# Properties

 Label 3549.2.ct Level $3549$ Weight $2$ Character orbit 3549.ct Rep. character $\chi_{3549}(79,\cdot)$ Character field $\Q(\zeta_{39})$ Dimension $5808$ Sturm bound $970$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$3549 = 3 \cdot 7 \cdot 13^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3549.ct (of order $$39$$ and degree $$24$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$1183$$ Character field: $$\Q(\zeta_{39})$$ Sturm bound: $$970$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(3549, [\chi])$$.

Total New Old
Modular forms 11760 5808 5952
Cusp forms 11568 5808 5760
Eisenstein series 192 0 192

## Trace form

 $$5808q + 2q^{3} + 240q^{4} + 2q^{7} + 242q^{9} + O(q^{10})$$ $$5808q + 2q^{3} + 240q^{4} + 2q^{7} + 242q^{9} + 8q^{10} - 8q^{11} + 4q^{12} - 72q^{13} - 24q^{14} + 220q^{16} - 14q^{19} + 32q^{20} - 8q^{21} + 24q^{22} - 12q^{24} + 238q^{25} + 2q^{26} - 4q^{27} + 24q^{28} + 6q^{31} + 110q^{32} - 16q^{34} - 16q^{35} - 480q^{36} - 10q^{37} - 220q^{38} + q^{39} + 4q^{40} + 72q^{41} - 98q^{42} - 28q^{43} - 40q^{44} - 40q^{46} + 24q^{47} - 16q^{48} + 282q^{49} + 8q^{50} + 8q^{51} - 10q^{52} - 176q^{53} - 40q^{55} + 8q^{56} + 12q^{57} + 12q^{58} + 192q^{59} + 4q^{60} + 32q^{61} - 96q^{62} + 2q^{63} - 416q^{64} - 6q^{65} + 16q^{66} + 66q^{67} + 110q^{68} - 32q^{69} - 200q^{70} - 100q^{71} - 42q^{73} - 184q^{74} - 2q^{75} - 224q^{76} - 60q^{77} - 4q^{78} - 10q^{79} - 68q^{80} + 242q^{81} - 40q^{82} - 16q^{83} - 20q^{84} + 376q^{85} + 100q^{86} + 12q^{87} + 32q^{89} - 16q^{90} + 221q^{91} + 144q^{92} + 33q^{93} + 38q^{94} - 136q^{95} - 44q^{96} - 352q^{97} - 56q^{98} + 16q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(3549, [\chi])$$ into newform subspaces

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

## Decomposition of $$S_{2}^{\mathrm{old}}(3549, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(3549, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(1183, [\chi])$$$$^{\oplus 2}$$