# Properties

 Label 567.2.a Level $567$ Weight $2$ Character orbit 567.a Rep. character $\chi_{567}(1,\cdot)$ Character field $\Q$ Dimension $24$ Newform subspaces $9$ Sturm bound $144$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$567 = 3^{4} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 567.a (trivial) Character field: $$\Q$$ Newform subspaces: $$9$$ Sturm bound: $$144$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_0(567))$$.

Total New Old
Modular forms 84 24 60
Cusp forms 61 24 37
Eisenstein series 23 0 23

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

$$3$$$$7$$FrickeDim
$$+$$$$+$$$+$$$5$$
$$+$$$$-$$$-$$$9$$
$$-$$$$+$$$-$$$7$$
$$-$$$$-$$$+$$$3$$
Plus space$$+$$$$8$$
Minus space$$-$$$$16$$

## Trace form

 $$24 q + 24 q^{4} + O(q^{10})$$ $$24 q + 24 q^{4} + 12 q^{10} + 12 q^{13} + 36 q^{16} - 12 q^{19} + 24 q^{25} + 12 q^{28} - 12 q^{31} - 24 q^{34} + 24 q^{37} + 12 q^{40} - 12 q^{43} - 12 q^{46} + 24 q^{49} - 12 q^{55} - 12 q^{58} + 36 q^{61} - 12 q^{64} - 24 q^{73} - 60 q^{76} + 12 q^{79} - 24 q^{82} + 48 q^{85} - 48 q^{88} - 12 q^{91} - 84 q^{94} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_0(567))$$ into newform subspaces

Label Dim $A$ Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 7
567.2.a.a $1$ $4.528$ $$\Q$$ None $$-1$$ $$0$$ $$1$$ $$-1$$ $+$ $+$ $$q-q^{2}-q^{4}+q^{5}-q^{7}+3q^{8}-q^{10}+\cdots$$
567.2.a.b $1$ $4.528$ $$\Q$$ None $$1$$ $$0$$ $$-1$$ $$-1$$ $+$ $+$ $$q+q^{2}-q^{4}-q^{5}-q^{7}-3q^{8}-q^{10}+\cdots$$
567.2.a.c $3$ $4.528$ $$\Q(\zeta_{18})^+$$ None $$-3$$ $$0$$ $$-3$$ $$3$$ $-$ $-$ $$q+(-1+\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+\cdots$$
567.2.a.d $3$ $4.528$ 3.3.321.1 None $$-1$$ $$0$$ $$-5$$ $$-3$$ $+$ $+$ $$q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(-2-\beta _{2})q^{5}+\cdots$$
567.2.a.e $3$ $4.528$ 3.3.621.1 None $$0$$ $$0$$ $$-3$$ $$3$$ $+$ $-$ $$q+\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2})q^{4}+(-1-\beta _{2})q^{5}+\cdots$$
567.2.a.f $3$ $4.528$ 3.3.621.1 None $$0$$ $$0$$ $$3$$ $$3$$ $+$ $-$ $$q-\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2})q^{4}+(1+\beta _{2})q^{5}+\cdots$$
567.2.a.g $3$ $4.528$ 3.3.321.1 None $$1$$ $$0$$ $$5$$ $$-3$$ $-$ $+$ $$q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(2+\beta _{2})q^{5}+\cdots$$
567.2.a.h $3$ $4.528$ $$\Q(\zeta_{18})^+$$ None $$3$$ $$0$$ $$3$$ $$3$$ $+$ $-$ $$q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$$
567.2.a.i $4$ $4.528$ $$\Q(\sqrt{3}, \sqrt{7})$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $-$ $+$ $$q+\beta _{3}q^{2}-\beta _{2}q^{4}-2\beta _{1}q^{5}-q^{7}+(\beta _{1}+\cdots)q^{8}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_0(567))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_0(567)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_0(21))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(27))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(63))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(81))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(189))$$$$^{\oplus 2}$$