# Properties

 Label 1216.4.bb Level $1216$ Weight $4$ Character orbit 1216.bb Rep. character $\chi_{1216}(335,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $472$ Sturm bound $640$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1216 = 2^{6} \cdot 19$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 1216.bb (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$304$$ Character field: $$\Q(\zeta_{12})$$ Sturm bound: $$640$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(1216, [\chi])$$.

Total New Old
Modular forms 1952 488 1464
Cusp forms 1888 472 1416
Eisenstein series 64 16 48

## Trace form

 $$472q + 6q^{3} - 2q^{5} + 16q^{7} + O(q^{10})$$ $$472q + 6q^{3} - 2q^{5} + 16q^{7} + 8q^{11} - 6q^{13} - 4q^{17} - 20q^{19} - 168q^{21} + 4q^{23} - 6q^{29} - 12q^{33} - 204q^{35} + 16q^{39} + 2q^{43} - 400q^{45} + 20760q^{49} + 2238q^{51} - 6q^{53} + 4q^{55} + 6q^{59} + 1822q^{61} + 6q^{67} + 12q^{71} - 2752q^{77} + 16520q^{81} - 2672q^{83} + 258q^{85} + 2592q^{87} + 2064q^{91} - 56q^{93} - 12q^{97} - 4004q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(1216, [\chi])$$ into newform subspaces

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

## Decomposition of $$S_{4}^{\mathrm{old}}(1216, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(1216, [\chi]) \cong$$ $$S_{4}^{\mathrm{new}}(304, [\chi])$$$$^{\oplus 3}$$