_{13} \)
\( T_{19} \)

Hecke characteristic polynomials

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