# Properties

 Label 96.4.a Level $96$ Weight $4$ Character orbit 96.a Rep. character $\chi_{96}(1,\cdot)$ Character field $\Q$ Dimension $6$ Newform subspaces $6$ Sturm bound $64$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$96 = 2^{5} \cdot 3$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 96.a (trivial) Character field: $$\Q$$ Newform subspaces: $$6$$ Sturm bound: $$64$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$5$$, $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_0(96))$$.

Total New Old
Modular forms 56 6 50
Cusp forms 40 6 34
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.

$$2$$$$3$$FrickeDim
$$+$$$$+$$$+$$$2$$
$$+$$$$-$$$-$$$1$$
$$-$$$$+$$$-$$$1$$
$$-$$$$-$$$+$$$2$$
Plus space$$+$$$$4$$
Minus space$$-$$$$2$$

## Trace form

 $$6 q - 4 q^{5} + 54 q^{9} + O(q^{10})$$ $$6 q - 4 q^{5} + 54 q^{9} + 164 q^{13} + 156 q^{17} - 120 q^{21} - 150 q^{25} + 284 q^{29} + 24 q^{33} - 636 q^{37} - 1300 q^{41} - 36 q^{45} + 854 q^{49} - 212 q^{53} + 168 q^{57} - 1324 q^{61} - 280 q^{65} + 1212 q^{73} + 3872 q^{77} + 486 q^{81} + 2456 q^{85} + 220 q^{89} - 2760 q^{93} - 2260 q^{97} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_0(96))$$ into newform subspaces

Label Dim $A$ Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3
96.4.a.a $1$ $5.664$ $$\Q$$ None $$0$$ $$-3$$ $$-14$$ $$36$$ $+$ $+$ $$q-3q^{3}-14q^{5}+6^{2}q^{7}+9q^{9}+6^{2}q^{11}+\cdots$$
96.4.a.b $1$ $5.664$ $$\Q$$ None $$0$$ $$-3$$ $$2$$ $$-12$$ $-$ $+$ $$q-3q^{3}+2q^{5}-12q^{7}+9q^{9}-60q^{11}+\cdots$$
96.4.a.c $1$ $5.664$ $$\Q$$ None $$0$$ $$-3$$ $$10$$ $$-4$$ $+$ $+$ $$q-3q^{3}+10q^{5}-4q^{7}+9q^{9}+20q^{11}+\cdots$$
96.4.a.d $1$ $5.664$ $$\Q$$ None $$0$$ $$3$$ $$-14$$ $$-36$$ $+$ $-$ $$q+3q^{3}-14q^{5}-6^{2}q^{7}+9q^{9}-6^{2}q^{11}+\cdots$$
96.4.a.e $1$ $5.664$ $$\Q$$ None $$0$$ $$3$$ $$2$$ $$12$$ $-$ $-$ $$q+3q^{3}+2q^{5}+12q^{7}+9q^{9}+60q^{11}+\cdots$$
96.4.a.f $1$ $5.664$ $$\Q$$ None $$0$$ $$3$$ $$10$$ $$4$$ $-$ $-$ $$q+3q^{3}+10q^{5}+4q^{7}+9q^{9}-20q^{11}+\cdots$$

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_0(96))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_0(96)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_0(6))$$$$^{\oplus 5}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_0(8))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_0(12))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_0(16))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_0(24))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_0(32))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_0(48))$$$$^{\oplus 2}$$