# Properties

 Label 128.4.a Level $128$ Weight $4$ Character orbit 128.a Rep. character $\chi_{128}(1,\cdot)$ Character field $\Q$ Dimension $12$ Newform subspaces $8$ Sturm bound $64$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$128 = 2^{7}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 128.a (trivial) Character field: $$\Q$$ Newform subspaces: $$8$$ Sturm bound: $$64$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$3$$, $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_0(128))$$.

Total New Old
Modular forms 56 12 44
Cusp forms 40 12 28
Eisenstein series 16 0 16

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

$$2$$Dim
$$+$$$$7$$
$$-$$$$5$$

## Trace form

 $$12 q + 108 q^{9} + O(q^{10})$$ $$12 q + 108 q^{9} + 104 q^{17} + 212 q^{25} + 464 q^{33} - 392 q^{41} - 852 q^{49} - 1360 q^{57} - 2512 q^{65} - 24 q^{73} + 1596 q^{81} + 1960 q^{89} + 4328 q^{97} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_0(128))$$ into newform subspaces

Label Dim $A$ Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2
128.4.a.a $1$ $7.552$ $$\Q$$ None $$0$$ $$-2$$ $$-6$$ $$20$$ $-$ $$q-2q^{3}-6q^{5}+20q^{7}-23q^{9}-14q^{11}+\cdots$$
128.4.a.b $1$ $7.552$ $$\Q$$ None $$0$$ $$-2$$ $$6$$ $$-20$$ $-$ $$q-2q^{3}+6q^{5}-20q^{7}-23q^{9}-14q^{11}+\cdots$$
128.4.a.c $1$ $7.552$ $$\Q$$ None $$0$$ $$2$$ $$-6$$ $$-20$$ $-$ $$q+2q^{3}-6q^{5}-20q^{7}-23q^{9}+14q^{11}+\cdots$$
128.4.a.d $1$ $7.552$ $$\Q$$ None $$0$$ $$2$$ $$6$$ $$20$$ $+$ $$q+2q^{3}+6q^{5}+20q^{7}-23q^{9}+14q^{11}+\cdots$$
128.4.a.e $2$ $7.552$ $$\Q(\sqrt{3})$$ None $$0$$ $$-4$$ $$-4$$ $$-8$$ $-$ $$q+(-2+\beta )q^{3}+(-2-2\beta )q^{5}+(-4+\cdots)q^{7}+\cdots$$
128.4.a.f $2$ $7.552$ $$\Q(\sqrt{3})$$ None $$0$$ $$-4$$ $$4$$ $$8$$ $+$ $$q+(-2+\beta )q^{3}+(2+2\beta )q^{5}+(4+2\beta )q^{7}+\cdots$$
128.4.a.g $2$ $7.552$ $$\Q(\sqrt{3})$$ None $$0$$ $$4$$ $$-4$$ $$8$$ $+$ $$q+(2+\beta )q^{3}+(-2+2\beta )q^{5}+(4-2\beta )q^{7}+\cdots$$
128.4.a.h $2$ $7.552$ $$\Q(\sqrt{3})$$ None $$0$$ $$4$$ $$4$$ $$-8$$ $+$ $$q+(2+\beta )q^{3}+(2-2\beta )q^{5}+(-4+2\beta )q^{7}+\cdots$$

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_0(128))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_0(128)) \simeq$$ $$S_{4}^{\mathrm{new}}(\Gamma_0(8))$$$$^{\oplus 5}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_0(16))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_0(32))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_0(64))$$$$^{\oplus 2}$$