Properties

Label 5415.2.a.c
Level $5415$
Weight $2$
Character orbit 5415.a
Self dual yes
Analytic conductor $43.239$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 5415 = 3 \cdot 5 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5415.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(43.2389926945\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 285)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

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

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 −2.00000 3.00000 1.00000 1.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \(-1\)
\(5\) \(1\)
\(19\) \(-1\)

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 5415.2.a.c 1
19.b odd 2 1 285.2.a.b 1
57.d even 2 1 855.2.a.b 1
76.d even 2 1 4560.2.a.v 1
95.d odd 2 1 1425.2.a.d 1
95.g even 4 2 1425.2.c.d 2
285.b even 2 1 4275.2.a.o 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
285.2.a.b 1 19.b odd 2 1
855.2.a.b 1 57.d even 2 1
1425.2.a.d 1 95.d odd 2 1
1425.2.c.d 2 95.g even 4 2
4275.2.a.o 1 285.b even 2 1
4560.2.a.v 1 76.d even 2 1
5415.2.a.c 1 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(5415))\):

\( T_{2} + 1 \)
\( T_{7} + 2 \)
\( T_{11} + 2 \)
\( T_{13} - 4 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + T \)
$3$ \( -1 + T \)
$5$ \( 1 + T \)
$7$ \( 2 + T \)
$11$ \( 2 + T \)
$13$ \( -4 + T \)
$17$ \( -2 + T \)
$19$ \( T \)
$23$ \( 4 + T \)
$29$ \( 4 + T \)
$31$ \( T \)
$37$ \( T \)
$41$ \( T \)
$43$ \( 10 + T \)
$47$ \( -12 + T \)
$53$ \( -2 + T \)
$59$ \( 4 + T \)
$61$ \( -2 + T \)
$67$ \( -16 + T \)
$71$ \( T \)
$73$ \( 2 + T \)
$79$ \( -8 + T \)
$83$ \( 12 + T \)
$89$ \( T \)
$97$ \( -16 + T \)
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