Properties

Label 1815.2.a.c
Level $1815$
Weight $2$
Character orbit 1815.a
Self dual yes
Analytic conductor $14.493$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1815.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(14.4928479669\)
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

\(f(q)\) \(=\) \( q + q^{3} - 2q^{4} - q^{5} + q^{7} + q^{9} + O(q^{10}) \) \( q + q^{3} - 2q^{4} - q^{5} + q^{7} + q^{9} - 2q^{12} - 2q^{13} - q^{15} + 4q^{16} - 6q^{17} + 7q^{19} + 2q^{20} + q^{21} - 6q^{23} + q^{25} + q^{27} - 2q^{28} - q^{31} - q^{35} - 2q^{36} - 7q^{37} - 2q^{39} + 6q^{41} - 8q^{43} - q^{45} + 4q^{48} - 6q^{49} - 6q^{51} + 4q^{52} - 6q^{53} + 7q^{57} - 12q^{59} + 2q^{60} + q^{61} + q^{63} - 8q^{64} + 2q^{65} - 7q^{67} + 12q^{68} - 6q^{69} + 6q^{71} + 13q^{73} + q^{75} - 14q^{76} - 11q^{79} - 4q^{80} + q^{81} - 2q^{84} + 6q^{85} - 18q^{89} - 2q^{91} + 12q^{92} - q^{93} - 7q^{95} - q^{97} + O(q^{100}) \)

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 −1.00000 0 1.00000 0 1.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \(-1\)
\(5\) \(1\)
\(11\) \(-1\)

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 1815.2.a.c yes 1
3.b odd 2 1 5445.2.a.g 1
5.b even 2 1 9075.2.a.j 1
11.b odd 2 1 1815.2.a.b 1
33.d even 2 1 5445.2.a.f 1
55.d odd 2 1 9075.2.a.k 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1815.2.a.b 1 11.b odd 2 1
1815.2.a.c yes 1 1.a even 1 1 trivial
5445.2.a.f 1 33.d even 2 1
5445.2.a.g 1 3.b odd 2 1
9075.2.a.j 1 5.b even 2 1
9075.2.a.k 1 55.d odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1815))\):

\( T_{2} \)
\( T_{7} - 1 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( -1 + T \)
$5$ \( 1 + T \)
$7$ \( -1 + T \)
$11$ \( T \)
$13$ \( 2 + T \)
$17$ \( 6 + T \)
$19$ \( -7 + T \)
$23$ \( 6 + T \)
$29$ \( T \)
$31$ \( 1 + T \)
$37$ \( 7 + T \)
$41$ \( -6 + T \)
$43$ \( 8 + T \)
$47$ \( T \)
$53$ \( 6 + T \)
$59$ \( 12 + T \)
$61$ \( -1 + T \)
$67$ \( 7 + T \)
$71$ \( -6 + T \)
$73$ \( -13 + T \)
$79$ \( 11 + T \)
$83$ \( T \)
$89$ \( 18 + T \)
$97$ \( 1 + T \)
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