Properties

Label 1155.2.a.m
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

\(f(q)\) \(=\) \( q + q^{2} + q^{3} - q^{4} + q^{5} + q^{6} + q^{7} - 3q^{8} + q^{9} + O(q^{10}) \) \( q + q^{2} + q^{3} - q^{4} + q^{5} + q^{6} + q^{7} - 3q^{8} + q^{9} + q^{10} - q^{11} - q^{12} + 6q^{13} + q^{14} + q^{15} - q^{16} + 2q^{17} + q^{18} + 4q^{19} - q^{20} + q^{21} - q^{22} - 4q^{23} - 3q^{24} + q^{25} + 6q^{26} + q^{27} - q^{28} - 2q^{29} + q^{30} + 4q^{31} + 5q^{32} - q^{33} + 2q^{34} + q^{35} - q^{36} - 2q^{37} + 4q^{38} + 6q^{39} - 3q^{40} + 6q^{41} + q^{42} + 4q^{43} + q^{44} + q^{45} - 4q^{46} + 8q^{47} - q^{48} + q^{49} + q^{50} + 2q^{51} - 6q^{52} - 2q^{53} + q^{54} - q^{55} - 3q^{56} + 4q^{57} - 2q^{58} - 8q^{59} - q^{60} + 10q^{61} + 4q^{62} + q^{63} + 7q^{64} + 6q^{65} - q^{66} - 8q^{67} - 2q^{68} - 4q^{69} + q^{70} - 3q^{72} - 14q^{73} - 2q^{74} + q^{75} - 4q^{76} - q^{77} + 6q^{78} - 16q^{79} - q^{80} + q^{81} + 6q^{82} - 4q^{83} - q^{84} + 2q^{85} + 4q^{86} - 2q^{87} + 3q^{88} - 6q^{89} + q^{90} + 6q^{91} + 4q^{92} + 4q^{93} + 8q^{94} + 4q^{95} + 5q^{96} + 18q^{97} + q^{98} - q^{99} + O(q^{100}) \)

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

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

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -1 + T \)
$3$ \( -1 + T \)
$5$ \( -1 + T \)
$7$ \( -1 + T \)
$11$ \( 1 + T \)
$13$ \( -6 + T \)
$17$ \( -2 + T \)
$19$ \( -4 + T \)
$23$ \( 4 + T \)
$29$ \( 2 + T \)
$31$ \( -4 + T \)
$37$ \( 2 + T \)
$41$ \( -6 + T \)
$43$ \( -4 + T \)
$47$ \( -8 + T \)
$53$ \( 2 + T \)
$59$ \( 8 + T \)
$61$ \( -10 + T \)
$67$ \( 8 + T \)
$71$ \( T \)
$73$ \( 14 + T \)
$79$ \( 16 + T \)
$83$ \( 4 + T \)
$89$ \( 6 + T \)
$97$ \( -18 + T \)
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