# Properties

 Label 185.2.e Level $185$ Weight $2$ Character orbit 185.e Rep. character $\chi_{185}(26,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $28$ Newform subspaces $2$ Sturm bound $38$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$185 = 5 \cdot 37$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 185.e (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$37$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$2$$ Sturm bound: $$38$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(185, [\chi])$$.

Total New Old
Modular forms 40 28 12
Cusp forms 32 28 4
Eisenstein series 8 0 8

## Trace form

 $$28q + 2q^{2} - 4q^{3} - 16q^{4} + 2q^{7} - 18q^{9} + O(q^{10})$$ $$28q + 2q^{2} - 4q^{3} - 16q^{4} + 2q^{7} - 18q^{9} + 4q^{10} - 12q^{11} - 2q^{12} + 10q^{13} - 16q^{14} - 12q^{16} - 4q^{17} - 10q^{18} - 8q^{19} + 14q^{21} + 6q^{22} + 12q^{23} - 6q^{24} - 14q^{25} - 20q^{26} + 8q^{27} + 22q^{28} - 24q^{29} + 4q^{30} - 8q^{31} + 22q^{32} - 10q^{33} + 22q^{34} - 2q^{35} + 32q^{36} + 30q^{37} + 12q^{38} - 2q^{39} - 6q^{40} - 10q^{41} + 6q^{44} + 16q^{45} - 4q^{46} + 12q^{47} + 16q^{48} - 2q^{49} + 2q^{50} + 44q^{51} + 38q^{52} - 8q^{53} + 14q^{54} - 4q^{55} - 6q^{56} - 22q^{57} - 24q^{58} - 16q^{59} - 28q^{60} - 24q^{61} - 46q^{62} + 56q^{63} - 12q^{64} - 2q^{65} - 44q^{66} - 28q^{67} + 136q^{68} + 6q^{69} - 28q^{70} + 22q^{71} + 14q^{72} - 36q^{73} - 48q^{74} + 8q^{75} + 28q^{76} - 6q^{77} - 16q^{78} + 14q^{79} - 32q^{80} - 6q^{81} + 128q^{82} - 20q^{83} - 72q^{84} + 4q^{85} + 14q^{86} - 72q^{87} - 76q^{88} - 28q^{89} - 2q^{90} - 12q^{91} - 40q^{92} - 22q^{93} + 32q^{94} - 20q^{95} - 82q^{96} - 32q^{97} + 30q^{98} + 60q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(185, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
185.2.e.a $$14$$ $$1.477$$ $$\mathbb{Q}[x]/(x^{14} + \cdots)$$ None $$0$$ $$-2$$ $$-7$$ $$0$$ $$q+(-\beta _{1}+\beta _{4})q^{2}-\beta _{6}q^{3}+(\beta _{2}+\beta _{9}+\cdots)q^{4}+\cdots$$
185.2.e.b $$14$$ $$1.477$$ $$\mathbb{Q}[x]/(x^{14} - \cdots)$$ None $$2$$ $$-2$$ $$7$$ $$2$$ $$q+\beta _{8}q^{2}+\beta _{6}q^{3}+(-1+\beta _{5}-\beta _{7}+\cdots)q^{4}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(185, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(185, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(37, [\chi])$$$$^{\oplus 2}$$