# Properties

 Label 55.4.b Level $55$ Weight $4$ Character orbit 55.b Rep. character $\chi_{55}(34,\cdot)$ Character field $\Q$ Dimension $16$ Newform subspaces $2$ Sturm bound $24$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$55 = 5 \cdot 11$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 55.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$24$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(55, [\chi])$$.

Total New Old
Modular forms 20 16 4
Cusp forms 16 16 0
Eisenstein series 4 0 4

## Trace form

 $$16 q - 60 q^{4} + 10 q^{5} + 4 q^{6} - 176 q^{9} + O(q^{10})$$ $$16 q - 60 q^{4} + 10 q^{5} + 4 q^{6} - 176 q^{9} + 62 q^{10} + 44 q^{11} - 16 q^{14} - 26 q^{15} + 360 q^{16} + 168 q^{19} - 116 q^{20} - 176 q^{21} - 200 q^{24} - 126 q^{25} + 36 q^{26} + 552 q^{29} - 950 q^{30} + 728 q^{31} + 72 q^{34} + 252 q^{35} + 912 q^{36} + 944 q^{39} - 1644 q^{40} - 408 q^{41} - 748 q^{44} - 220 q^{45} + 876 q^{46} - 1484 q^{49} - 214 q^{50} + 72 q^{51} - 2292 q^{54} + 198 q^{55} + 2496 q^{56} - 276 q^{59} + 1804 q^{60} - 560 q^{61} - 1900 q^{64} + 1864 q^{65} + 528 q^{66} - 3196 q^{69} - 2152 q^{70} - 768 q^{71} + 5108 q^{74} + 1614 q^{75} + 1832 q^{76} + 1240 q^{79} + 2384 q^{80} - 200 q^{81} + 5160 q^{84} - 684 q^{85} - 4396 q^{86} - 2104 q^{89} - 3064 q^{90} + 3384 q^{91} + 2200 q^{94} - 4584 q^{95} - 9208 q^{96} - 1408 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(55, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
55.4.b.a $6$ $3.245$ $$\mathbb{Q}[x]/(x^{6} + \cdots)$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{5})q^{3}+(1+\beta _{3})q^{4}+\cdots$$
55.4.b.b $10$ $3.245$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$0$$ $$0$$ $$14$$ $$0$$ $$q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-6+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$$