Properties

Label 1911.2.a.a
Level $1911$
Weight $2$
Character orbit 1911.a
Self dual yes
Analytic conductor $15.259$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1911 = 3 \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1911.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(15.2594118263\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 273)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - 2q^{2} + q^{3} + 2q^{4} + q^{5} - 2q^{6} + q^{9} + O(q^{10}) \) \( q - 2q^{2} + q^{3} + 2q^{4} + q^{5} - 2q^{6} + q^{9} - 2q^{10} - 2q^{11} + 2q^{12} - q^{13} + q^{15} - 4q^{16} + 4q^{17} - 2q^{18} - 3q^{19} + 2q^{20} + 4q^{22} - 9q^{23} - 4q^{25} + 2q^{26} + q^{27} - q^{29} - 2q^{30} + 5q^{31} + 8q^{32} - 2q^{33} - 8q^{34} + 2q^{36} - 8q^{37} + 6q^{38} - q^{39} - 6q^{41} - 9q^{43} - 4q^{44} + q^{45} + 18q^{46} + 3q^{47} - 4q^{48} + 8q^{50} + 4q^{51} - 2q^{52} + 3q^{53} - 2q^{54} - 2q^{55} - 3q^{57} + 2q^{58} + 2q^{60} - 10q^{61} - 10q^{62} - 8q^{64} - q^{65} + 4q^{66} - 2q^{67} + 8q^{68} - 9q^{69} + 12q^{71} - 5q^{73} + 16q^{74} - 4q^{75} - 6q^{76} + 2q^{78} - 13q^{79} - 4q^{80} + q^{81} + 12q^{82} + 11q^{83} + 4q^{85} + 18q^{86} - q^{87} - q^{89} - 2q^{90} - 18q^{92} + 5q^{93} - 6q^{94} - 3q^{95} + 8q^{96} - q^{97} - 2q^{99} + O(q^{100}) \)

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
−2.00000 1.00000 2.00000 1.00000 −2.00000 0 0 1.00000 −2.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \(-1\)
\(7\) \(-1\)
\(13\) \(1\)

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 1911.2.a.a 1
3.b odd 2 1 5733.2.a.m 1
7.b odd 2 1 273.2.a.a 1
21.c even 2 1 819.2.a.e 1
28.d even 2 1 4368.2.a.q 1
35.c odd 2 1 6825.2.a.l 1
91.b odd 2 1 3549.2.a.d 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
273.2.a.a 1 7.b odd 2 1
819.2.a.e 1 21.c even 2 1
1911.2.a.a 1 1.a even 1 1 trivial
3549.2.a.d 1 91.b odd 2 1
4368.2.a.q 1 28.d even 2 1
5733.2.a.m 1 3.b odd 2 1
6825.2.a.l 1 35.c odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1911))\):

\( T_{2} + 2 \)
\( T_{5} - 1 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 2 + T \)
$3$ \( -1 + T \)
$5$ \( -1 + T \)
$7$ \( T \)
$11$ \( 2 + T \)
$13$ \( 1 + T \)
$17$ \( -4 + T \)
$19$ \( 3 + T \)
$23$ \( 9 + T \)
$29$ \( 1 + T \)
$31$ \( -5 + T \)
$37$ \( 8 + T \)
$41$ \( 6 + T \)
$43$ \( 9 + T \)
$47$ \( -3 + T \)
$53$ \( -3 + T \)
$59$ \( T \)
$61$ \( 10 + T \)
$67$ \( 2 + T \)
$71$ \( -12 + T \)
$73$ \( 5 + T \)
$79$ \( 13 + T \)
$83$ \( -11 + T \)
$89$ \( 1 + T \)
$97$ \( 1 + T \)
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