Properties

Label 1014.2.a.d
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

\(f(q)\) \(=\) \( q + q^{2} - q^{3} + q^{4} - 2 q^{5} - q^{6} - 4 q^{7} + q^{8} + q^{9} + O(q^{10}) \) \( q + q^{2} - q^{3} + q^{4} - 2 q^{5} - q^{6} - 4 q^{7} + q^{8} + q^{9} - 2 q^{10} + 4 q^{11} - q^{12} - 4 q^{14} + 2 q^{15} + q^{16} + 2 q^{17} + q^{18} + 8 q^{19} - 2 q^{20} + 4 q^{21} + 4 q^{22} - q^{24} - q^{25} - q^{27} - 4 q^{28} + 6 q^{29} + 2 q^{30} + 4 q^{31} + q^{32} - 4 q^{33} + 2 q^{34} + 8 q^{35} + q^{36} + 2 q^{37} + 8 q^{38} - 2 q^{40} + 10 q^{41} + 4 q^{42} + 4 q^{43} + 4 q^{44} - 2 q^{45} - 8 q^{47} - q^{48} + 9 q^{49} - q^{50} - 2 q^{51} - 10 q^{53} - q^{54} - 8 q^{55} - 4 q^{56} - 8 q^{57} + 6 q^{58} - 4 q^{59} + 2 q^{60} - 2 q^{61} + 4 q^{62} - 4 q^{63} + q^{64} - 4 q^{66} + 16 q^{67} + 2 q^{68} + 8 q^{70} + 8 q^{71} + q^{72} - 2 q^{73} + 2 q^{74} + q^{75} + 8 q^{76} - 16 q^{77} + 8 q^{79} - 2 q^{80} + q^{81} + 10 q^{82} - 12 q^{83} + 4 q^{84} - 4 q^{85} + 4 q^{86} - 6 q^{87} + 4 q^{88} - 14 q^{89} - 2 q^{90} - 4 q^{93} - 8 q^{94} - 16 q^{95} - q^{96} - 10 q^{97} + 9 q^{98} + 4 q^{99} + O(q^{100}) \)

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 −2.00000 −1.00000 −4.00000 1.00000 1.00000 −2.00000
\(n\): 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.d 1
3.b odd 2 1 3042.2.a.f 1
4.b odd 2 1 8112.2.a.v 1
13.b even 2 1 78.2.a.a 1
13.c even 3 2 1014.2.e.c 2
13.d odd 4 2 1014.2.b.b 2
13.e even 6 2 1014.2.e.f 2
13.f odd 12 4 1014.2.i.d 4
39.d odd 2 1 234.2.a.c 1
39.f even 4 2 3042.2.b.g 2
52.b odd 2 1 624.2.a.h 1
65.d even 2 1 1950.2.a.w 1
65.h odd 4 2 1950.2.e.i 2
91.b odd 2 1 3822.2.a.j 1
104.e even 2 1 2496.2.a.t 1
104.h odd 2 1 2496.2.a.b 1
117.n odd 6 2 2106.2.e.j 2
117.t even 6 2 2106.2.e.q 2
143.d odd 2 1 9438.2.a.t 1
156.h even 2 1 1872.2.a.c 1
195.e odd 2 1 5850.2.a.d 1
195.s even 4 2 5850.2.e.bb 2
312.b odd 2 1 7488.2.a.bz 1
312.h even 2 1 7488.2.a.bk 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
78.2.a.a 1 13.b even 2 1
234.2.a.c 1 39.d odd 2 1
624.2.a.h 1 52.b odd 2 1
1014.2.a.d 1 1.a even 1 1 trivial
1014.2.b.b 2 13.d odd 4 2
1014.2.e.c 2 13.c even 3 2
1014.2.e.f 2 13.e even 6 2
1014.2.i.d 4 13.f odd 12 4
1872.2.a.c 1 156.h even 2 1
1950.2.a.w 1 65.d even 2 1
1950.2.e.i 2 65.h odd 4 2
2106.2.e.j 2 117.n odd 6 2
2106.2.e.q 2 117.t even 6 2
2496.2.a.b 1 104.h odd 2 1
2496.2.a.t 1 104.e even 2 1
3042.2.a.f 1 3.b odd 2 1
3042.2.b.g 2 39.f even 4 2
3822.2.a.j 1 91.b odd 2 1
5850.2.a.d 1 195.e odd 2 1
5850.2.e.bb 2 195.s even 4 2
7488.2.a.bk 1 312.h even 2 1
7488.2.a.bz 1 312.b odd 2 1
8112.2.a.v 1 4.b odd 2 1
9438.2.a.t 1 143.d odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1014))\):

\( T_{5} + 2 \)
\( T_{7} + 4 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -1 + T \)
$3$ \( 1 + T \)
$5$ \( 2 + T \)
$7$ \( 4 + T \)
$11$ \( -4 + T \)
$13$ \( T \)
$17$ \( -2 + T \)
$19$ \( -8 + T \)
$23$ \( T \)
$29$ \( -6 + T \)
$31$ \( -4 + T \)
$37$ \( -2 + T \)
$41$ \( -10 + T \)
$43$ \( -4 + T \)
$47$ \( 8 + T \)
$53$ \( 10 + T \)
$59$ \( 4 + T \)
$61$ \( 2 + T \)
$67$ \( -16 + T \)
$71$ \( -8 + T \)
$73$ \( 2 + T \)
$79$ \( -8 + T \)
$83$ \( 12 + T \)
$89$ \( 14 + T \)
$97$ \( 10 + T \)
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