Properties

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

Related objects

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: yes Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

 $$f(q)$$ $$=$$ $$q + 2 q^{2} - q^{3} + 2 q^{4} - 3 q^{5} - 2 q^{6} - q^{7} + q^{9}+O(q^{10})$$ q + 2 * q^2 - q^3 + 2 * q^4 - 3 * q^5 - 2 * q^6 - q^7 + q^9 $$q + 2 q^{2} - q^{3} + 2 q^{4} - 3 q^{5} - 2 q^{6} - q^{7} + q^{9} - 6 q^{10} - 2 q^{12} + 2 q^{13} - 2 q^{14} + 3 q^{15} - 4 q^{16} + 3 q^{17} + 2 q^{18} - 4 q^{19} - 6 q^{20} + q^{21} + 2 q^{23} + 4 q^{25} + 4 q^{26} - q^{27} - 2 q^{28} + 8 q^{29} + 6 q^{30} + 2 q^{31} - 8 q^{32} + 6 q^{34} + 3 q^{35} + 2 q^{36} + 10 q^{37} - 8 q^{38} - 2 q^{39} + 2 q^{41} + 2 q^{42} + 9 q^{43} - 3 q^{45} + 4 q^{46} + 9 q^{47} + 4 q^{48} + q^{49} + 8 q^{50} - 3 q^{51} + 4 q^{52} - 8 q^{53} - 2 q^{54} + 4 q^{57} + 16 q^{58} - 3 q^{59} + 6 q^{60} - 10 q^{61} + 4 q^{62} - q^{63} - 8 q^{64} - 6 q^{65} + 13 q^{67} + 6 q^{68} - 2 q^{69} + 6 q^{70} + 14 q^{71} - 10 q^{73} + 20 q^{74} - 4 q^{75} - 8 q^{76} - 4 q^{78} - 4 q^{79} + 12 q^{80} + q^{81} + 4 q^{82} + q^{83} + 2 q^{84} - 9 q^{85} + 18 q^{86} - 8 q^{87} - 9 q^{89} - 6 q^{90} - 2 q^{91} + 4 q^{92} - 2 q^{93} + 18 q^{94} + 12 q^{95} + 8 q^{96} - 16 q^{97} + 2 q^{98}+O(q^{100})$$ q + 2 * q^2 - q^3 + 2 * q^4 - 3 * q^5 - 2 * q^6 - q^7 + q^9 - 6 * q^10 - 2 * q^12 + 2 * q^13 - 2 * q^14 + 3 * q^15 - 4 * q^16 + 3 * q^17 + 2 * q^18 - 4 * q^19 - 6 * q^20 + q^21 + 2 * q^23 + 4 * q^25 + 4 * q^26 - q^27 - 2 * q^28 + 8 * q^29 + 6 * q^30 + 2 * q^31 - 8 * q^32 + 6 * q^34 + 3 * q^35 + 2 * q^36 + 10 * q^37 - 8 * q^38 - 2 * q^39 + 2 * q^41 + 2 * q^42 + 9 * q^43 - 3 * q^45 + 4 * q^46 + 9 * q^47 + 4 * q^48 + q^49 + 8 * q^50 - 3 * q^51 + 4 * q^52 - 8 * q^53 - 2 * q^54 + 4 * q^57 + 16 * q^58 - 3 * q^59 + 6 * q^60 - 10 * q^61 + 4 * q^62 - q^63 - 8 * q^64 - 6 * q^65 + 13 * q^67 + 6 * q^68 - 2 * q^69 + 6 * q^70 + 14 * q^71 - 10 * q^73 + 20 * q^74 - 4 * q^75 - 8 * q^76 - 4 * q^78 - 4 * q^79 + 12 * q^80 + q^81 + 4 * q^82 + q^83 + 2 * q^84 - 9 * q^85 + 18 * q^86 - 8 * q^87 - 9 * q^89 - 6 * q^90 - 2 * q^91 + 4 * q^92 - 2 * q^93 + 18 * q^94 + 12 * q^95 + 8 * q^96 - 16 * q^97 + 2 * q^98

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
2.00000 −1.00000 2.00000 −3.00000 −2.00000 −1.00000 0 1.00000 −6.00000
 $$n$$: e.g. 2-40 or 990-1000 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

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.k yes 1
3.b odd 2 1 7623.2.a.d 1
11.b odd 2 1 2541.2.a.a 1
33.d even 2 1 7623.2.a.s 1

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2541.2.a.a 1 11.b odd 2 1
2541.2.a.k yes 1 1.a even 1 1 trivial
7623.2.a.d 1 3.b odd 2 1
7623.2.a.s 1 33.d even 2 1

Hecke kernels

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

 $$T_{2} - 2$$ T2 - 2 $$T_{5} + 3$$ T5 + 3 $$T_{13} - 2$$ T13 - 2

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$T - 2$$
$3$ $$T + 1$$
$5$ $$T + 3$$
$7$ $$T + 1$$
$11$ $$T$$
$13$ $$T - 2$$
$17$ $$T - 3$$
$19$ $$T + 4$$
$23$ $$T - 2$$
$29$ $$T - 8$$
$31$ $$T - 2$$
$37$ $$T - 10$$
$41$ $$T - 2$$
$43$ $$T - 9$$
$47$ $$T - 9$$
$53$ $$T + 8$$
$59$ $$T + 3$$
$61$ $$T + 10$$
$67$ $$T - 13$$
$71$ $$T - 14$$
$73$ $$T + 10$$
$79$ $$T + 4$$
$83$ $$T - 1$$
$89$ $$T + 9$$
$97$ $$T + 16$$