# Properties

 Label 1323.2.bn Level $1323$ Weight $2$ Character orbit 1323.bn Rep. character $\chi_{1323}(109,\cdot)$ Character field $\Q(\zeta_{21})$ Dimension $900$ Sturm bound $336$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1323 = 3^{3} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1323.bn (of order $$21$$ and degree $$12$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$49$$ Character field: $$\Q(\zeta_{21})$$ Sturm bound: $$336$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1323, [\chi])$$.

Total New Old
Modular forms 2088 900 1188
Cusp forms 1944 900 1044
Eisenstein series 144 0 144

## Trace form

 $$900q + 76q^{4} - 9q^{7} + O(q^{10})$$ $$900q + 76q^{4} - 9q^{7} + 2q^{10} + 78q^{16} + 9q^{19} - 2q^{22} + 83q^{25} + 62q^{28} - 13q^{31} + 56q^{34} + 77q^{37} - 28q^{40} + 62q^{43} + 10q^{46} - 45q^{49} - 188q^{52} + 80q^{55} - 172q^{58} - 43q^{61} - 200q^{64} + 2q^{67} - 68q^{70} - 7q^{73} - 260q^{76} - 10q^{79} + 188q^{82} + 60q^{85} + 30q^{88} - 88q^{91} - 170q^{94} + 14q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1323, [\chi])$$ into newform subspaces

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

## Decomposition of $$S_{2}^{\mathrm{old}}(1323, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1323, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(49, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(147, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(441, [\chi])$$$$^{\oplus 2}$$