Properties

 Label 1110.2.bg Level $1110$ Weight $2$ Character orbit 1110.bg Rep. character $\chi_{1110}(233,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $304$ Sturm bound $456$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$1110 = 2 \cdot 3 \cdot 5 \cdot 37$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1110.bg (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$555$$ Character field: $$\Q(\zeta_{12})$$ Sturm bound: $$456$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1110, [\chi])$$.

Total New Old
Modular forms 944 304 640
Cusp forms 880 304 576
Eisenstein series 64 0 64

Trace form

 $$304q + 4q^{3} + O(q^{10})$$ $$304q + 4q^{3} + 4q^{12} + 12q^{15} + 152q^{16} + 40q^{25} + 40q^{27} + 24q^{30} - 4q^{33} - 48q^{37} + 8q^{40} + 12q^{42} - 16q^{46} + 8q^{48} + 48q^{55} + 48q^{57} + 8q^{58} - 48q^{61} - 8q^{67} - 8q^{70} + 32q^{73} + 112q^{75} + 20q^{78} + 24q^{81} + 144q^{85} + 36q^{87} + 60q^{90} - 192q^{91} - 24q^{93} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(1110, [\chi])$$ into newform subspaces

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

Decomposition of $$S_{2}^{\mathrm{old}}(1110, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1110, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(555, [\chi])$$$$^{\oplus 2}$$