Properties

Label 5775.2.a.o
Level 5775
Weight 2
Character orbit 5775.a
Self dual yes
Analytic conductor 46.114
Analytic rank 1
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 5775 = 3 \cdot 5^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5775.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(46.1136071673\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1155)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{3} - 2q^{4} - q^{7} + q^{9} + O(q^{10}) \) \( q + q^{3} - 2q^{4} - q^{7} + q^{9} + q^{11} - 2q^{12} + 4q^{16} - 3q^{17} - 3q^{19} - q^{21} + q^{23} + q^{27} + 2q^{28} - 7q^{29} + 6q^{31} + q^{33} - 2q^{36} + 8q^{37} - 2q^{41} + 5q^{43} - 2q^{44} + 6q^{47} + 4q^{48} + q^{49} - 3q^{51} + 3q^{53} - 3q^{57} - 5q^{59} - 7q^{61} - q^{63} - 8q^{64} - 6q^{67} + 6q^{68} + q^{69} - 10q^{71} - 12q^{73} + 6q^{76} - q^{77} - 16q^{79} + q^{81} + 3q^{83} + 2q^{84} - 7q^{87} + 3q^{89} - 2q^{92} + 6q^{93} + q^{97} + q^{99} + O(q^{100}) \)

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
0 1.00000 −2.00000 0 0 −1.00000 0 1.00000 0
\(n\): 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 5775.2.a.o 1
5.b even 2 1 1155.2.a.g 1
15.d odd 2 1 3465.2.a.i 1
35.c odd 2 1 8085.2.a.q 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1155.2.a.g 1 5.b even 2 1
3465.2.a.i 1 15.d odd 2 1
5775.2.a.o 1 1.a even 1 1 trivial
8085.2.a.q 1 35.c 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(5775))\):

\( T_{2} \)
\( T_{13} \)
\( T_{17} + 3 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + 2 T^{2} \)
$3$ \( 1 - T \)
$5$ 1
$7$ \( 1 + T \)
$11$ \( 1 - T \)
$13$ \( 1 + 13 T^{2} \)
$17$ \( 1 + 3 T + 17 T^{2} \)
$19$ \( 1 + 3 T + 19 T^{2} \)
$23$ \( 1 - T + 23 T^{2} \)
$29$ \( 1 + 7 T + 29 T^{2} \)
$31$ \( 1 - 6 T + 31 T^{2} \)
$37$ \( 1 - 8 T + 37 T^{2} \)
$41$ \( 1 + 2 T + 41 T^{2} \)
$43$ \( 1 - 5 T + 43 T^{2} \)
$47$ \( 1 - 6 T + 47 T^{2} \)
$53$ \( 1 - 3 T + 53 T^{2} \)
$59$ \( 1 + 5 T + 59 T^{2} \)
$61$ \( 1 + 7 T + 61 T^{2} \)
$67$ \( 1 + 6 T + 67 T^{2} \)
$71$ \( 1 + 10 T + 71 T^{2} \)
$73$ \( 1 + 12 T + 73 T^{2} \)
$79$ \( 1 + 16 T + 79 T^{2} \)
$83$ \( 1 - 3 T + 83 T^{2} \)
$89$ \( 1 - 3 T + 89 T^{2} \)
$97$ \( 1 - T + 97 T^{2} \)
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