# Properties

 Label 1148.2.n Level $1148$ Weight $2$ Character orbit 1148.n Rep. character $\chi_{1148}(57,\cdot)$ Character field $\Q(\zeta_{5})$ Dimension $80$ Newform subspaces $5$ Sturm bound $336$ Trace bound $3$

# Learn more about

## Defining parameters

 Level: $$N$$ $$=$$ $$1148 = 2^{2} \cdot 7 \cdot 41$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1148.n (of order $$5$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$41$$ Character field: $$\Q(\zeta_{5})$$ Newform subspaces: $$5$$ Sturm bound: $$336$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

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

Total New Old
Modular forms 696 80 616
Cusp forms 648 80 568
Eisenstein series 48 0 48

## Trace form

 $$80q + 4q^{3} + 4q^{5} + 68q^{9} + O(q^{10})$$ $$80q + 4q^{3} + 4q^{5} + 68q^{9} - 10q^{11} + 12q^{15} + 14q^{17} - 26q^{19} + 4q^{21} + 12q^{23} + 12q^{25} + 4q^{27} - 4q^{29} + 2q^{31} - 26q^{33} - 4q^{35} - 10q^{37} + 12q^{39} + 50q^{41} - 6q^{43} + 44q^{45} + 28q^{47} - 20q^{49} + 40q^{51} + 12q^{53} - 56q^{55} - 16q^{57} + 60q^{59} - 12q^{61} - 8q^{63} - 6q^{65} - 26q^{67} - 4q^{69} - 36q^{71} - 40q^{73} - 18q^{75} + 8q^{77} - 4q^{79} + 48q^{81} + 28q^{83} - 140q^{85} + 24q^{87} + 16q^{89} - 8q^{91} - 76q^{93} + 16q^{95} - 56q^{97} + 76q^{99} + O(q^{100})$$

## 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.n.a $$8$$ $$9.167$$ 8.0.64000000.2 None $$0$$ $$-4$$ $$-2$$ $$-2$$ $$q+(-\beta _{3}+\beta _{4}+\beta _{6}-\beta _{7})q^{3}+(-\beta _{1}+\cdots)q^{5}+\cdots$$
1148.2.n.b $$8$$ $$9.167$$ 8.0.64000000.2 None $$0$$ $$8$$ $$-2$$ $$-2$$ $$q+(1+\beta _{5})q^{3}+(\beta _{2}+\beta _{7})q^{5}+\beta _{4}q^{7}+\cdots$$
1148.2.n.c $$16$$ $$9.167$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$-2$$ $$-13$$ $$4$$ $$q+(-\beta _{1}-\beta _{2}+\beta _{5}-\beta _{6})q^{3}+(-1+\cdots)q^{5}+\cdots$$
1148.2.n.d $$24$$ $$9.167$$ None $$0$$ $$-10$$ $$4$$ $$-6$$
1148.2.n.e $$24$$ $$9.167$$ None $$0$$ $$12$$ $$17$$ $$6$$

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

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