# Properties

 Label 1110.2.k Level $1110$ Weight $2$ Character orbit 1110.k Rep. character $\chi_{1110}(179,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $152$ Sturm bound $456$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1110 = 2 \cdot 3 \cdot 5 \cdot 37$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1110.k (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$555$$ 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 472 152 320
Cusp forms 440 152 288
Eisenstein series 32 0 32

## Trace form

 $$152q - 16q^{9} + O(q^{10})$$ $$152q - 16q^{9} + 8q^{15} - 152q^{16} + 16q^{19} + 72q^{31} - 16q^{34} - 16q^{39} - 16q^{45} + 32q^{46} - 120q^{49} + 40q^{51} + 40q^{55} - 8q^{60} - 48q^{61} + 48q^{66} - 16q^{69} - 16q^{70} - 20q^{75} + 16q^{76} + 24q^{79} + 48q^{81} + 20q^{90} - 16q^{91} + 24q^{94} + O(q^{100})$$

## 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

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