Properties

Label 1274.2.a.d
Level $1274$
Weight $2$
Character orbit 1274.a
Self dual yes
Analytic conductor $10.173$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1274 = 2 \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1274.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(10.1729412175\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 26)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{2} - q^{3} + q^{4} + 3 q^{5} + q^{6} - q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - q^{2} - q^{3} + q^{4} + 3 q^{5} + q^{6} - q^{8} - 2 q^{9} - 3 q^{10} + 6 q^{11} - q^{12} - q^{13} - 3 q^{15} + q^{16} + 3 q^{17} + 2 q^{18} - 2 q^{19} + 3 q^{20} - 6 q^{22} + q^{24} + 4 q^{25} + q^{26} + 5 q^{27} + 6 q^{29} + 3 q^{30} + 4 q^{31} - q^{32} - 6 q^{33} - 3 q^{34} - 2 q^{36} - 7 q^{37} + 2 q^{38} + q^{39} - 3 q^{40} - q^{43} + 6 q^{44} - 6 q^{45} - 3 q^{47} - q^{48} - 4 q^{50} - 3 q^{51} - q^{52} - 5 q^{54} + 18 q^{55} + 2 q^{57} - 6 q^{58} + 6 q^{59} - 3 q^{60} - 8 q^{61} - 4 q^{62} + q^{64} - 3 q^{65} + 6 q^{66} + 14 q^{67} + 3 q^{68} - 3 q^{71} + 2 q^{72} - 2 q^{73} + 7 q^{74} - 4 q^{75} - 2 q^{76} - q^{78} + 8 q^{79} + 3 q^{80} + q^{81} - 12 q^{83} + 9 q^{85} + q^{86} - 6 q^{87} - 6 q^{88} + 6 q^{89} + 6 q^{90} - 4 q^{93} + 3 q^{94} - 6 q^{95} + q^{96} + 10 q^{97} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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 0 −1.00000 −2.00000 −3.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(7\) \(-1\)
\(13\) \(1\)

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 1274.2.a.d 1
7.b odd 2 1 26.2.a.a 1
7.c even 3 2 1274.2.f.r 2
7.d odd 6 2 1274.2.f.p 2
21.c even 2 1 234.2.a.e 1
28.d even 2 1 208.2.a.a 1
35.c odd 2 1 650.2.a.j 1
35.f even 4 2 650.2.b.d 2
56.e even 2 1 832.2.a.i 1
56.h odd 2 1 832.2.a.d 1
63.l odd 6 2 2106.2.e.ba 2
63.o even 6 2 2106.2.e.b 2
77.b even 2 1 3146.2.a.n 1
84.h odd 2 1 1872.2.a.q 1
91.b odd 2 1 338.2.a.f 1
91.i even 4 2 338.2.b.c 2
91.n odd 6 2 338.2.c.d 2
91.t odd 6 2 338.2.c.a 2
91.bc even 12 4 338.2.e.a 4
105.g even 2 1 5850.2.a.p 1
105.k odd 4 2 5850.2.e.a 2
112.j even 4 2 3328.2.b.j 2
112.l odd 4 2 3328.2.b.m 2
119.d odd 2 1 7514.2.a.c 1
133.c even 2 1 9386.2.a.j 1
140.c even 2 1 5200.2.a.x 1
168.e odd 2 1 7488.2.a.h 1
168.i even 2 1 7488.2.a.g 1
273.g even 2 1 3042.2.a.a 1
273.o odd 4 2 3042.2.b.a 2
364.h even 2 1 2704.2.a.f 1
364.p odd 4 2 2704.2.f.d 2
455.h odd 2 1 8450.2.a.c 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
26.2.a.a 1 7.b odd 2 1
208.2.a.a 1 28.d even 2 1
234.2.a.e 1 21.c even 2 1
338.2.a.f 1 91.b odd 2 1
338.2.b.c 2 91.i even 4 2
338.2.c.a 2 91.t odd 6 2
338.2.c.d 2 91.n odd 6 2
338.2.e.a 4 91.bc even 12 4
650.2.a.j 1 35.c odd 2 1
650.2.b.d 2 35.f even 4 2
832.2.a.d 1 56.h odd 2 1
832.2.a.i 1 56.e even 2 1
1274.2.a.d 1 1.a even 1 1 trivial
1274.2.f.p 2 7.d odd 6 2
1274.2.f.r 2 7.c even 3 2
1872.2.a.q 1 84.h odd 2 1
2106.2.e.b 2 63.o even 6 2
2106.2.e.ba 2 63.l odd 6 2
2704.2.a.f 1 364.h even 2 1
2704.2.f.d 2 364.p odd 4 2
3042.2.a.a 1 273.g even 2 1
3042.2.b.a 2 273.o odd 4 2
3146.2.a.n 1 77.b even 2 1
3328.2.b.j 2 112.j even 4 2
3328.2.b.m 2 112.l odd 4 2
5200.2.a.x 1 140.c even 2 1
5850.2.a.p 1 105.g even 2 1
5850.2.e.a 2 105.k odd 4 2
7488.2.a.g 1 168.i even 2 1
7488.2.a.h 1 168.e odd 2 1
7514.2.a.c 1 119.d odd 2 1
8450.2.a.c 1 455.h odd 2 1
9386.2.a.j 1 133.c even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1274))\):

\( T_{3} + 1 \) Copy content Toggle raw display
\( T_{5} - 3 \) Copy content Toggle raw display
\( T_{11} - 6 \) Copy content Toggle raw display
\( T_{17} - 3 \) Copy content Toggle raw display

Hecke characteristic polynomials

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