# Properties

 Label 1148.2.r Level $1148$ Weight $2$ Character orbit 1148.r Rep. character $\chi_{1148}(81,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $56$ Newform subspaces $1$ Sturm bound $336$ Trace bound $0$

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## Defining parameters

 Level: $$N$$ $$=$$ $$1148 = 2^{2} \cdot 7 \cdot 41$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1148.r (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$287$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$1$$ Sturm bound: $$336$$ Trace bound: $$0$$

## Dimensions

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

Total New Old
Modular forms 348 56 292
Cusp forms 324 56 268
Eisenstein series 24 0 24

## Trace form

 $$56q + 4q^{5} + 32q^{9} + O(q^{10})$$ $$56q + 4q^{5} + 32q^{9} - 6q^{21} + 2q^{23} - 24q^{25} - 4q^{31} + 10q^{33} + 10q^{37} + 10q^{39} + 20q^{41} + 8q^{43} - 22q^{45} - 4q^{49} + 18q^{51} + 28q^{57} - 16q^{59} + 16q^{61} + 2q^{73} + 34q^{77} - 28q^{81} - 48q^{83} - 2q^{87} - 42q^{91} + O(q^{100})$$

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

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1148.2.r.a $$56$$ $$9.167$$ None $$0$$ $$0$$ $$4$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1148, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1148, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(287, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(574, [\chi])$$$$^{\oplus 2}$$