# Properties

 Label 1050.3.bp Level $1050$ Weight $3$ Character orbit 1050.bp Rep. character $\chi_{1050}(19,\cdot)$ Character field $\Q(\zeta_{30})$ Dimension $640$ Sturm bound $720$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 1050.bp (of order $$30$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$175$$ Character field: $$\Q(\zeta_{30})$$ Sturm bound: $$720$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(1050, [\chi])$$.

Total New Old
Modular forms 3904 640 3264
Cusp forms 3776 640 3136
Eisenstein series 128 0 128

## Trace form

 $$640 q - 160 q^{4} - 12 q^{5} + 240 q^{9} + O(q^{10})$$ $$640 q - 160 q^{4} - 12 q^{5} + 240 q^{9} + 24 q^{10} + 60 q^{11} - 24 q^{15} + 320 q^{16} - 80 q^{22} - 40 q^{23} - 72 q^{25} + 40 q^{28} + 240 q^{29} - 96 q^{30} - 180 q^{31} + 152 q^{35} + 960 q^{36} + 48 q^{40} + 120 q^{42} + 80 q^{44} + 36 q^{45} + 120 q^{46} + 80 q^{49} - 192 q^{50} - 120 q^{53} + 720 q^{59} + 96 q^{60} + 360 q^{61} - 180 q^{63} + 1280 q^{64} - 172 q^{65} + 320 q^{71} + 480 q^{73} + 320 q^{74} + 144 q^{75} - 200 q^{79} + 48 q^{80} + 720 q^{81} - 1704 q^{85} - 240 q^{86} - 160 q^{88} - 700 q^{91} - 480 q^{94} + 604 q^{95} - 320 q^{98} + 240 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(1050, [\chi])$$ into newform subspaces

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

## Decomposition of $$S_{3}^{\mathrm{old}}(1050, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(1050, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(175, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(350, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(525, [\chi])$$$$^{\oplus 2}$$