Properties

Label 1155.4.a.b
Level 1155
Weight 4
Character orbit 1155.a
Self dual yes
Analytic conductor 68.147
Analytic rank 1
Dimension 1
CM no
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 1155.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(68.1472060566\)
Analytic rank: \(1\)
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

\(f(q)\) \(=\) \( q - 3q^{2} - 3q^{3} + q^{4} - 5q^{5} + 9q^{6} + 7q^{7} + 21q^{8} + 9q^{9} + O(q^{10}) \) \( q - 3q^{2} - 3q^{3} + q^{4} - 5q^{5} + 9q^{6} + 7q^{7} + 21q^{8} + 9q^{9} + 15q^{10} - 11q^{11} - 3q^{12} + 44q^{13} - 21q^{14} + 15q^{15} - 71q^{16} - 72q^{17} - 27q^{18} - 4q^{19} - 5q^{20} - 21q^{21} + 33q^{22} - 162q^{23} - 63q^{24} + 25q^{25} - 132q^{26} - 27q^{27} + 7q^{28} + 102q^{29} - 45q^{30} + 56q^{31} + 45q^{32} + 33q^{33} + 216q^{34} - 35q^{35} + 9q^{36} - 124q^{37} + 12q^{38} - 132q^{39} - 105q^{40} + 18q^{41} + 63q^{42} + 224q^{43} - 11q^{44} - 45q^{45} + 486q^{46} + 120q^{47} + 213q^{48} + 49q^{49} - 75q^{50} + 216q^{51} + 44q^{52} + 414q^{53} + 81q^{54} + 55q^{55} + 147q^{56} + 12q^{57} - 306q^{58} + 660q^{59} + 15q^{60} - 334q^{61} - 168q^{62} + 63q^{63} + 433q^{64} - 220q^{65} - 99q^{66} + 314q^{67} - 72q^{68} + 486q^{69} + 105q^{70} - 36q^{71} + 189q^{72} + 110q^{73} + 372q^{74} - 75q^{75} - 4q^{76} - 77q^{77} + 396q^{78} - 316q^{79} + 355q^{80} + 81q^{81} - 54q^{82} - 732q^{83} - 21q^{84} + 360q^{85} - 672q^{86} - 306q^{87} - 231q^{88} - 924q^{89} + 135q^{90} + 308q^{91} - 162q^{92} - 168q^{93} - 360q^{94} + 20q^{95} - 135q^{96} + 1154q^{97} - 147q^{98} - 99q^{99} + O(q^{100}) \)

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
−3.00000 −3.00000 1.00000 −5.00000 9.00000 7.00000 21.0000 9.00000 15.0000
\(n\): 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 1155.4.a.b 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1155.4.a.b 1 1.a even 1 1 trivial

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 \(S_{4}^{\mathrm{new}}(\Gamma_0(1155))\):

\( T_{2} + 3 \)
\( T_{13} - 44 \)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( 1 + 3 T + 8 T^{2} \)
$3$ \( 1 + 3 T \)
$5$ \( 1 + 5 T \)
$7$ \( 1 - 7 T \)
$11$ \( 1 + 11 T \)
$13$ \( 1 - 44 T + 2197 T^{2} \)
$17$ \( 1 + 72 T + 4913 T^{2} \)
$19$ \( 1 + 4 T + 6859 T^{2} \)
$23$ \( 1 + 162 T + 12167 T^{2} \)
$29$ \( 1 - 102 T + 24389 T^{2} \)
$31$ \( 1 - 56 T + 29791 T^{2} \)
$37$ \( 1 + 124 T + 50653 T^{2} \)
$41$ \( 1 - 18 T + 68921 T^{2} \)
$43$ \( 1 - 224 T + 79507 T^{2} \)
$47$ \( 1 - 120 T + 103823 T^{2} \)
$53$ \( 1 - 414 T + 148877 T^{2} \)
$59$ \( 1 - 660 T + 205379 T^{2} \)
$61$ \( 1 + 334 T + 226981 T^{2} \)
$67$ \( 1 - 314 T + 300763 T^{2} \)
$71$ \( 1 + 36 T + 357911 T^{2} \)
$73$ \( 1 - 110 T + 389017 T^{2} \)
$79$ \( 1 + 316 T + 493039 T^{2} \)
$83$ \( 1 + 732 T + 571787 T^{2} \)
$89$ \( 1 + 924 T + 704969 T^{2} \)
$97$ \( 1 - 1154 T + 912673 T^{2} \)
show more
show less