Properties

Label 1078.2.a.k
Level $1078$
Weight $2$
Character orbit 1078.a
Self dual yes
Analytic conductor $8.608$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

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Newspace parameters

Level: \( N \) \(=\) \( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1078.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(8.60787333789\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 154)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} + q^{3} + q^{4} + q^{6} + q^{8} - 2q^{9} + O(q^{10}) \) \( q + q^{2} + q^{3} + q^{4} + q^{6} + q^{8} - 2q^{9} - q^{11} + q^{12} + 5q^{13} + q^{16} + 6q^{17} - 2q^{18} + 2q^{19} - q^{22} + 6q^{23} + q^{24} - 5q^{25} + 5q^{26} - 5q^{27} + 3q^{29} + 8q^{31} + q^{32} - q^{33} + 6q^{34} - 2q^{36} + 2q^{37} + 2q^{38} + 5q^{39} - 6q^{41} - 4q^{43} - q^{44} + 6q^{46} + 6q^{47} + q^{48} - 5q^{50} + 6q^{51} + 5q^{52} - 12q^{53} - 5q^{54} + 2q^{57} + 3q^{58} - 3q^{59} - 7q^{61} + 8q^{62} + q^{64} - q^{66} - 13q^{67} + 6q^{68} + 6q^{69} - 12q^{71} - 2q^{72} - 10q^{73} + 2q^{74} - 5q^{75} + 2q^{76} + 5q^{78} - q^{79} + q^{81} - 6q^{82} + 6q^{83} - 4q^{86} + 3q^{87} - q^{88} + 6q^{89} + 6q^{92} + 8q^{93} + 6q^{94} + q^{96} - 13q^{97} + 2q^{99} + O(q^{100}) \)

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(7\) \(1\)
\(11\) \(1\)

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 1078.2.a.k 1
3.b odd 2 1 9702.2.a.o 1
4.b odd 2 1 8624.2.a.l 1
7.b odd 2 1 1078.2.a.i 1
7.c even 3 2 154.2.e.b 2
7.d odd 6 2 1078.2.e.d 2
21.c even 2 1 9702.2.a.l 1
21.h odd 6 2 1386.2.k.n 2
28.d even 2 1 8624.2.a.t 1
28.g odd 6 2 1232.2.q.c 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
154.2.e.b 2 7.c even 3 2
1078.2.a.i 1 7.b odd 2 1
1078.2.a.k 1 1.a even 1 1 trivial
1078.2.e.d 2 7.d odd 6 2
1232.2.q.c 2 28.g odd 6 2
1386.2.k.n 2 21.h odd 6 2
8624.2.a.l 1 4.b odd 2 1
8624.2.a.t 1 28.d even 2 1
9702.2.a.l 1 21.c even 2 1
9702.2.a.o 1 3.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1078))\):

\( T_{3} - 1 \)
\( T_{5} \)
\( T_{13} - 5 \)

Hecke characteristic polynomials

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