# Properties

 Label 544.2.a Level $544$ Weight $2$ Character orbit 544.a Rep. character $\chi_{544}(1,\cdot)$ Character field $\Q$ Dimension $16$ Newform subspaces $10$ Sturm bound $144$ Trace bound $9$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$544 = 2^{5} \cdot 17$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 544.a (trivial) Character field: $$\Q$$ Newform subspaces: $$10$$ Sturm bound: $$144$$ Trace bound: $$9$$ Distinguishing $$T_p$$: $$3$$, $$5$$, $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_0(544))$$.

Total New Old
Modular forms 80 16 64
Cusp forms 65 16 49
Eisenstein series 15 0 15

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

$$2$$$$17$$FrickeDim.
$$+$$$$+$$$$+$$$$3$$
$$+$$$$-$$$$-$$$$5$$
$$-$$$$+$$$$-$$$$5$$
$$-$$$$-$$$$+$$$$3$$
Plus space$$+$$$$6$$
Minus space$$-$$$$10$$

## Trace form

 $$16 q + 16 q^{9} + O(q^{10})$$ $$16 q + 16 q^{9} - 16 q^{13} + 32 q^{25} + 16 q^{29} + 16 q^{33} - 16 q^{37} + 16 q^{41} - 32 q^{45} + 32 q^{49} - 48 q^{53} + 16 q^{57} - 16 q^{61} + 48 q^{65} - 16 q^{69} + 16 q^{77} - 16 q^{89} - 48 q^{93} - 48 q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_0(544))$$ into newform subspaces

Label Dim $A$ Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 17
544.2.a.a $1$ $4.344$ $$\Q$$ None $$0$$ $$-2$$ $$2$$ $$-2$$ $+$ $-$ $$q-2q^{3}+2q^{5}-2q^{7}+q^{9}+2q^{11}+\cdots$$
544.2.a.b $1$ $4.344$ $$\Q$$ None $$0$$ $$-2$$ $$4$$ $$4$$ $-$ $+$ $$q-2q^{3}+4q^{5}+4q^{7}+q^{9}-2q^{11}+\cdots$$
544.2.a.c $1$ $4.344$ $$\Q$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $+$ $+$ $$q-2q^{7}-3q^{9}-4q^{11}+2q^{13}-q^{17}+\cdots$$
544.2.a.d $1$ $4.344$ $$\Q$$ None $$0$$ $$0$$ $$0$$ $$2$$ $-$ $+$ $$q+2q^{7}-3q^{9}+4q^{11}+2q^{13}-q^{17}+\cdots$$
544.2.a.e $1$ $4.344$ $$\Q$$ None $$0$$ $$2$$ $$2$$ $$2$$ $+$ $-$ $$q+2q^{3}+2q^{5}+2q^{7}+q^{9}-2q^{11}+\cdots$$
544.2.a.f $1$ $4.344$ $$\Q$$ None $$0$$ $$2$$ $$4$$ $$-4$$ $-$ $+$ $$q+2q^{3}+4q^{5}-4q^{7}+q^{9}+2q^{11}+\cdots$$
544.2.a.g $2$ $4.344$ $$\Q(\sqrt{2})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $+$ $+$ $$q+\beta q^{3}-2q^{5}-3\beta q^{7}-q^{9}+\beta q^{11}+\cdots$$
544.2.a.h $2$ $4.344$ $$\Q(\sqrt{10})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $-$ $+$ $$q+\beta q^{3}-2q^{5}+\beta q^{7}+7q^{9}+\beta q^{11}+\cdots$$
544.2.a.i $3$ $4.344$ 3.3.148.1 None $$0$$ $$-2$$ $$-2$$ $$-2$$ $-$ $-$ $$q+(-1+\beta _{1})q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots$$
544.2.a.j $3$ $4.344$ 3.3.148.1 None $$0$$ $$2$$ $$-2$$ $$2$$ $+$ $-$ $$q+(1-\beta _{1})q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(1-\beta _{2})q^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_0(544))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_0(544)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_0(17))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(32))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(34))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(68))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(136))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(272))$$$$^{\oplus 2}$$