# Properties

 Label 27.4.a Level $27$ Weight $4$ Character orbit 27.a Rep. character $\chi_{27}(1,\cdot)$ Character field $\Q$ Dimension $4$ Newform subspaces $3$ Sturm bound $12$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$27 = 3^{3}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 27.a (trivial) Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$12$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_0(27))$$.

Total New Old
Modular forms 12 4 8
Cusp forms 6 4 2
Eisenstein series 6 0 6

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

$$3$$Dim.
$$+$$$$3$$
$$-$$$$1$$

## Trace form

 $$4 q + 22 q^{4} - 28 q^{7} + O(q^{10})$$ $$4 q + 22 q^{4} - 28 q^{7} - 54 q^{10} + 98 q^{13} - 230 q^{16} + 62 q^{19} + 54 q^{22} + 526 q^{25} + 170 q^{28} - 334 q^{31} - 694 q^{37} - 918 q^{40} - 244 q^{43} + 1404 q^{46} + 120 q^{49} + 620 q^{52} - 1026 q^{55} + 2484 q^{58} + 782 q^{61} - 590 q^{64} - 1522 q^{67} - 3834 q^{70} + 1844 q^{73} + 584 q^{76} + 26 q^{79} - 2484 q^{82} + 3888 q^{85} + 918 q^{88} - 362 q^{91} - 5292 q^{94} - 568 q^{97} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_0(27))$$ into newform subspaces

Label Dim $A$ Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3
27.4.a.a $1$ $1.593$ $$\Q$$ None $$-3$$ $$0$$ $$-15$$ $$-25$$ $-$ $$q-3q^{2}+q^{4}-15q^{5}-5^{2}q^{7}+21q^{8}+\cdots$$
27.4.a.b $1$ $1.593$ $$\Q$$ None $$3$$ $$0$$ $$15$$ $$-25$$ $+$ $$q+3q^{2}+q^{4}+15q^{5}-5^{2}q^{7}-21q^{8}+\cdots$$
27.4.a.c $2$ $1.593$ $$\Q(\sqrt{2})$$ None $$0$$ $$0$$ $$0$$ $$22$$ $+$ $$q+\beta q^{2}+10q^{4}-4\beta q^{5}+11q^{7}+2\beta q^{8}+\cdots$$

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_0(27))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_0(27)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_0(9))$$$$^{\oplus 2}$$