Properties

Label 5929.2.a.p
Level $5929$
Weight $2$
Character orbit 5929.a
Self dual yes
Analytic conductor $47.343$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 5929 = 7^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5929.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(47.3433033584\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{13}) \)
Defining polynomial: \( x^{2} - x - 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 847)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \frac{1}{2}(1 + \sqrt{13})\). We also show the integral \(q\)-expansion of the trace form.

\(f(q)\) \(=\) \( q + \beta q^{2} + \beta q^{3} + (\beta + 1) q^{4} + ( - 2 \beta + 1) q^{5} + (\beta + 3) q^{6} + 3 q^{8} + \beta q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + \beta q^{2} + \beta q^{3} + (\beta + 1) q^{4} + ( - 2 \beta + 1) q^{5} + (\beta + 3) q^{6} + 3 q^{8} + \beta q^{9} + ( - \beta - 6) q^{10} + (2 \beta + 3) q^{12} + ( - 2 \beta - 2) q^{13} + ( - \beta - 6) q^{15} + (\beta - 2) q^{16} + (\beta - 5) q^{17} + (\beta + 3) q^{18} + 3 q^{19} + ( - 3 \beta - 5) q^{20} + (\beta - 5) q^{23} + 3 \beta q^{24} + 8 q^{25} + ( - 4 \beta - 6) q^{26} + ( - 2 \beta + 3) q^{27} + ( - \beta + 7) q^{29} + ( - 7 \beta - 3) q^{30} - q^{31} + ( - \beta - 3) q^{32} + ( - 4 \beta + 3) q^{34} + (2 \beta + 3) q^{36} + ( - 4 \beta + 4) q^{37} + 3 \beta q^{38} + ( - 4 \beta - 6) q^{39} + ( - 6 \beta + 3) q^{40} - 7 q^{41} + ( - \beta + 4) q^{43} + ( - \beta - 6) q^{45} + ( - 4 \beta + 3) q^{46} + (3 \beta - 5) q^{47} + ( - \beta + 3) q^{48} + 8 \beta q^{50} + ( - 4 \beta + 3) q^{51} + ( - 6 \beta - 8) q^{52} + ( - 3 \beta - 6) q^{53} + (\beta - 6) q^{54} + 3 \beta q^{57} + (6 \beta - 3) q^{58} + (\beta - 9) q^{59} + ( - 8 \beta - 9) q^{60} + (\beta + 2) q^{61} - \beta q^{62} + ( - 6 \beta + 1) q^{64} + (6 \beta + 10) q^{65} + (5 \beta - 3) q^{67} + ( - 3 \beta - 2) q^{68} + ( - 4 \beta + 3) q^{69} + ( - \beta - 2) q^{71} + 3 \beta q^{72} + 5 q^{73} - 12 q^{74} + 8 \beta q^{75} + (3 \beta + 3) q^{76} + ( - 10 \beta - 12) q^{78} + ( - \beta - 6) q^{79} + (3 \beta - 8) q^{80} + ( - 2 \beta - 6) q^{81} - 7 \beta q^{82} - 3 q^{83} + (9 \beta - 11) q^{85} + (3 \beta - 3) q^{86} + (6 \beta - 3) q^{87} + (9 \beta - 6) q^{89} + ( - 7 \beta - 3) q^{90} + ( - 3 \beta - 2) q^{92} - \beta q^{93} + ( - 2 \beta + 9) q^{94} + ( - 6 \beta + 3) q^{95} + ( - 4 \beta - 3) q^{96} + (2 \beta - 1) q^{97} +O(q^{100}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} + q^{3} + 3 q^{4} + 7 q^{6} + 6 q^{8} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} + q^{3} + 3 q^{4} + 7 q^{6} + 6 q^{8} + q^{9} - 13 q^{10} + 8 q^{12} - 6 q^{13} - 13 q^{15} - 3 q^{16} - 9 q^{17} + 7 q^{18} + 6 q^{19} - 13 q^{20} - 9 q^{23} + 3 q^{24} + 16 q^{25} - 16 q^{26} + 4 q^{27} + 13 q^{29} - 13 q^{30} - 2 q^{31} - 7 q^{32} + 2 q^{34} + 8 q^{36} + 4 q^{37} + 3 q^{38} - 16 q^{39} - 14 q^{41} + 7 q^{43} - 13 q^{45} + 2 q^{46} - 7 q^{47} + 5 q^{48} + 8 q^{50} + 2 q^{51} - 22 q^{52} - 15 q^{53} - 11 q^{54} + 3 q^{57} - 17 q^{59} - 26 q^{60} + 5 q^{61} - q^{62} - 4 q^{64} + 26 q^{65} - q^{67} - 7 q^{68} + 2 q^{69} - 5 q^{71} + 3 q^{72} + 10 q^{73} - 24 q^{74} + 8 q^{75} + 9 q^{76} - 34 q^{78} - 13 q^{79} - 13 q^{80} - 14 q^{81} - 7 q^{82} - 6 q^{83} - 13 q^{85} - 3 q^{86} - 3 q^{89} - 13 q^{90} - 7 q^{92} - q^{93} + 16 q^{94} - 10 q^{96}+O(q^{100}) \) 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
−1.30278
2.30278
−1.30278 −1.30278 −0.302776 3.60555 1.69722 0 3.00000 −1.30278 −4.69722
1.2 2.30278 2.30278 3.30278 −3.60555 5.30278 0 3.00000 2.30278 −8.30278
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(7\) \(-1\)
\(11\) \(-1\)

