# Properties

 Label 2667.2.a.h Level $2667$ Weight $2$ Character orbit 2667.a Self dual yes Analytic conductor $21.296$ Analytic rank $0$ Dimension $2$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$2667 = 3 \cdot 7 \cdot 127$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2667.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$21.2961022191$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\sqrt{6})$$ Defining polynomial: $$x^{2} - 6$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## $q$-expansion

Coefficients of the $$q$$-expansion are expressed in terms of $$\beta = \sqrt{6}$$. We also show the integral $$q$$-expansion of the trace form.

 $$f(q)$$ $$=$$ $$q + \beta q^{2} + q^{3} + 4 q^{4} + \beta q^{5} + \beta q^{6} + q^{7} + 2 \beta q^{8} + q^{9} +O(q^{10})$$ $$q + \beta q^{2} + q^{3} + 4 q^{4} + \beta q^{5} + \beta q^{6} + q^{7} + 2 \beta q^{8} + q^{9} + 6 q^{10} + 4 q^{12} + ( 2 - 2 \beta ) q^{13} + \beta q^{14} + \beta q^{15} + 4 q^{16} + ( -3 - \beta ) q^{17} + \beta q^{18} + ( 2 + \beta ) q^{19} + 4 \beta q^{20} + q^{21} + 6 q^{23} + 2 \beta q^{24} + q^{25} + ( -12 + 2 \beta ) q^{26} + q^{27} + 4 q^{28} + ( -3 - 2 \beta ) q^{29} + 6 q^{30} + 8 q^{31} + ( -6 - 3 \beta ) q^{34} + \beta q^{35} + 4 q^{36} -7 q^{37} + ( 6 + 2 \beta ) q^{38} + ( 2 - 2 \beta ) q^{39} + 12 q^{40} + ( 3 + \beta ) q^{41} + \beta q^{42} + 2 q^{43} + \beta q^{45} + 6 \beta q^{46} -12 q^{47} + 4 q^{48} + q^{49} + \beta q^{50} + ( -3 - \beta ) q^{51} + ( 8 - 8 \beta ) q^{52} + ( -3 + 2 \beta ) q^{53} + \beta q^{54} + 2 \beta q^{56} + ( 2 + \beta ) q^{57} + ( -12 - 3 \beta ) q^{58} -\beta q^{59} + 4 \beta q^{60} + ( 2 + \beta ) q^{61} + 8 \beta q^{62} + q^{63} -8 q^{64} + ( -12 + 2 \beta ) q^{65} + ( 2 - 5 \beta ) q^{67} + ( -12 - 4 \beta ) q^{68} + 6 q^{69} + 6 q^{70} + ( 6 - \beta ) q^{71} + 2 \beta q^{72} + ( -4 + 3 \beta ) q^{73} -7 \beta q^{74} + q^{75} + ( 8 + 4 \beta ) q^{76} + ( -12 + 2 \beta ) q^{78} + ( -1 + 2 \beta ) q^{79} + 4 \beta q^{80} + q^{81} + ( 6 + 3 \beta ) q^{82} + 6 q^{83} + 4 q^{84} + ( -6 - 3 \beta ) q^{85} + 2 \beta q^{86} + ( -3 - 2 \beta ) q^{87} -4 \beta q^{89} + 6 q^{90} + ( 2 - 2 \beta ) q^{91} + 24 q^{92} + 8 q^{93} -12 \beta q^{94} + ( 6 + 2 \beta ) q^{95} + ( 5 - 3 \beta ) q^{97} + \beta q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + 2q^{3} + 8q^{4} + 2q^{7} + 2q^{9} + O(q^{10})$$ $$2q + 2q^{3} + 8q^{4} + 2q^{7} + 2q^{9} + 12q^{10} + 8q^{12} + 4q^{13} + 8q^{16} - 6q^{17} + 4q^{19} + 2q^{21} + 12q^{23} + 2q^{25} - 24q^{26} + 2q^{27} + 8q^{28} - 6q^{29} + 12q^{30} + 16q^{31} - 12q^{34} + 8q^{36} - 14q^{37} + 12q^{38} + 4q^{39} + 24q^{40} + 6q^{41} + 4q^{43} - 24q^{47} + 8q^{48} + 2q^{49} - 6q^{51} + 16q^{52} - 6q^{53} + 4q^{57} - 24q^{58} + 4q^{61} + 2q^{63} - 16q^{64} - 24q^{65} + 4q^{67} - 24q^{68} + 12q^{69} + 12q^{70} + 12q^{71} - 8q^{73} + 2q^{75} + 16q^{76} - 24q^{78} - 2q^{79} + 2q^{81} + 12q^{82} + 12q^{83} + 8q^{84} - 12q^{85} - 6q^{87} + 12q^{90} + 4q^{91} + 48q^{92} + 16q^{93} + 12q^{95} + 10q^{97} + O(q^{100})$$

## 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
 −2.44949 2.44949
−2.44949 1.00000 4.00000 −2.44949 −2.44949 1.00000 −4.89898 1.00000 6.00000
1.2 2.44949 1.00000 4.00000 2.44949 2.44949 1.00000 4.89898 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
$$3$$ $$-1$$
$$7$$ $$-1$$
$$127$$ $$-1$$

## 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 2667.2.a.h 2
3.b odd 2 1 8001.2.a.k 2

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2667.2.a.h 2 1.a even 1 1 trivial
8001.2.a.k 2 3.b odd 2 1

## Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(2667))$$:

 $$T_{2}^{2} - 6$$ $$T_{5}^{2} - 6$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$-6 + T^{2}$$
$3$ $$( -1 + T )^{2}$$
$5$ $$-6 + T^{2}$$
$7$ $$( -1 + T )^{2}$$
$11$ $$T^{2}$$
$13$ $$-20 - 4 T + T^{2}$$
$17$ $$3 + 6 T + T^{2}$$
$19$ $$-2 - 4 T + T^{2}$$
$23$ $$( -6 + T )^{2}$$
$29$ $$-15 + 6 T + T^{2}$$
$31$ $$( -8 + T )^{2}$$
$37$ $$( 7 + T )^{2}$$
$41$ $$3 - 6 T + T^{2}$$
$43$ $$( -2 + T )^{2}$$
$47$ $$( 12 + T )^{2}$$
$53$ $$-15 + 6 T + T^{2}$$
$59$ $$-6 + T^{2}$$
$61$ $$-2 - 4 T + T^{2}$$
$67$ $$-146 - 4 T + T^{2}$$
$71$ $$30 - 12 T + T^{2}$$
$73$ $$-38 + 8 T + T^{2}$$
$79$ $$-23 + 2 T + T^{2}$$
$83$ $$( -6 + T )^{2}$$
$89$ $$-96 + T^{2}$$
$97$ $$-29 - 10 T + T^{2}$$