# Properties

 Label 2790.2.a.bc Level $2790$ Weight $2$ Character orbit 2790.a Self dual yes Analytic conductor $22.278$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$2790 = 2 \cdot 3^{2} \cdot 5 \cdot 31$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2790.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$22.2782621639$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 930) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## $q$-expansion

 $$f(q)$$ $$=$$ $$q + q^{2} + q^{4} + q^{5} + 4 q^{7} + q^{8}+O(q^{10})$$ q + q^2 + q^4 + q^5 + 4 * q^7 + q^8 $$q + q^{2} + q^{4} + q^{5} + 4 q^{7} + q^{8} + q^{10} + 4 q^{11} + 2 q^{13} + 4 q^{14} + q^{16} - 2 q^{17} + 4 q^{19} + q^{20} + 4 q^{22} - 4 q^{23} + q^{25} + 2 q^{26} + 4 q^{28} + 2 q^{29} - q^{31} + q^{32} - 2 q^{34} + 4 q^{35} - 6 q^{37} + 4 q^{38} + q^{40} - 10 q^{41} - 4 q^{43} + 4 q^{44} - 4 q^{46} - 8 q^{47} + 9 q^{49} + q^{50} + 2 q^{52} + 6 q^{53} + 4 q^{55} + 4 q^{56} + 2 q^{58} - 8 q^{59} + 10 q^{61} - q^{62} + q^{64} + 2 q^{65} - 12 q^{67} - 2 q^{68} + 4 q^{70} + 14 q^{73} - 6 q^{74} + 4 q^{76} + 16 q^{77} - 8 q^{79} + q^{80} - 10 q^{82} - 4 q^{83} - 2 q^{85} - 4 q^{86} + 4 q^{88} + 6 q^{89} + 8 q^{91} - 4 q^{92} - 8 q^{94} + 4 q^{95} - 6 q^{97} + 9 q^{98}+O(q^{100})$$ q + q^2 + q^4 + q^5 + 4 * q^7 + q^8 + q^10 + 4 * q^11 + 2 * q^13 + 4 * q^14 + q^16 - 2 * q^17 + 4 * q^19 + q^20 + 4 * q^22 - 4 * q^23 + q^25 + 2 * q^26 + 4 * q^28 + 2 * q^29 - q^31 + q^32 - 2 * q^34 + 4 * q^35 - 6 * q^37 + 4 * q^38 + q^40 - 10 * q^41 - 4 * q^43 + 4 * q^44 - 4 * q^46 - 8 * q^47 + 9 * q^49 + q^50 + 2 * q^52 + 6 * q^53 + 4 * q^55 + 4 * q^56 + 2 * q^58 - 8 * q^59 + 10 * q^61 - q^62 + q^64 + 2 * q^65 - 12 * q^67 - 2 * q^68 + 4 * q^70 + 14 * q^73 - 6 * q^74 + 4 * q^76 + 16 * q^77 - 8 * q^79 + q^80 - 10 * q^82 - 4 * q^83 - 2 * q^85 - 4 * q^86 + 4 * q^88 + 6 * q^89 + 8 * q^91 - 4 * q^92 - 8 * q^94 + 4 * q^95 - 6 * q^97 + 9 * 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
1.00000 0 1.00000 1.00000 0 4.00000 1.00000 0 1.00000
 $$n$$: e.g. 2-40 or 990-1000 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## Atkin-Lehner signs

$$p$$ Sign
$$2$$ $$-1$$
$$3$$ $$-1$$
$$5$$ $$-1$$
$$31$$ $$1$$

## 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 2790.2.a.bc 1
3.b odd 2 1 930.2.a.g 1
12.b even 2 1 7440.2.a.a 1
15.d odd 2 1 4650.2.a.w 1
15.e even 4 2 4650.2.d.c 2

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
930.2.a.g 1 3.b odd 2 1
2790.2.a.bc 1 1.a even 1 1 trivial
4650.2.a.w 1 15.d odd 2 1
4650.2.d.c 2 15.e even 4 2
7440.2.a.a 1 12.b even 2 1

## Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(2790))$$:

 $$T_{7} - 4$$ T7 - 4 $$T_{11} - 4$$ T11 - 4 $$T_{13} - 2$$ T13 - 2 $$T_{17} + 2$$ T17 + 2 $$T_{19} - 4$$ T19 - 4

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$T - 1$$
$3$ $$T$$
$5$ $$T - 1$$
$7$ $$T - 4$$
$11$ $$T - 4$$
$13$ $$T - 2$$
$17$ $$T + 2$$
$19$ $$T - 4$$
$23$ $$T + 4$$
$29$ $$T - 2$$
$31$ $$T + 1$$
$37$ $$T + 6$$
$41$ $$T + 10$$
$43$ $$T + 4$$
$47$ $$T + 8$$
$53$ $$T - 6$$
$59$ $$T + 8$$
$61$ $$T - 10$$
$67$ $$T + 12$$
$71$ $$T$$
$73$ $$T - 14$$
$79$ $$T + 8$$
$83$ $$T + 4$$
$89$ $$T - 6$$
$97$ $$T + 6$$