# Properties

 Label 1344.4.cx Level $1344$ Weight $4$ Character orbit 1344.cx Rep. character $\chi_{1344}(11,\cdot)$ Character field $\Q(\zeta_{48})$ Dimension $12224$ Sturm bound $1024$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1344 = 2^{6} \cdot 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 1344.cx (of order $$48$$ and degree $$16$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$1344$$ Character field: $$\Q(\zeta_{48})$$ Sturm bound: $$1024$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(1344, [\chi])$$.

Total New Old
Modular forms 12352 12352 0
Cusp forms 12224 12224 0
Eisenstein series 128 128 0

## Trace form

 $$12224q - 8q^{3} - 16q^{4} - 32q^{6} - 32q^{7} - 8q^{9} + O(q^{10})$$ $$12224q - 8q^{3} - 16q^{4} - 32q^{6} - 32q^{7} - 8q^{9} - 16q^{10} - 8q^{12} - 64q^{13} - 32q^{15} - 16q^{16} - 8q^{18} - 16q^{19} - 16q^{21} - 64q^{22} + 1992q^{24} - 16q^{25} - 32q^{27} - 32q^{28} - 2328q^{30} - 32q^{31} - 64q^{34} + 1728q^{36} - 16q^{37} - 8q^{39} - 16q^{40} + 3144q^{42} - 64q^{43} - 8q^{45} - 16q^{46} - 32q^{48} - 32q^{49} - 8q^{51} + 3296q^{52} - 8q^{54} - 64q^{55} - 32q^{57} - 16q^{58} - 8q^{60} - 16q^{61} + 12032q^{64} + 120q^{66} - 6544q^{67} - 32q^{69} - 32q^{70} - 8q^{72} - 16q^{73} - 8q^{75} - 64q^{76} - 32q^{78} - 16q^{79} - 8q^{81} + 6944q^{82} - 4160q^{84} - 64q^{85} - 8q^{87} - 16q^{88} + 18688q^{90} - 32q^{91} + 424q^{93} - 16q^{94} - 12928q^{96} - 32q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(1344, [\chi])$$ into newform subspaces

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