Properties

 Label 6498.2.a.h Level $6498$ Weight $2$ Character orbit 6498.a Self dual yes Analytic conductor $51.887$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$6498 = 2 \cdot 3^{2} \cdot 19^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 6498.a (trivial)

Newform invariants

 Self dual: yes Analytic conductor: $$51.8867912334$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 114) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

 $$f(q)$$ $$=$$ $$q - q^{2} + q^{4} + 4q^{7} - q^{8} + O(q^{10})$$ $$q - q^{2} + q^{4} + 4q^{7} - q^{8} - 4q^{11} - 4q^{14} + q^{16} + 2q^{17} + 4q^{22} + 2q^{23} - 5q^{25} + 4q^{28} - 6q^{29} - 6q^{31} - q^{32} - 2q^{34} + 8q^{37} + 10q^{41} - 12q^{43} - 4q^{44} - 2q^{46} - 10q^{47} + 9q^{49} + 5q^{50} + 2q^{53} - 4q^{56} + 6q^{58} + 4q^{59} - 10q^{61} + 6q^{62} + q^{64} + 2q^{68} - 16q^{71} - 2q^{73} - 8q^{74} - 16q^{77} - 10q^{79} - 10q^{82} + 16q^{83} + 12q^{86} + 4q^{88} - 2q^{89} + 2q^{92} + 10q^{94} + 10q^{97} - 9q^{98} + O(q^{100})$$

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 0 0 4.00000 −1.00000 0 0
 $$n$$: e.g. 2-40 or 990-1000 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

Atkin-Lehner signs

$$p$$ Sign
$$2$$ $$1$$
$$3$$ $$-1$$
$$19$$ $$-1$$

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 6498.2.a.h 1
3.b odd 2 1 2166.2.a.i 1
19.b odd 2 1 342.2.a.f 1
57.d even 2 1 114.2.a.a 1
76.d even 2 1 2736.2.a.j 1
95.d odd 2 1 8550.2.a.a 1
228.b odd 2 1 912.2.a.h 1
285.b even 2 1 2850.2.a.x 1
285.j odd 4 2 2850.2.d.s 2
399.h odd 2 1 5586.2.a.p 1
456.l odd 2 1 3648.2.a.j 1
456.p even 2 1 3648.2.a.bb 1

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
114.2.a.a 1 57.d even 2 1
342.2.a.f 1 19.b odd 2 1
912.2.a.h 1 228.b odd 2 1
2166.2.a.i 1 3.b odd 2 1
2736.2.a.j 1 76.d even 2 1
2850.2.a.x 1 285.b even 2 1
2850.2.d.s 2 285.j odd 4 2
3648.2.a.j 1 456.l odd 2 1
3648.2.a.bb 1 456.p even 2 1
5586.2.a.p 1 399.h odd 2 1
6498.2.a.h 1 1.a even 1 1 trivial
8550.2.a.a 1 95.d odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(6498))$$:

 $$T_{5}$$ $$T_{7} - 4$$ $$T_{11} + 4$$ $$T_{13}$$ $$T_{29} + 6$$

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$1 + T$$
$3$ $$T$$
$5$ $$T$$
$7$ $$-4 + T$$
$11$ $$4 + T$$
$13$ $$T$$
$17$ $$-2 + T$$
$19$ $$T$$
$23$ $$-2 + T$$
$29$ $$6 + T$$
$31$ $$6 + T$$
$37$ $$-8 + T$$
$41$ $$-10 + T$$
$43$ $$12 + T$$
$47$ $$10 + T$$
$53$ $$-2 + T$$
$59$ $$-4 + T$$
$61$ $$10 + T$$
$67$ $$T$$
$71$ $$16 + T$$
$73$ $$2 + T$$
$79$ $$10 + T$$
$83$ $$-16 + T$$
$89$ $$2 + T$$
$97$ $$-10 + T$$