# Properties

 Label 1148.2.k Level $1148$ Weight $2$ Character orbit 1148.k Rep. character $\chi_{1148}(337,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $44$ Newform subspaces $2$ Sturm bound $336$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1148 = 2^{2} \cdot 7 \cdot 41$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1148.k (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$41$$ Character field: $$\Q(i)$$ Newform subspaces: $$2$$ Sturm bound: $$336$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

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

Total New Old
Modular forms 348 44 304
Cusp forms 324 44 280
Eisenstein series 24 0 24

## Trace form

 $$44q - 4q^{3} + O(q^{10})$$ $$44q - 4q^{3} + 4q^{13} - 8q^{15} - 8q^{17} + 4q^{19} - 8q^{23} - 68q^{25} + 20q^{27} + 4q^{35} + 16q^{37} + 4q^{41} + 32q^{45} + 32q^{47} - 32q^{51} + 20q^{53} + 8q^{55} + 40q^{57} - 8q^{63} - 4q^{65} - 48q^{67} + 28q^{69} - 12q^{71} + 84q^{75} - 20q^{79} - 116q^{81} - 104q^{83} - 64q^{85} - 12q^{89} + 16q^{93} + 24q^{95} + 40q^{97} + 68q^{99} + O(q^{100})$$

## 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.k.a $$8$$ $$9.167$$ 8.0.110166016.2 None $$0$$ $$-4$$ $$0$$ $$0$$ $$q+(-1-\beta _{5})q^{3}+(-1+\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots$$
1148.2.k.b $$36$$ $$9.167$$ None $$0$$ $$0$$ $$0$$ $$0$$

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

$$S_{2}^{\mathrm{old}}(1148, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(41, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(82, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(164, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(287, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(574, [\chi])$$$$^{\oplus 2}$$