# Properties

 Label 63.4.a.c Level $63$ Weight $4$ Character orbit 63.a Self dual yes Analytic conductor $3.717$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$63 = 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 63.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$3.71712033036$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 21) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## $q$-expansion

 $$f(q)$$ $$=$$ $$q + 3q^{2} + q^{4} + 18q^{5} + 7q^{7} - 21q^{8} + O(q^{10})$$ $$q + 3q^{2} + q^{4} + 18q^{5} + 7q^{7} - 21q^{8} + 54q^{10} + 36q^{11} - 34q^{13} + 21q^{14} - 71q^{16} - 42q^{17} - 124q^{19} + 18q^{20} + 108q^{22} + 199q^{25} - 102q^{26} + 7q^{28} - 102q^{29} - 160q^{31} - 45q^{32} - 126q^{34} + 126q^{35} + 398q^{37} - 372q^{38} - 378q^{40} + 318q^{41} - 268q^{43} + 36q^{44} - 240q^{47} + 49q^{49} + 597q^{50} - 34q^{52} + 498q^{53} + 648q^{55} - 147q^{56} - 306q^{58} + 132q^{59} + 398q^{61} - 480q^{62} + 433q^{64} - 612q^{65} + 92q^{67} - 42q^{68} + 378q^{70} + 720q^{71} - 502q^{73} + 1194q^{74} - 124q^{76} + 252q^{77} - 1024q^{79} - 1278q^{80} + 954q^{82} + 204q^{83} - 756q^{85} - 804q^{86} - 756q^{88} - 354q^{89} - 238q^{91} - 720q^{94} - 2232q^{95} - 286q^{97} + 147q^{98} + O(q^{100})$$

## 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
3.00000 0 1.00000 18.0000 0 7.00000 −21.0000 0 54.0000
 $$n$$: e.g. 2-40 or 990-1000 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## Atkin-Lehner signs

$$p$$ Sign
$$3$$ $$-1$$
$$7$$ $$-1$$

## 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 63.4.a.c 1
3.b odd 2 1 21.4.a.a 1
4.b odd 2 1 1008.4.a.v 1
5.b even 2 1 1575.4.a.b 1
7.b odd 2 1 441.4.a.j 1
7.c even 3 2 441.4.e.b 2
7.d odd 6 2 441.4.e.d 2
12.b even 2 1 336.4.a.f 1
15.d odd 2 1 525.4.a.g 1
15.e even 4 2 525.4.d.c 2
21.c even 2 1 147.4.a.c 1
21.g even 6 2 147.4.e.g 2
21.h odd 6 2 147.4.e.i 2
24.f even 2 1 1344.4.a.n 1
24.h odd 2 1 1344.4.a.ba 1
84.h odd 2 1 2352.4.a.r 1

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
21.4.a.a 1 3.b odd 2 1
63.4.a.c 1 1.a even 1 1 trivial
147.4.a.c 1 21.c even 2 1
147.4.e.g 2 21.g even 6 2
147.4.e.i 2 21.h odd 6 2
336.4.a.f 1 12.b even 2 1
441.4.a.j 1 7.b odd 2 1
441.4.e.b 2 7.c even 3 2
441.4.e.d 2 7.d odd 6 2
525.4.a.g 1 15.d odd 2 1
525.4.d.c 2 15.e even 4 2
1008.4.a.v 1 4.b odd 2 1
1344.4.a.n 1 24.f even 2 1
1344.4.a.ba 1 24.h odd 2 1
1575.4.a.b 1 5.b even 2 1
2352.4.a.r 1 84.h odd 2 1

## Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $$T_{2} - 3$$ acting on $$S_{4}^{\mathrm{new}}(\Gamma_0(63))$$.