# Properties

 Label 1110.2.m Level $1110$ Weight $2$ Character orbit 1110.m Rep. character $\chi_{1110}(593,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $144$ Sturm bound $456$

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## Defining parameters

 Level: $$N$$ $$=$$ $$1110 = 2 \cdot 3 \cdot 5 \cdot 37$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1110.m (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$15$$ Character field: $$\Q(i)$$ Sturm bound: $$456$$

## Dimensions

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

Total New Old
Modular forms 472 144 328
Cusp forms 440 144 296
Eisenstein series 32 0 32

## Trace form

 $$144q + 8q^{6} + 8q^{7} + O(q^{10})$$ $$144q + 8q^{6} + 8q^{7} - 8q^{10} - 16q^{13} - 24q^{15} - 144q^{16} - 16q^{18} - 16q^{21} - 8q^{22} + 24q^{27} + 8q^{28} + 16q^{33} + 8q^{36} - 48q^{43} - 16q^{45} - 48q^{46} + 48q^{51} + 16q^{52} - 8q^{55} + 56q^{58} + 16q^{60} + 48q^{61} + 8q^{63} - 48q^{66} + 16q^{67} - 24q^{70} + 16q^{72} + 56q^{73} + 40q^{75} + 20q^{78} + 24q^{81} - 32q^{82} + 48q^{85} - 64q^{87} - 8q^{88} + 96q^{91} - 80q^{93} - 8q^{96} - 40q^{97} + O(q^{100})$$

## 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

$$S_{2}^{\mathrm{old}}(1110, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(555, [\chi])$$$$^{\oplus 2}$$