Properties

Label 2601.2.a.g
Level $2601$
Weight $2$
Character orbit 2601.a
Self dual yes
Analytic conductor $20.769$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 2601 = 3^{2} \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2601.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(20.7690895657\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 17)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} - q^{4} - 2q^{5} - 4q^{7} - 3q^{8} + O(q^{10}) \) \( q + q^{2} - q^{4} - 2q^{5} - 4q^{7} - 3q^{8} - 2q^{10} - 2q^{13} - 4q^{14} - q^{16} - 4q^{19} + 2q^{20} + 4q^{23} - q^{25} - 2q^{26} + 4q^{28} + 6q^{29} - 4q^{31} + 5q^{32} + 8q^{35} + 2q^{37} - 4q^{38} + 6q^{40} - 6q^{41} + 4q^{43} + 4q^{46} + 9q^{49} - q^{50} + 2q^{52} - 6q^{53} + 12q^{56} + 6q^{58} + 12q^{59} + 10q^{61} - 4q^{62} + 7q^{64} + 4q^{65} + 4q^{67} + 8q^{70} - 4q^{71} + 6q^{73} + 2q^{74} + 4q^{76} - 12q^{79} + 2q^{80} - 6q^{82} + 4q^{83} + 4q^{86} - 10q^{89} + 8q^{91} - 4q^{92} + 8q^{95} - 2q^{97} + 9q^{98} + O(q^{100}) \)

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 0 −1.00000 −2.00000 0 −4.00000 −3.00000 0 −2.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \(-1\)
\(17\) \(1\)

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 2601.2.a.g 1
3.b odd 2 1 289.2.a.a 1
12.b even 2 1 4624.2.a.d 1
15.d odd 2 1 7225.2.a.g 1
17.b even 2 1 153.2.a.c 1
51.c odd 2 1 17.2.a.a 1
51.f odd 4 2 289.2.b.a 2
51.g odd 8 4 289.2.c.a 4
51.i even 16 8 289.2.d.d 8
68.d odd 2 1 2448.2.a.o 1
85.c even 2 1 3825.2.a.d 1
119.d odd 2 1 7497.2.a.l 1
136.e odd 2 1 9792.2.a.i 1
136.h even 2 1 9792.2.a.n 1
204.h even 2 1 272.2.a.b 1
255.h odd 2 1 425.2.a.d 1
255.o even 4 2 425.2.b.b 2
357.c even 2 1 833.2.a.a 1
357.q odd 6 2 833.2.e.b 2
357.s even 6 2 833.2.e.a 2
408.b odd 2 1 1088.2.a.i 1
408.h even 2 1 1088.2.a.h 1
561.h even 2 1 2057.2.a.e 1
663.g odd 2 1 2873.2.a.c 1
969.h even 2 1 6137.2.a.b 1
1020.b even 2 1 6800.2.a.n 1
1173.b even 2 1 8993.2.a.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
17.2.a.a 1 51.c odd 2 1
153.2.a.c 1 17.b even 2 1
272.2.a.b 1 204.h even 2 1
289.2.a.a 1 3.b odd 2 1
289.2.b.a 2 51.f odd 4 2
289.2.c.a 4 51.g odd 8 4
289.2.d.d 8 51.i even 16 8
425.2.a.d 1 255.h odd 2 1
425.2.b.b 2 255.o even 4 2
833.2.a.a 1 357.c even 2 1
833.2.e.a 2 357.s even 6 2
833.2.e.b 2 357.q odd 6 2
1088.2.a.h 1 408.h even 2 1
1088.2.a.i 1 408.b odd 2 1
2057.2.a.e 1 561.h even 2 1
2448.2.a.o 1 68.d odd 2 1
2601.2.a.g 1 1.a even 1 1 trivial
2873.2.a.c 1 663.g odd 2 1
3825.2.a.d 1 85.c even 2 1
4624.2.a.d 1 12.b even 2 1
6137.2.a.b 1 969.h even 2 1
6800.2.a.n 1 1020.b even 2 1
7225.2.a.g 1 15.d odd 2 1
7497.2.a.l 1 119.d odd 2 1
8993.2.a.a 1 1173.b even 2 1
9792.2.a.i 1 136.e odd 2 1
9792.2.a.n 1 136.h even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(2601))\):

\( T_{2} - 1 \)
\( T_{5} + 2 \)
\( T_{7} + 4 \)

Hecke characteristic polynomials

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