Properties

Label 1014.2.a.c
Level $1014$
Weight $2$
Character orbit 1014.a
Self dual yes
Analytic conductor $8.097$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1014.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(8.09683076496\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 78)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{2} + q^{3} + q^{4} + 3 q^{5} - q^{6} + 2 q^{7} - q^{8} + q^{9} + O(q^{10}) \) \( q - q^{2} + q^{3} + q^{4} + 3 q^{5} - q^{6} + 2 q^{7} - q^{8} + q^{9} - 3 q^{10} + 6 q^{11} + q^{12} - 2 q^{14} + 3 q^{15} + q^{16} - 3 q^{17} - q^{18} + 2 q^{19} + 3 q^{20} + 2 q^{21} - 6 q^{22} - 6 q^{23} - q^{24} + 4 q^{25} + q^{27} + 2 q^{28} + 3 q^{29} - 3 q^{30} - 4 q^{31} - q^{32} + 6 q^{33} + 3 q^{34} + 6 q^{35} + q^{36} - 7 q^{37} - 2 q^{38} - 3 q^{40} - 3 q^{41} - 2 q^{42} - 10 q^{43} + 6 q^{44} + 3 q^{45} + 6 q^{46} + 6 q^{47} + q^{48} - 3 q^{49} - 4 q^{50} - 3 q^{51} + 3 q^{53} - q^{54} + 18 q^{55} - 2 q^{56} + 2 q^{57} - 3 q^{58} + 3 q^{60} - 7 q^{61} + 4 q^{62} + 2 q^{63} + q^{64} - 6 q^{66} - 10 q^{67} - 3 q^{68} - 6 q^{69} - 6 q^{70} + 6 q^{71} - q^{72} - 13 q^{73} + 7 q^{74} + 4 q^{75} + 2 q^{76} + 12 q^{77} - 4 q^{79} + 3 q^{80} + q^{81} + 3 q^{82} - 6 q^{83} + 2 q^{84} - 9 q^{85} + 10 q^{86} + 3 q^{87} - 6 q^{88} + 18 q^{89} - 3 q^{90} - 6 q^{92} - 4 q^{93} - 6 q^{94} + 6 q^{95} - q^{96} + 14 q^{97} + 3 q^{98} + 6 q^{99} + O(q^{100}) \)

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 3.00000 −1.00000 2.00000 −1.00000 1.00000 −3.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(3\) \(-1\)
\(13\) \(1\)

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 1014.2.a.c 1
3.b odd 2 1 3042.2.a.i 1
4.b odd 2 1 8112.2.a.m 1
13.b even 2 1 1014.2.a.f 1
13.c even 3 2 78.2.e.a 2
13.d odd 4 2 1014.2.b.c 2
13.e even 6 2 1014.2.e.a 2
13.f odd 12 4 1014.2.i.b 4
39.d odd 2 1 3042.2.a.h 1
39.f even 4 2 3042.2.b.h 2
39.i odd 6 2 234.2.h.a 2
52.b odd 2 1 8112.2.a.c 1
52.j odd 6 2 624.2.q.g 2
65.n even 6 2 1950.2.i.m 2
65.q odd 12 4 1950.2.z.g 4
156.p even 6 2 1872.2.t.c 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
78.2.e.a 2 13.c even 3 2
234.2.h.a 2 39.i odd 6 2
624.2.q.g 2 52.j odd 6 2
1014.2.a.c 1 1.a even 1 1 trivial
1014.2.a.f 1 13.b even 2 1
1014.2.b.c 2 13.d odd 4 2
1014.2.e.a 2 13.e even 6 2
1014.2.i.b 4 13.f odd 12 4
1872.2.t.c 2 156.p even 6 2
1950.2.i.m 2 65.n even 6 2
1950.2.z.g 4 65.q odd 12 4
3042.2.a.h 1 39.d odd 2 1
3042.2.a.i 1 3.b odd 2 1
3042.2.b.h 2 39.f even 4 2
8112.2.a.c 1 52.b odd 2 1
8112.2.a.m 1 4.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 \(S_{2}^{\mathrm{new}}(\Gamma_0(1014))\):

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

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + T \)
$3$ \( -1 + T \)
$5$ \( -3 + T \)
$7$ \( -2 + T \)
$11$ \( -6 + T \)
$13$ \( T \)
$17$ \( 3 + T \)
$19$ \( -2 + T \)
$23$ \( 6 + T \)
$29$ \( -3 + T \)
$31$ \( 4 + T \)
$37$ \( 7 + T \)
$41$ \( 3 + T \)
$43$ \( 10 + T \)
$47$ \( -6 + T \)
$53$ \( -3 + T \)
$59$ \( T \)
$61$ \( 7 + T \)
$67$ \( 10 + T \)
$71$ \( -6 + T \)
$73$ \( 13 + T \)
$79$ \( 4 + T \)
$83$ \( 6 + T \)
$89$ \( -18 + T \)
$97$ \( -14 + T \)
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