Properties

 Label 96.4.d Level $96$ Weight $4$ Character orbit 96.d Rep. character $\chi_{96}(49,\cdot)$ Character field $\Q$ Dimension $6$ Newform subspaces $1$ Sturm bound $64$ Trace bound $0$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$96 = 2^{5} \cdot 3$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 96.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$8$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$64$$ Trace bound: $$0$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(96, [\chi])$$.

Total New Old
Modular forms 56 6 50
Cusp forms 40 6 34
Eisenstein series 16 0 16

Trace form

 $$6 q - 28 q^{7} - 54 q^{9} + O(q^{10})$$ $$6 q - 28 q^{7} - 54 q^{9} + 60 q^{15} + 52 q^{17} - 328 q^{23} - 106 q^{25} + 636 q^{31} - 312 q^{39} + 236 q^{41} + 408 q^{47} + 654 q^{49} - 1024 q^{55} - 168 q^{57} + 252 q^{63} - 1744 q^{65} + 1704 q^{71} + 956 q^{73} + 44 q^{79} + 486 q^{81} - 1044 q^{87} - 220 q^{89} - 5104 q^{95} - 2444 q^{97} + O(q^{100})$$

Decomposition of $$S_{4}^{\mathrm{new}}(96, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
96.4.d.a $6$ $5.664$ 6.0.8248384.1 None $$0$$ $$0$$ $$0$$ $$-28$$ $$q+\beta _{2}q^{3}+(-\beta _{2}+\beta _{3})q^{5}+(-5+\beta _{1}+\cdots)q^{7}+\cdots$$

Decomposition of $$S_{4}^{\mathrm{old}}(96, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(96, [\chi]) \simeq$$ $$S_{4}^{\mathrm{new}}(8, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(16, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(24, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(32, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(48, [\chi])$$$$^{\oplus 2}$$