Properties

Label 1155.2.a.j
Level $1155$
Weight $2$
Character orbit 1155.a
Self dual yes
Analytic conductor $9.223$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1155.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(9.22272143346\)
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

\(f(q)\) \(=\) \( q + q^{2} - q^{3} - q^{4} - q^{5} - q^{6} + q^{7} - 3q^{8} + q^{9} + O(q^{10}) \) \( q + q^{2} - q^{3} - q^{4} - q^{5} - q^{6} + q^{7} - 3q^{8} + q^{9} - q^{10} - q^{11} + q^{12} - 2q^{13} + q^{14} + q^{15} - q^{16} + 6q^{17} + q^{18} + 4q^{19} + q^{20} - q^{21} - q^{22} - 4q^{23} + 3q^{24} + q^{25} - 2q^{26} - q^{27} - q^{28} + 10q^{29} + q^{30} - 4q^{31} + 5q^{32} + q^{33} + 6q^{34} - q^{35} - q^{36} - 2q^{37} + 4q^{38} + 2q^{39} + 3q^{40} + 10q^{41} - q^{42} + 12q^{43} + q^{44} - q^{45} - 4q^{46} + q^{48} + q^{49} + q^{50} - 6q^{51} + 2q^{52} + 10q^{53} - q^{54} + q^{55} - 3q^{56} - 4q^{57} + 10q^{58} - 12q^{59} - q^{60} - 2q^{61} - 4q^{62} + q^{63} + 7q^{64} + 2q^{65} + q^{66} + 4q^{67} - 6q^{68} + 4q^{69} - q^{70} + 8q^{71} - 3q^{72} - 14q^{73} - 2q^{74} - q^{75} - 4q^{76} - q^{77} + 2q^{78} + 4q^{79} + q^{80} + q^{81} + 10q^{82} + 8q^{83} + q^{84} - 6q^{85} + 12q^{86} - 10q^{87} + 3q^{88} + 6q^{89} - q^{90} - 2q^{91} + 4q^{92} + 4q^{93} - 4q^{95} - 5q^{96} - 10q^{97} + q^{98} - q^{99} + O(q^{100}) \)

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 −1.00000 −1.00000 1.00000 −3.00000 1.00000 −1.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \(1\)
\(5\) \(1\)
\(7\) \(-1\)
\(11\) \(1\)

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 1155.2.a.j 1
3.b odd 2 1 3465.2.a.g 1
5.b even 2 1 5775.2.a.f 1
7.b odd 2 1 8085.2.a.w 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1155.2.a.j 1 1.a even 1 1 trivial
3465.2.a.g 1 3.b odd 2 1
5775.2.a.f 1 5.b even 2 1
8085.2.a.w 1 7.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 \(S_{2}^{\mathrm{new}}(\Gamma_0(1155))\):

\( T_{2} - 1 \)
\( T_{13} + 2 \)
\( T_{17} - 6 \)

Hecke characteristic polynomials

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