Properties

Label 1155.4.a.a
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

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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

\(f(q)\) \(=\) \( q - 3q^{2} - 3q^{3} + q^{4} - 5q^{5} + 9q^{6} + 7q^{7} + 21q^{8} + 9q^{9} + O(q^{10}) \) \( q - 3q^{2} - 3q^{3} + q^{4} - 5q^{5} + 9q^{6} + 7q^{7} + 21q^{8} + 9q^{9} + 15q^{10} - 11q^{11} - 3q^{12} - 82q^{13} - 21q^{14} + 15q^{15} - 71q^{16} + 54q^{17} - 27q^{18} + 80q^{19} - 5q^{20} - 21q^{21} + 33q^{22} + 48q^{23} - 63q^{24} + 25q^{25} + 246q^{26} - 27q^{27} + 7q^{28} - 234q^{29} - 45q^{30} - 28q^{31} + 45q^{32} + 33q^{33} - 162q^{34} - 35q^{35} + 9q^{36} - 82q^{37} - 240q^{38} + 246q^{39} - 105q^{40} + 270q^{41} + 63q^{42} - 28q^{43} - 11q^{44} - 45q^{45} - 144q^{46} - 300q^{47} + 213q^{48} + 49q^{49} - 75q^{50} - 162q^{51} - 82q^{52} + 582q^{53} + 81q^{54} + 55q^{55} + 147q^{56} - 240q^{57} + 702q^{58} - 684q^{59} + 15q^{60} + 758q^{61} + 84q^{62} + 63q^{63} + 433q^{64} + 410q^{65} - 99q^{66} + 524q^{67} + 54q^{68} - 144q^{69} + 105q^{70} + 552q^{71} + 189q^{72} + 110q^{73} + 246q^{74} - 75q^{75} + 80q^{76} - 77q^{77} - 738q^{78} + 944q^{79} + 355q^{80} + 81q^{81} - 810q^{82} + 1368q^{83} - 21q^{84} - 270q^{85} + 84q^{86} + 702q^{87} - 231q^{88} + 42q^{89} + 135q^{90} - 574q^{91} + 48q^{92} + 84q^{93} + 900q^{94} - 400q^{95} - 135q^{96} + 1658q^{97} - 147q^{98} - 99q^{99} + O(q^{100}) \)

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.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1155.4.a.a 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 \(S_{4}^{\mathrm{new}}(\Gamma_0(1155))\):

\( T_{2} + 3 \)
\( T_{13} + 82 \)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( 1 + 3 T + 8 T^{2} \)
$3$ \( 1 + 3 T \)
$5$ \( 1 + 5 T \)
$7$ \( 1 - 7 T \)
$11$ \( 1 + 11 T \)
$13$ \( 1 + 82 T + 2197 T^{2} \)
$17$ \( 1 - 54 T + 4913 T^{2} \)
$19$ \( 1 - 80 T + 6859 T^{2} \)
$23$ \( 1 - 48 T + 12167 T^{2} \)
$29$ \( 1 + 234 T + 24389 T^{2} \)
$31$ \( 1 + 28 T + 29791 T^{2} \)
$37$ \( 1 + 82 T + 50653 T^{2} \)
$41$ \( 1 - 270 T + 68921 T^{2} \)
$43$ \( 1 + 28 T + 79507 T^{2} \)
$47$ \( 1 + 300 T + 103823 T^{2} \)
$53$ \( 1 - 582 T + 148877 T^{2} \)
$59$ \( 1 + 684 T + 205379 T^{2} \)
$61$ \( 1 - 758 T + 226981 T^{2} \)
$67$ \( 1 - 524 T + 300763 T^{2} \)
$71$ \( 1 - 552 T + 357911 T^{2} \)
$73$ \( 1 - 110 T + 389017 T^{2} \)
$79$ \( 1 - 944 T + 493039 T^{2} \)
$83$ \( 1 - 1368 T + 571787 T^{2} \)
$89$ \( 1 - 42 T + 704969 T^{2} \)
$97$ \( 1 - 1658 T + 912673 T^{2} \)
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