Properties

 Label 2736.3.de Level $2736$ Weight $3$ Character orbit 2736.de Rep. character $\chi_{2736}(673,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $476$ Sturm bound $1440$

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Defining parameters

 Level: $$N$$ $$=$$ $$2736 = 2^{4} \cdot 3^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 2736.de (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$171$$ Character field: $$\Q(\zeta_{6})$$ Sturm bound: $$1440$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(2736, [\chi])$$.

Total New Old
Modular forms 1944 484 1460
Cusp forms 1896 476 1420
Eisenstein series 48 8 40

Trace form

 $$476q + 3q^{3} - 2q^{5} + 2q^{7} - 5q^{9} + O(q^{10})$$ $$476q + 3q^{3} - 2q^{5} + 2q^{7} - 5q^{9} + 2q^{11} - 3q^{13} + 3q^{15} - 26q^{17} + 4q^{19} - 3q^{21} - q^{23} + 2298q^{25} - 72q^{31} + 57q^{33} - 23q^{35} - 5q^{39} - 49q^{43} - 29q^{45} + 2q^{47} - 1584q^{49} + 3q^{51} - 6q^{53} - 23q^{55} + 25q^{57} - 2q^{61} - 94q^{63} - 6q^{65} + 3q^{67} + 27q^{69} + 6q^{71} + 10q^{73} + 534q^{75} + 194q^{77} + 3q^{79} - 133q^{81} + 2q^{83} - 49q^{85} - 117q^{87} - 6q^{89} - 429q^{91} + 8q^{93} + 242q^{95} + 177q^{97} - 46q^{99} + O(q^{100})$$

Decomposition of $$S_{3}^{\mathrm{new}}(2736, [\chi])$$ into newform subspaces

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

Decomposition of $$S_{3}^{\mathrm{old}}(2736, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(2736, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(171, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(342, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(684, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(1368, [\chi])$$$$^{\oplus 2}$$