Properties

Label 2541.2.a.j
Level $2541$
Weight $2$
Character orbit 2541.a
Self dual yes
Analytic conductor $20.290$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2541 = 3 \cdot 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2541.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(20.2899871536\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 21)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} + q^{3} - q^{4} - 2 q^{5} + q^{6} + q^{7} - 3 q^{8} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + q^{2} + q^{3} - q^{4} - 2 q^{5} + q^{6} + q^{7} - 3 q^{8} + q^{9} - 2 q^{10} - q^{12} + 2 q^{13} + q^{14} - 2 q^{15} - q^{16} + 6 q^{17} + q^{18} - 4 q^{19} + 2 q^{20} + q^{21} - 3 q^{24} - q^{25} + 2 q^{26} + q^{27} - q^{28} + 2 q^{29} - 2 q^{30} + 5 q^{32} + 6 q^{34} - 2 q^{35} - q^{36} + 6 q^{37} - 4 q^{38} + 2 q^{39} + 6 q^{40} - 2 q^{41} + q^{42} + 4 q^{43} - 2 q^{45} - q^{48} + q^{49} - q^{50} + 6 q^{51} - 2 q^{52} + 6 q^{53} + q^{54} - 3 q^{56} - 4 q^{57} + 2 q^{58} + 12 q^{59} + 2 q^{60} + 2 q^{61} + q^{63} + 7 q^{64} - 4 q^{65} + 4 q^{67} - 6 q^{68} - 2 q^{70} - 3 q^{72} + 6 q^{73} + 6 q^{74} - q^{75} + 4 q^{76} + 2 q^{78} + 16 q^{79} + 2 q^{80} + q^{81} - 2 q^{82} + 12 q^{83} - q^{84} - 12 q^{85} + 4 q^{86} + 2 q^{87} - 14 q^{89} - 2 q^{90} + 2 q^{91} + 8 q^{95} + 5 q^{96} + 18 q^{97} + q^{98}+O(q^{100}) \) 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 −2.00000 1.00000 1.00000 −3.00000 1.00000 −2.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \(-1\)
\(7\) \(-1\)
\(11\) \(-1\)

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 2541.2.a.j 1
3.b odd 2 1 7623.2.a.g 1
11.b odd 2 1 21.2.a.a 1
33.d even 2 1 63.2.a.a 1
44.c even 2 1 336.2.a.a 1
55.d odd 2 1 525.2.a.d 1
55.e even 4 2 525.2.d.a 2
77.b even 2 1 147.2.a.a 1
77.h odd 6 2 147.2.e.b 2
77.i even 6 2 147.2.e.c 2
88.b odd 2 1 1344.2.a.g 1
88.g even 2 1 1344.2.a.s 1
99.g even 6 2 567.2.f.b 2
99.h odd 6 2 567.2.f.g 2
132.d odd 2 1 1008.2.a.l 1
143.d odd 2 1 3549.2.a.c 1
165.d even 2 1 1575.2.a.c 1
165.l odd 4 2 1575.2.d.a 2
176.i even 4 2 5376.2.c.l 2
176.l odd 4 2 5376.2.c.r 2
187.b odd 2 1 6069.2.a.b 1
209.d even 2 1 7581.2.a.d 1
220.g even 2 1 8400.2.a.bn 1
231.h odd 2 1 441.2.a.f 1
231.k odd 6 2 441.2.e.b 2
231.l even 6 2 441.2.e.a 2
264.m even 2 1 4032.2.a.h 1
264.p odd 2 1 4032.2.a.k 1
308.g odd 2 1 2352.2.a.v 1
308.m odd 6 2 2352.2.q.e 2
308.n even 6 2 2352.2.q.x 2
385.h even 2 1 3675.2.a.n 1
616.g odd 2 1 9408.2.a.m 1
616.o even 2 1 9408.2.a.bv 1
924.n even 2 1 7056.2.a.p 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
21.2.a.a 1 11.b odd 2 1
63.2.a.a 1 33.d even 2 1
147.2.a.a 1 77.b even 2 1
147.2.e.b 2 77.h odd 6 2
147.2.e.c 2 77.i even 6 2
336.2.a.a 1 44.c even 2 1
441.2.a.f 1 231.h odd 2 1
441.2.e.a 2 231.l even 6 2
441.2.e.b 2 231.k odd 6 2
525.2.a.d 1 55.d odd 2 1
525.2.d.a 2 55.e even 4 2
567.2.f.b 2 99.g even 6 2
567.2.f.g 2 99.h odd 6 2
1008.2.a.l 1 132.d odd 2 1
1344.2.a.g 1 88.b odd 2 1
1344.2.a.s 1 88.g even 2 1
1575.2.a.c 1 165.d even 2 1
1575.2.d.a 2 165.l odd 4 2
2352.2.a.v 1 308.g odd 2 1
2352.2.q.e 2 308.m odd 6 2
2352.2.q.x 2 308.n even 6 2
2541.2.a.j 1 1.a even 1 1 trivial
3549.2.a.c 1 143.d odd 2 1
3675.2.a.n 1 385.h even 2 1
4032.2.a.h 1 264.m even 2 1
4032.2.a.k 1 264.p odd 2 1
5376.2.c.l 2 176.i even 4 2
5376.2.c.r 2 176.l odd 4 2
6069.2.a.b 1 187.b odd 2 1
7056.2.a.p 1 924.n even 2 1
7581.2.a.d 1 209.d even 2 1
7623.2.a.g 1 3.b odd 2 1
8400.2.a.bn 1 220.g even 2 1
9408.2.a.m 1 616.g odd 2 1
9408.2.a.bv 1 616.o even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(2541))\):

\( T_{2} - 1 \) Copy content Toggle raw display
\( T_{5} + 2 \) Copy content Toggle raw display
\( T_{13} - 2 \) 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
$5$ \( T + 2 \) Copy content Toggle raw display
$7$ \( T - 1 \) Copy content Toggle raw display
$11$ \( T \) Copy content Toggle raw display
$13$ \( T - 2 \) Copy content Toggle raw display
$17$ \( T - 6 \) Copy content Toggle raw display
$19$ \( T + 4 \) Copy content Toggle raw display
$23$ \( T \) Copy content Toggle raw display
$29$ \( T - 2 \) Copy content Toggle raw display
$31$ \( T \) Copy content Toggle raw display
$37$ \( T - 6 \) Copy content Toggle raw display
$41$ \( T + 2 \) Copy content Toggle raw display
$43$ \( T - 4 \) Copy content Toggle raw display
$47$ \( T \) Copy content Toggle raw display
$53$ \( T - 6 \) Copy content Toggle raw display
$59$ \( T - 12 \) Copy content Toggle raw display
$61$ \( T - 2 \) Copy content Toggle raw display
$67$ \( T - 4 \) Copy content Toggle raw display
$71$ \( T \) Copy content Toggle raw display
$73$ \( T - 6 \) Copy content Toggle raw display
$79$ \( T - 16 \) Copy content Toggle raw display
$83$ \( T - 12 \) Copy content Toggle raw display
$89$ \( T + 14 \) Copy content Toggle raw display
$97$ \( T - 18 \) Copy content Toggle raw display
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