# Properties

 Label 152.2.c Level $152$ Weight $2$ Character orbit 152.c Rep. character $\chi_{152}(77,\cdot)$ Character field $\Q$ Dimension $18$ Newform subspaces $2$ Sturm bound $40$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$152 = 2^{3} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 152.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$8$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$40$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(152, [\chi])$$.

Total New Old
Modular forms 22 18 4
Cusp forms 18 18 0
Eisenstein series 4 0 4

## Trace form

 $$18q - 2q^{2} + 2q^{4} + 6q^{6} - 4q^{7} - 8q^{8} - 18q^{9} + O(q^{10})$$ $$18q - 2q^{2} + 2q^{4} + 6q^{6} - 4q^{7} - 8q^{8} - 18q^{9} - 8q^{10} + 4q^{12} - 6q^{16} - 4q^{17} + 14q^{18} + 8q^{20} + 12q^{22} - 4q^{23} + 6q^{24} - 14q^{25} - 6q^{26} - 14q^{28} + 4q^{30} - 12q^{32} - 4q^{34} + 8q^{36} + 8q^{39} + 28q^{40} + 4q^{41} - 2q^{42} - 12q^{44} - 44q^{46} + 20q^{47} + 36q^{48} + 18q^{49} + 2q^{50} - 34q^{54} + 16q^{55} - 40q^{56} + 42q^{58} - 28q^{60} - 20q^{63} + 14q^{64} + 16q^{65} - 24q^{66} - 26q^{68} - 32q^{70} + 24q^{71} + 12q^{72} - 20q^{73} + 56q^{78} - 40q^{79} + 4q^{80} + 2q^{81} + 64q^{84} + 56q^{86} - 48q^{87} + 24q^{88} - 4q^{89} + 12q^{90} + 62q^{92} - 32q^{94} + 16q^{95} - 70q^{96} + 12q^{97} - 42q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(152, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
152.2.c.a $$2$$ $$1.214$$ $$\Q(\sqrt{-1})$$ None $$-2$$ $$0$$ $$0$$ $$4$$ $$q+(-1+i)q^{2}-2iq^{4}+2q^{7}+(2+2i)q^{8}+\cdots$$
152.2.c.b $$16$$ $$1.214$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$-8$$ $$q+\beta _{9}q^{2}+\beta _{4}q^{3}+\beta _{2}q^{4}+(\beta _{1}+\beta _{6}+\cdots)q^{5}+\cdots$$