Properties

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

Related objects

Downloads

Learn more

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: \(1\)
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

\(f(q)\) \(=\) \( q + q^{2} - 3q^{3} + q^{4} - 2q^{5} - 3q^{6} + q^{8} + 6q^{9} + O(q^{10}) \) \( q + q^{2} - 3q^{3} + q^{4} - 2q^{5} - 3q^{6} + q^{8} + 6q^{9} - 2q^{10} - q^{11} - 3q^{12} + 7q^{13} + 6q^{15} + q^{16} - 2q^{17} + 6q^{18} - 2q^{20} - q^{22} - 8q^{23} - 3q^{24} - q^{25} + 7q^{26} - 9q^{27} - 5q^{29} + 6q^{30} - 4q^{31} + q^{32} + 3q^{33} - 2q^{34} + 6q^{36} + 4q^{37} - 21q^{39} - 2q^{40} - 4q^{41} - 8q^{43} - q^{44} - 12q^{45} - 8q^{46} - 2q^{47} - 3q^{48} - q^{50} + 6q^{51} + 7q^{52} - 6q^{53} - 9q^{54} + 2q^{55} - 5q^{58} - 3q^{59} + 6q^{60} - q^{61} - 4q^{62} + q^{64} - 14q^{65} + 3q^{66} + 9q^{67} - 2q^{68} + 24q^{69} - 2q^{71} + 6q^{72} - 4q^{73} + 4q^{74} + 3q^{75} - 21q^{78} + 9q^{79} - 2q^{80} + 9q^{81} - 4q^{82} - 6q^{83} + 4q^{85} - 8q^{86} + 15q^{87} - q^{88} - 6q^{89} - 12q^{90} - 8q^{92} + 12q^{93} - 2q^{94} - 3q^{96} - 7q^{97} - 6q^{99} + O(q^{100}) \)

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 −3.00000 1.00000 −2.00000 −3.00000 0 1.00000 6.00000 −2.00000
\(n\): 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.g 1
3.b odd 2 1 9702.2.a.y 1
4.b odd 2 1 8624.2.a.be 1
7.b odd 2 1 1078.2.a.m 1
7.c even 3 2 1078.2.e.f 2
7.d odd 6 2 154.2.e.a 2
21.c even 2 1 9702.2.a.i 1
21.g even 6 2 1386.2.k.o 2
28.d even 2 1 8624.2.a.b 1
28.f even 6 2 1232.2.q.e 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
154.2.e.a 2 7.d odd 6 2
1078.2.a.g 1 1.a even 1 1 trivial
1078.2.a.m 1 7.b odd 2 1
1078.2.e.f 2 7.c even 3 2
1232.2.q.e 2 28.f even 6 2
1386.2.k.o 2 21.g even 6 2
8624.2.a.b 1 28.d even 2 1
8624.2.a.be 1 4.b odd 2 1
9702.2.a.i 1 21.c even 2 1
9702.2.a.y 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(1078))\):

\( T_{3} + 3 \)
\( T_{5} + 2 \)
\( T_{13} - 7 \)

Hecke characteristic polynomials

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