# Properties

 Label 1148.2.i Level $1148$ Weight $2$ Character orbit 1148.i Rep. character $\chi_{1148}(165,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $52$ Newform subspaces $5$ Sturm bound $336$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1148 = 2^{2} \cdot 7 \cdot 41$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1148.i (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$5$$ Sturm bound: $$336$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$3$$, $$11$$

## Dimensions

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

Total New Old
Modular forms 348 52 296
Cusp forms 324 52 272
Eisenstein series 24 0 24

## Trace form

 $$52q + 2q^{3} + 2q^{5} + 8q^{7} - 28q^{9} + O(q^{10})$$ $$52q + 2q^{3} + 2q^{5} + 8q^{7} - 28q^{9} - 2q^{11} - 8q^{13} + 2q^{19} + 4q^{23} - 24q^{25} + 8q^{27} + 16q^{29} - 18q^{31} - 12q^{33} - 26q^{35} - 8q^{37} - 6q^{39} - 16q^{41} + 24q^{43} + 2q^{45} - 10q^{47} - 8q^{51} - 12q^{53} + 64q^{55} + 2q^{59} + 14q^{61} - 38q^{63} - 4q^{65} - 10q^{67} + 24q^{69} - 16q^{71} - 16q^{73} + 54q^{75} - 24q^{77} - 36q^{79} - 18q^{81} - 16q^{83} + 36q^{85} + 10q^{87} + 32q^{89} - 38q^{91} - 34q^{93} + 18q^{95} + 12q^{97} - 56q^{99} + O(q^{100})$$

## 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.i.a $$2$$ $$9.167$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$3$$ $$5$$ $$q+(-1+\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+\cdots$$
1148.2.i.b $$2$$ $$9.167$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$1$$ $$-4$$ $$q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-1-2\zeta_{6})q^{7}+\cdots$$
1148.2.i.c $$2$$ $$9.167$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$1$$ $$4$$ $$q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots$$
1148.2.i.d $$16$$ $$9.167$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{3}+\beta _{14}q^{5}+(-\beta _{5}+\beta _{8})q^{7}+\cdots$$
1148.2.i.e $$30$$ $$9.167$$ None $$0$$ $$1$$ $$-3$$ $$3$$

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

$$S_{2}^{\mathrm{old}}(1148, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(28, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(287, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(574, [\chi])$$$$^{\oplus 2}$$