Properties

Label 1815.2.a.a
Level $1815$
Weight $2$
Character orbit 1815.a
Self dual yes
Analytic conductor $14.493$
Analytic rank $0$
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: \(0\)
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

\(f(q)\) \(=\) \( q - q^{2} + q^{3} - q^{4} - q^{5} - q^{6} - 2q^{7} + 3q^{8} + q^{9} + O(q^{10}) \) \( q - q^{2} + q^{3} - q^{4} - q^{5} - q^{6} - 2q^{7} + 3q^{8} + q^{9} + q^{10} - q^{12} + 4q^{13} + 2q^{14} - q^{15} - q^{16} - 6q^{17} - q^{18} - 6q^{19} + q^{20} - 2q^{21} + 4q^{23} + 3q^{24} + q^{25} - 4q^{26} + q^{27} + 2q^{28} + 6q^{29} + q^{30} + 8q^{31} - 5q^{32} + 6q^{34} + 2q^{35} - q^{36} - 6q^{37} + 6q^{38} + 4q^{39} - 3q^{40} - 6q^{41} + 2q^{42} - 6q^{43} - q^{45} - 4q^{46} + 8q^{47} - q^{48} - 3q^{49} - q^{50} - 6q^{51} - 4q^{52} + 6q^{53} - q^{54} - 6q^{56} - 6q^{57} - 6q^{58} + q^{60} + 4q^{61} - 8q^{62} - 2q^{63} + 7q^{64} - 4q^{65} + 12q^{67} + 6q^{68} + 4q^{69} - 2q^{70} + 8q^{71} + 3q^{72} + 16q^{73} + 6q^{74} + q^{75} + 6q^{76} - 4q^{78} + 2q^{79} + q^{80} + q^{81} + 6q^{82} + 2q^{84} + 6q^{85} + 6q^{86} + 6q^{87} + 10q^{89} + q^{90} - 8q^{91} - 4q^{92} + 8q^{93} - 8q^{94} + 6q^{95} - 5q^{96} - 6q^{97} + 3q^{98} + O(q^{100}) \)

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

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

Hecke kernels

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

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

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + T \)
$3$ \( -1 + T \)
$5$ \( 1 + T \)
$7$ \( 2 + T \)
$11$ \( T \)
$13$ \( -4 + T \)
$17$ \( 6 + T \)
$19$ \( 6 + T \)
$23$ \( -4 + T \)
$29$ \( -6 + T \)
$31$ \( -8 + T \)
$37$ \( 6 + T \)
$41$ \( 6 + T \)
$43$ \( 6 + T \)
$47$ \( -8 + T \)
$53$ \( -6 + T \)
$59$ \( T \)
$61$ \( -4 + T \)
$67$ \( -12 + T \)
$71$ \( -8 + T \)
$73$ \( -16 + T \)
$79$ \( -2 + T \)
$83$ \( T \)
$89$ \( -10 + T \)
$97$ \( 6 + T \)
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