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 5929.2.a.p 2
7.b odd 2 1 847.2.a.g yes 2
11.b odd 2 1 5929.2.a.k 2
21.c even 2 1 7623.2.a.bc 2
77.b even 2 1 847.2.a.e 2
77.j odd 10 4 847.2.f.o 8
77.l even 10 4 847.2.f.r 8
231.h odd 2 1 7623.2.a.bs 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
847.2.a.e 2 77.b even 2 1
847.2.a.g yes 2 7.b odd 2 1
847.2.f.o 8 77.j odd 10 4
847.2.f.r 8 77.l even 10 4
5929.2.a.k 2 11.b odd 2 1
5929.2.a.p 2 1.a even 1 1 trivial
7623.2.a.bc 2 21.c even 2 1
7623.2.a.bs 2 231.h odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(5929))\):

\( T_{2}^{2} - T_{2} - 3 \) Copy content Toggle raw display
\( T_{3}^{2} - T_{3} - 3 \) Copy content Toggle raw display
\( T_{5}^{2} - 13 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T^{2} - T - 3 \) Copy content Toggle raw display
$3$ \( T^{2} - T - 3 \) Copy content Toggle raw display
$5$ \( T^{2} - 13 \) Copy content Toggle raw display
$7$ \( T^{2} \) Copy content Toggle raw display
$11$ \( T^{2} \) Copy content Toggle raw display
$13$ \( T^{2} + 6T - 4 \) Copy content Toggle raw display
$17$ \( T^{2} + 9T + 17 \) Copy content Toggle raw display
$19$ \( (T - 3)^{2} \) Copy content Toggle raw display
$23$ \( T^{2} + 9T + 17 \) Copy content Toggle raw display
$29$ \( T^{2} - 13T + 39 \) Copy content Toggle raw display
$31$ \( (T + 1)^{2} \) Copy content Toggle raw display
$37$ \( T^{2} - 4T - 48 \) Copy content Toggle raw display
$41$ \( (T + 7)^{2} \) Copy content Toggle raw display
$43$ \( T^{2} - 7T + 9 \) Copy content Toggle raw display
$47$ \( T^{2} + 7T - 17 \) Copy content Toggle raw display
$53$ \( T^{2} + 15T + 27 \) Copy content Toggle raw display
$59$ \( T^{2} + 17T + 69 \) Copy content Toggle raw display
$61$ \( T^{2} - 5T + 3 \) Copy content Toggle raw display
$67$ \( T^{2} + T - 81 \) Copy content Toggle raw display
$71$ \( T^{2} + 5T + 3 \) Copy content Toggle raw display
$73$ \( (T - 5)^{2} \) Copy content Toggle raw display
$79$ \( T^{2} + 13T + 39 \) Copy content Toggle raw display
$83$ \( (T + 3)^{2} \) Copy content Toggle raw display
$89$ \( T^{2} + 3T - 261 \) Copy content Toggle raw display
$97$ \( T^{2} - 13 \) Copy content Toggle raw display
show more
show less