Properties

Label 1155.2.a.f
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

Related objects

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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

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

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:

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.f 1
3.b odd 2 1 3465.2.a.n 1
5.b even 2 1 5775.2.a.q 1
7.b odd 2 1 8085.2.a.f 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1155.2.a.f 1 1.a even 1 1 trivial
3465.2.a.n 1 3.b odd 2 1
5775.2.a.q 1 5.b even 2 1
8085.2.a.f 1 7.b odd 2 1

Atkin-Lehner signs

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

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1155))\):

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

Hecke Characteristic Polynomials

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