Properties

 Label 36.2.a.a Level 36 Weight 2 Character orbit 36.a Self dual Yes Analytic conductor 0.287 Analytic rank 0 Dimension 1 CM disc. -3 Inner twists 2

Related objects

Newspace parameters

 Level: $$N$$ = $$36 = 2^{2} \cdot 3^{2}$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 36.a (trivial)

Newform invariants

 Self dual: Yes Analytic conductor: $$0.287461447277$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Fricke sign: $$-1$$ Sato-Tate group: $N(\mathrm{U}(1))$

$q$-expansion

 $$f(q)$$ $$=$$ $$q$$ $$\mathstrut -\mathstrut 4q^{7}$$ $$\mathstrut +\mathstrut O(q^{10})$$ $$q$$ $$\mathstrut -\mathstrut 4q^{7}$$ $$\mathstrut +\mathstrut 2q^{13}$$ $$\mathstrut +\mathstrut 8q^{19}$$ $$\mathstrut -\mathstrut 5q^{25}$$ $$\mathstrut -\mathstrut 4q^{31}$$ $$\mathstrut -\mathstrut 10q^{37}$$ $$\mathstrut +\mathstrut 8q^{43}$$ $$\mathstrut +\mathstrut 9q^{49}$$ $$\mathstrut +\mathstrut 14q^{61}$$ $$\mathstrut -\mathstrut 16q^{67}$$ $$\mathstrut -\mathstrut 10q^{73}$$ $$\mathstrut -\mathstrut 4q^{79}$$ $$\mathstrut -\mathstrut 8q^{91}$$ $$\mathstrut +\mathstrut 14q^{97}$$ $$\mathstrut +\mathstrut O(q^{100})$$

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

Inner twists

Char. orbit Parity Mult. Self Twist Proved
1.a Even 1 trivial yes
3.b Odd 1 CM by $$\Q(\sqrt{-3})$$ yes

Atkin-Lehner signs

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

Hecke kernels

There are no other newforms in $$S_{2}^{\mathrm{new}}(\Gamma_0(36))$$.