Properties

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

Related objects

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: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 153) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

 $$f(q)$$ $$=$$ $$q + 2q^{2} + 2q^{4} - q^{5} + 2q^{7} + O(q^{10})$$ $$q + 2q^{2} + 2q^{4} - q^{5} + 2q^{7} - 2q^{10} - 3q^{11} - 5q^{13} + 4q^{14} - 4q^{16} - q^{19} - 2q^{20} - 6q^{22} - 7q^{23} - 4q^{25} - 10q^{26} + 4q^{28} + 6q^{29} - 4q^{31} - 8q^{32} - 2q^{35} - 10q^{37} - 2q^{38} + 9q^{41} + q^{43} - 6q^{44} - 14q^{46} + 12q^{47} - 3q^{49} - 8q^{50} - 10q^{52} + 12q^{53} + 3q^{55} + 12q^{58} - 6q^{59} - 2q^{61} - 8q^{62} - 8q^{64} + 5q^{65} + 4q^{67} - 4q^{70} - 8q^{71} - 20q^{74} - 2q^{76} - 6q^{77} + 6q^{79} + 4q^{80} + 18q^{82} - 4q^{83} + 2q^{86} - 2q^{89} - 10q^{91} - 14q^{92} + 24q^{94} + q^{95} - 8q^{97} - 6q^{98} + O(q^{100})$$

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

Atkin-Lehner signs

$$p$$ Sign
$$3$$ $$1$$
$$17$$ $$1$$

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.l 1
3.b odd 2 1 2601.2.a.b 1
17.b even 2 1 153.2.a.d yes 1
51.c odd 2 1 153.2.a.a 1
68.d odd 2 1 2448.2.a.m 1
85.c even 2 1 3825.2.a.b 1
119.d odd 2 1 7497.2.a.p 1
136.e odd 2 1 9792.2.a.w 1
136.h even 2 1 9792.2.a.p 1
204.h even 2 1 2448.2.a.g 1
255.h odd 2 1 3825.2.a.o 1
357.c even 2 1 7497.2.a.a 1
408.b odd 2 1 9792.2.a.bm 1
408.h even 2 1 9792.2.a.bp 1

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
153.2.a.a 1 51.c odd 2 1
153.2.a.d yes 1 17.b even 2 1
2448.2.a.g 1 204.h even 2 1
2448.2.a.m 1 68.d odd 2 1
2601.2.a.b 1 3.b odd 2 1
2601.2.a.l 1 1.a even 1 1 trivial
3825.2.a.b 1 85.c even 2 1
3825.2.a.o 1 255.h odd 2 1
7497.2.a.a 1 357.c even 2 1
7497.2.a.p 1 119.d odd 2 1
9792.2.a.p 1 136.h even 2 1
9792.2.a.w 1 136.e odd 2 1
9792.2.a.bm 1 408.b odd 2 1
9792.2.a.bp 1 408.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 $$S_{2}^{\mathrm{new}}(\Gamma_0(2601))$$:

 $$T_{2} - 2$$ $$T_{5} + 1$$ $$T_{7} - 2$$

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$-2 + T$$
$3$ $$T$$
$5$ $$1 + T$$
$7$ $$-2 + T$$
$11$ $$3 + T$$
$13$ $$5 + T$$
$17$ $$T$$
$19$ $$1 + T$$
$23$ $$7 + T$$
$29$ $$-6 + T$$
$31$ $$4 + T$$
$37$ $$10 + T$$
$41$ $$-9 + T$$
$43$ $$-1 + T$$
$47$ $$-12 + T$$
$53$ $$-12 + T$$
$59$ $$6 + T$$
$61$ $$2 + T$$
$67$ $$-4 + T$$
$71$ $$8 + T$$
$73$ $$T$$
$79$ $$-6 + T$$
$83$ $$4 + T$$
$89$ $$2 + T$$
$97$ $$8 + T$$