# Properties

 Label 784.4.x Level $784$ Weight $4$ Character orbit 784.x Rep. character $\chi_{784}(165,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $944$ Sturm bound $448$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$784 = 2^{4} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 784.x (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$112$$ Character field: $$\Q(\zeta_{12})$$ Sturm bound: $$448$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(784, [\chi])$$.

Total New Old
Modular forms 1376 976 400
Cusp forms 1312 944 368
Eisenstein series 64 32 32

## Trace form

 $$944q + 2q^{2} + 2q^{3} + 22q^{4} + 2q^{5} + 8q^{6} - 100q^{8} + O(q^{10})$$ $$944q + 2q^{2} + 2q^{3} + 22q^{4} + 2q^{5} + 8q^{6} - 100q^{8} + 8q^{10} + 42q^{11} + 2q^{12} + 8q^{13} - 32q^{15} + 302q^{16} + 4q^{17} + 48q^{18} + 2q^{19} - 72q^{20} - 48q^{22} - 498q^{24} + 2q^{26} + 116q^{27} + 784q^{29} + 1178q^{30} + 748q^{31} - 488q^{32} + 4q^{33} - 312q^{34} - 640q^{36} - 14q^{37} - 218q^{38} + 494q^{40} + 1600q^{43} - 1884q^{44} + 556q^{45} - 412q^{46} - 1876q^{47} + 984q^{48} - 12q^{50} + 918q^{51} + 1604q^{52} - 750q^{53} + 1274q^{54} + 3916q^{58} - 686q^{59} + 5998q^{60} + 2q^{61} + 1748q^{62} + 124q^{64} + 4q^{65} - 2498q^{66} + 1118q^{67} - 1264q^{68} + 116q^{69} - 1938q^{72} - 6032q^{74} + 360q^{75} - 3052q^{76} + 2052q^{78} + 4q^{79} - 108q^{80} + 33052q^{81} + 1726q^{82} - 2432q^{83} - 516q^{85} + 8358q^{86} + 3868q^{88} + 9332q^{90} - 7348q^{92} + 218q^{93} + 150q^{94} - 3860q^{95} - 4032q^{96} + 16q^{97} - 808q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(784, [\chi])$$ into newform subspaces

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

## Decomposition of $$S_{4}^{\mathrm{old}}(784, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(784, [\chi]) \cong$$ $$S_{4}^{\mathrm{new}}(112, [\chi])$$$$^{\oplus 2}$$