Properties

Label 1078.2.a.d
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

\(f(q)\) \(=\) \( q - q^{2} + q^{4} + 4q^{5} - q^{8} - 3q^{9} + O(q^{10}) \) \( q - q^{2} + q^{4} + 4q^{5} - q^{8} - 3q^{9} - 4q^{10} - q^{11} - 2q^{13} + q^{16} + 4q^{17} + 3q^{18} + 6q^{19} + 4q^{20} + q^{22} + 4q^{23} + 11q^{25} + 2q^{26} - 2q^{29} + 2q^{31} - q^{32} - 4q^{34} - 3q^{36} + 10q^{37} - 6q^{38} - 4q^{40} - 4q^{41} - 8q^{43} - q^{44} - 12q^{45} - 4q^{46} - 2q^{47} - 11q^{50} - 2q^{52} + 6q^{53} - 4q^{55} + 2q^{58} + 12q^{59} + 14q^{61} - 2q^{62} + q^{64} - 8q^{65} - 12q^{67} + 4q^{68} - 8q^{71} + 3q^{72} - 4q^{73} - 10q^{74} + 6q^{76} + 4q^{80} + 9q^{81} + 4q^{82} + 6q^{83} + 16q^{85} + 8q^{86} + q^{88} + 6q^{89} + 12q^{90} + 4q^{92} + 2q^{94} + 24q^{95} + 14q^{97} + 3q^{99} + O(q^{100}) \)

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 0 1.00000 4.00000 0 0 −1.00000 −3.00000 −4.00000
\(n\): 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.d 1
3.b odd 2 1 9702.2.a.ba 1
4.b odd 2 1 8624.2.a.r 1
7.b odd 2 1 154.2.a.a 1
7.c even 3 2 1078.2.e.i 2
7.d odd 6 2 1078.2.e.j 2
21.c even 2 1 1386.2.a.l 1
28.d even 2 1 1232.2.a.e 1
35.c odd 2 1 3850.2.a.u 1
35.f even 4 2 3850.2.c.j 2
56.e even 2 1 4928.2.a.w 1
56.h odd 2 1 4928.2.a.v 1
77.b even 2 1 1694.2.a.g 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
154.2.a.a 1 7.b odd 2 1
1078.2.a.d 1 1.a even 1 1 trivial
1078.2.e.i 2 7.c even 3 2
1078.2.e.j 2 7.d odd 6 2
1232.2.a.e 1 28.d even 2 1
1386.2.a.l 1 21.c even 2 1
1694.2.a.g 1 77.b even 2 1
3850.2.a.u 1 35.c odd 2 1
3850.2.c.j 2 35.f even 4 2
4928.2.a.v 1 56.h odd 2 1
4928.2.a.w 1 56.e even 2 1
8624.2.a.r 1 4.b odd 2 1
9702.2.a.ba 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(1078))\):

\( T_{3} \)
\( T_{5} - 4 \)
\( T_{13} + 2 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + T \)
$3$ \( T \)
$5$ \( -4 + T \)
$7$ \( T \)
$11$ \( 1 + T \)
$13$ \( 2 + T \)
$17$ \( -4 + T \)
$19$ \( -6 + T \)
$23$ \( -4 + T \)
$29$ \( 2 + T \)
$31$ \( -2 + T \)
$37$ \( -10 + T \)
$41$ \( 4 + T \)
$43$ \( 8 + T \)
$47$ \( 2 + T \)
$53$ \( -6 + T \)
$59$ \( -12 + T \)
$61$ \( -14 + T \)
$67$ \( 12 + T \)
$71$ \( 8 + T \)
$73$ \( 4 + T \)
$79$ \( T \)
$83$ \( -6 + T \)
$89$ \( -6 + T \)
$97$ \( -14 + T \)
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