# Properties

 Label 608.4.t Level $608$ Weight $4$ Character orbit 608.t Rep. character $\chi_{608}(49,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $116$ Sturm bound $320$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$608 = 2^{5} \cdot 19$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 608.t (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$152$$ Character field: $$\Q(\zeta_{6})$$ Sturm bound: $$320$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(608, [\chi])$$.

Total New Old
Modular forms 496 124 372
Cusp forms 464 116 348
Eisenstein series 32 8 24

## Trace form

 $$116q + 8q^{7} + 484q^{9} + O(q^{10})$$ $$116q + 8q^{7} + 484q^{9} + 230q^{15} - 2q^{17} + 2q^{23} + 1248q^{25} - 208q^{31} - 180q^{33} + 116q^{39} - 22q^{41} - 202q^{47} + 5220q^{49} - 248q^{55} - 398q^{57} + 796q^{63} - 508q^{65} - 1986q^{71} - 218q^{73} - 1250q^{79} - 3810q^{81} + 1404q^{87} - 2q^{89} - 438q^{95} - 1586q^{97} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(608, [\chi])$$ into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

## Decomposition of $$S_{4}^{\mathrm{old}}(608, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(608, [\chi]) \cong$$ $$S_{4}^{\mathrm{new}}(152, [\chi])$$$$^{\oplus 3}$$