# Properties

 Label 1045.2.cn Level $1045$ Weight $2$ Character orbit 1045.cn Rep. character $\chi_{1045}(29,\cdot)$ Character field $\Q(\zeta_{90})$ Dimension $2784$ Sturm bound $240$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1045 = 5 \cdot 11 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1045.cn (of order $$90$$ and degree $$24$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$1045$$ Character field: $$\Q(\zeta_{90})$$ Sturm bound: $$240$$

## Dimensions

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

Total New Old
Modular forms 2976 2976 0
Cusp forms 2784 2784 0
Eisenstein series 192 192 0

## Trace form

 $$2784 q - 36 q^{4} - 18 q^{5} - 60 q^{6} - 36 q^{9} + O(q^{10})$$ $$2784 q - 36 q^{4} - 18 q^{5} - 60 q^{6} - 36 q^{9} - 30 q^{11} - 96 q^{14} - 42 q^{15} - 12 q^{16} - 60 q^{19} + 102 q^{20} - 90 q^{25} + 42 q^{26} - 60 q^{29} - 15 q^{30} - 54 q^{31} - 96 q^{34} - 30 q^{35} - 30 q^{36} - 120 q^{39} - 240 q^{40} - 150 q^{41} - 90 q^{44} + 42 q^{45} - 90 q^{46} + 348 q^{49} - 45 q^{50} - 60 q^{51} + 24 q^{55} + 72 q^{59} - 93 q^{60} - 60 q^{61} - 282 q^{64} - 456 q^{66} - 54 q^{69} + 33 q^{70} - 60 q^{71} - 60 q^{74} - 60 q^{79} + 30 q^{80} - 264 q^{81} - 90 q^{84} - 90 q^{85} - 96 q^{86} - 168 q^{89} + 60 q^{90} - 162 q^{91} + 120 q^{95} + 840 q^{96} + O(q^{100})$$

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

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