# Properties

 Label 1045.2.bp Level $1045$ Weight $2$ Character orbit 1045.bp Rep. character $\chi_{1045}(37,\cdot)$ Character field $\Q(\zeta_{20})$ Dimension $928$ Sturm bound $240$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1045 = 5 \cdot 11 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1045.bp (of order $$20$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$1045$$ Character field: $$\Q(\zeta_{20})$$ Sturm bound: $$240$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1045, [\chi])$$.

Total New Old
Modular forms 992 992 0
Cusp forms 928 928 0
Eisenstein series 64 64 0

## Trace form

 $$928 q - 16 q^{5} - 24 q^{6} - 18 q^{7} + O(q^{10})$$ $$928 q - 16 q^{5} - 24 q^{6} - 18 q^{7} - 24 q^{11} + 184 q^{16} - 18 q^{17} + 16 q^{20} - 48 q^{23} - 56 q^{25} - 72 q^{26} - 12 q^{28} + 60 q^{30} - 16 q^{35} - 232 q^{36} + 10 q^{38} + 20 q^{42} - 76 q^{43} - 136 q^{45} + 24 q^{47} + 20 q^{55} + 94 q^{57} + 108 q^{58} - 24 q^{61} - 116 q^{62} - 2 q^{63} - 32 q^{66} - 148 q^{68} + 32 q^{73} - 40 q^{76} - 118 q^{77} - 24 q^{80} + 80 q^{81} - 36 q^{82} - 92 q^{83} - 100 q^{85} - 8 q^{87} + 160 q^{92} - 44 q^{93} - 66 q^{95} - 120 q^{96} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1045, [\chi])$$ into newform subspaces

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