# Properties

 Label 1148.2.bb Level $1148$ Weight $2$ Character orbit 1148.bb Rep. character $\chi_{1148}(195,\cdot)$ Character field $\Q(\zeta_{10})$ Dimension $656$ Sturm bound $336$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1148 = 2^{2} \cdot 7 \cdot 41$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1148.bb (of order $$10$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$1148$$ Character field: $$\Q(\zeta_{10})$$ Sturm bound: $$336$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1148, [\chi])$$.

Total New Old
Modular forms 688 688 0
Cusp forms 656 656 0
Eisenstein series 32 32 0

## Trace form

 $$656q - 6q^{2} - 6q^{4} + 6q^{8} - 656q^{9} + O(q^{10})$$ $$656q - 6q^{2} - 6q^{4} + 6q^{8} - 656q^{9} - 6q^{16} + 20q^{21} - 10q^{22} + 136q^{25} - 30q^{28} - 60q^{29} + 20q^{30} + 24q^{32} - 52q^{36} - 12q^{37} - 20q^{42} + 76q^{46} + 2q^{49} + 4q^{50} - 20q^{53} - 75q^{56} + 24q^{57} - 10q^{58} - 30q^{60} - 90q^{64} - 20q^{65} - 155q^{70} - 62q^{72} - 84q^{74} + 22q^{77} - 22q^{78} + 512q^{81} - 100q^{84} + 44q^{86} + 6q^{92} - 49q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1148, [\chi])$$ into newform subspaces

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