# Properties

 Label 55.2.j Level $55$ Weight $2$ Character orbit 55.j Rep. character $\chi_{55}(4,\cdot)$ Character field $\Q(\zeta_{10})$ Dimension $16$ Newform subspaces $1$ Sturm bound $12$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$55 = 5 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 55.j (of order $$10$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$55$$ Character field: $$\Q(\zeta_{10})$$ Newform subspaces: $$1$$ Sturm bound: $$12$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(55, [\chi])$$.

Total New Old
Modular forms 32 32 0
Cusp forms 16 16 0
Eisenstein series 16 16 0

## Trace form

 $$16 q - 4 q^{4} - 2 q^{5} - 18 q^{6} + 2 q^{9} + O(q^{10})$$ $$16 q - 4 q^{4} - 2 q^{5} - 18 q^{6} + 2 q^{9} - 6 q^{11} - 12 q^{14} - 16 q^{15} + 16 q^{16} + 6 q^{19} - 8 q^{20} + 8 q^{21} + 6 q^{24} - 16 q^{25} + 40 q^{26} + 2 q^{29} + 26 q^{30} + 8 q^{31} - 16 q^{34} + 22 q^{35} + 10 q^{36} + 30 q^{39} + 12 q^{40} - 52 q^{41} + 4 q^{44} + 12 q^{45} - 62 q^{46} - 10 q^{49} + 28 q^{50} - 42 q^{51} - 40 q^{54} - 8 q^{55} - 20 q^{56} + 2 q^{59} - 32 q^{60} - 40 q^{61} - 8 q^{64} - 40 q^{65} + 58 q^{66} + 26 q^{69} - 34 q^{70} + 36 q^{71} + 48 q^{74} - 20 q^{75} + 56 q^{76} + 38 q^{79} + 34 q^{80} + 68 q^{81} + 12 q^{84} + 58 q^{85} + 22 q^{86} + 24 q^{89} + 78 q^{90} - 20 q^{91} + 14 q^{94} + 48 q^{95} - 86 q^{96} - 72 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(55, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
55.2.j.a $16$ $0.439$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+(\beta _{1}-\beta _{12}-\beta _{13})q^{2}+(\beta _{5}+\beta _{13}+\cdots)q^{3}+\cdots$$