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Properties

Label 1078.4.a.h
Level $1078$
Weight $4$
Character orbit 1078.a
Self dual yes
Analytic conductor $63.604$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1078.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(63.6040589862\)
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

\(f(q)\) \(=\) \( q + 2 q^{2} + 10 q^{3} + 4 q^{4} + 14 q^{5} + 20 q^{6} + 8 q^{8} + 73 q^{9} + O(q^{10}) \) \( q + 2 q^{2} + 10 q^{3} + 4 q^{4} + 14 q^{5} + 20 q^{6} + 8 q^{8} + 73 q^{9} + 28 q^{10} - 11 q^{11} + 40 q^{12} + 16 q^{13} + 140 q^{15} + 16 q^{16} - 108 q^{17} + 146 q^{18} - 116 q^{19} + 56 q^{20} - 22 q^{22} + 68 q^{23} + 80 q^{24} + 71 q^{25} + 32 q^{26} + 460 q^{27} + 122 q^{29} + 280 q^{30} + 262 q^{31} + 32 q^{32} - 110 q^{33} - 216 q^{34} + 292 q^{36} + 130 q^{37} - 232 q^{38} + 160 q^{39} + 112 q^{40} - 204 q^{41} - 396 q^{43} - 44 q^{44} + 1022 q^{45} + 136 q^{46} - 166 q^{47} + 160 q^{48} + 142 q^{50} - 1080 q^{51} + 64 q^{52} + 442 q^{53} + 920 q^{54} - 154 q^{55} - 1160 q^{57} + 244 q^{58} - 702 q^{59} + 560 q^{60} - 196 q^{61} + 524 q^{62} + 64 q^{64} + 224 q^{65} - 220 q^{66} - 416 q^{67} - 432 q^{68} + 680 q^{69} + 492 q^{71} + 584 q^{72} - 408 q^{73} + 260 q^{74} + 710 q^{75} - 464 q^{76} + 320 q^{78} + 600 q^{79} + 224 q^{80} + 2629 q^{81} - 408 q^{82} + 1212 q^{83} - 1512 q^{85} - 792 q^{86} + 1220 q^{87} - 88 q^{88} - 1146 q^{89} + 2044 q^{90} + 272 q^{92} + 2620 q^{93} - 332 q^{94} - 1624 q^{95} + 320 q^{96} + 482 q^{97} - 803 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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 10.0000 4.00000 14.0000 20.0000 0 8.00000 73.0000 28.0000
\(n\): 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 1078.4.a.h 1
7.b odd 2 1 154.4.a.c ✓ 1
21.c even 2 1 1386.4.a.g 1
28.d even 2 1 1232.4.a.i 1
77.b even 2 1 1694.4.a.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
154.4.a.c ✓ 1 7.b odd 2 1
1078.4.a.h 1 1.a even 1 1 trivial
1232.4.a.i 1 28.d even 2 1
1386.4.a.g 1 21.c even 2 1
1694.4.a.a 1 77.b even 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3} - 10 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1078))\).

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -2 + T \)
$3$ \( -10 + T \)
$5$ \( -14 + T \)
$7$ \( T \)
$11$ \( 11 + T \)
$13$ \( -16 + T \)
$17$ \( 108 + T \)
$19$ \( 116 + T \)
$23$ \( -68 + T \)
$29$ \( -122 + T \)
$31$ \( -262 + T \)
$37$ \( -130 + T \)
$41$ \( 204 + T \)
$43$ \( 396 + T \)
$47$ \( 166 + T \)
$53$ \( -442 + T \)
$59$ \( 702 + T \)
$61$ \( 196 + T \)
$67$ \( 416 + T \)
$71$ \( -492 + T \)
$73$ \( 408 + T \)
$79$ \( -600 + T \)
$83$ \( -1212 + T \)
$89$ \( 1146 + T \)
$97$ \( -482 + T \)
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