Properties

Label 49.26.a.a
Level $49$
Weight $26$
Character orbit 49.a
Self dual yes
Analytic conductor $194.038$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 49 = 7^{2} \)
Weight: \( k \) \(=\) \( 26 \)
Character orbit: \([\chi]\) \(=\) 49.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(194.038422177\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - 48 q^{2} + 195804 q^{3} - 33552128 q^{4} + 741989850 q^{5} - 9398592 q^{6} + 3221114880 q^{8} - 808949403027 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - 48 q^{2} + 195804 q^{3} - 33552128 q^{4} + 741989850 q^{5} - 9398592 q^{6} + 3221114880 q^{8} - 808949403027 q^{9} - 35615512800 q^{10} + 8419515299052 q^{11} - 6569640870912 q^{12} + 81651045335314 q^{13} + 145284580589400 q^{15} + 11\!\cdots\!56 q^{16}+ \cdots - 68\!\cdots\!04 q^{99}+O(q^{100}) \) 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
−48.0000 195804. −3.35521e7 7.41990e8 −9.39859e6 0 3.22111e9 −8.08949e11 −3.56155e10
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

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

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 49.26.a.a 1
7.b odd 2 1 1.26.a.a 1
21.c even 2 1 9.26.a.a 1
28.d even 2 1 16.26.a.b 1
35.c odd 2 1 25.26.a.a 1
35.f even 4 2 25.26.b.a 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1.26.a.a 1 7.b odd 2 1
9.26.a.a 1 21.c even 2 1
16.26.a.b 1 28.d even 2 1
25.26.a.a 1 35.c odd 2 1
25.26.b.a 2 35.f even 4 2
49.26.a.a 1 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{26}^{\mathrm{new}}(\Gamma_0(49))\):

\( T_{2} + 48 \) Copy content Toggle raw display
\( T_{3} - 195804 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T + 48 \) Copy content Toggle raw display
$3$ \( T - 195804 \) Copy content Toggle raw display
$5$ \( T - 741989850 \) Copy content Toggle raw display
$7$ \( T \) Copy content Toggle raw display
$11$ \( T - 8419515299052 \) Copy content Toggle raw display
$13$ \( T - 81651045335314 \) Copy content Toggle raw display
$17$ \( T - 2519900028948078 \) Copy content Toggle raw display
$19$ \( T - 6082056370308940 \) Copy content Toggle raw display
$23$ \( T + 94\!\cdots\!24 \) Copy content Toggle raw display
$29$ \( T + 27\!\cdots\!10 \) Copy content Toggle raw display
$31$ \( T + 42\!\cdots\!52 \) Copy content Toggle raw display
$37$ \( T - 20\!\cdots\!82 \) Copy content Toggle raw display
$41$ \( T - 18\!\cdots\!98 \) Copy content Toggle raw display
$43$ \( T - 30\!\cdots\!56 \) Copy content Toggle raw display
$47$ \( T - 92\!\cdots\!88 \) Copy content Toggle raw display
$53$ \( T + 99\!\cdots\!54 \) Copy content Toggle raw display
$59$ \( T + 13\!\cdots\!80 \) Copy content Toggle raw display
$61$ \( T + 90\!\cdots\!02 \) Copy content Toggle raw display
$67$ \( T + 26\!\cdots\!28 \) Copy content Toggle raw display
$71$ \( T + 19\!\cdots\!48 \) Copy content Toggle raw display
$73$ \( T + 42\!\cdots\!26 \) Copy content Toggle raw display
$79$ \( T + 27\!\cdots\!60 \) Copy content Toggle raw display
$83$ \( T - 93\!\cdots\!84 \) Copy content Toggle raw display
$89$ \( T - 17\!\cdots\!30 \) Copy content Toggle raw display
$97$ \( T + 28\!\cdots\!62 \) Copy content Toggle raw display
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