# Properties

 Label 70.3.b Level $70$ Weight $3$ Character orbit 70.b Rep. character $\chi_{70}(41,\cdot)$ Character field $\Q$ Dimension $8$ Newform subspaces $1$ Sturm bound $36$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$70 = 2 \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 70.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$36$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(70, [\chi])$$.

Total New Old
Modular forms 28 8 20
Cusp forms 20 8 12
Eisenstein series 8 0 8

## Trace form

 $$8 q + 16 q^{4} - 4 q^{7} - 36 q^{9} + O(q^{10})$$ $$8 q + 16 q^{4} - 4 q^{7} - 36 q^{9} + 20 q^{11} - 4 q^{14} + 20 q^{15} + 32 q^{16} + 32 q^{18} - 64 q^{21} - 48 q^{22} - 72 q^{23} - 40 q^{25} - 8 q^{28} + 12 q^{29} - 40 q^{30} + 40 q^{35} - 72 q^{36} + 136 q^{37} + 36 q^{39} + 80 q^{42} + 128 q^{43} + 40 q^{44} - 56 q^{46} + 4 q^{49} + 268 q^{51} - 208 q^{53} - 8 q^{56} - 24 q^{57} - 224 q^{58} + 40 q^{60} + 380 q^{63} + 64 q^{64} - 100 q^{65} - 112 q^{67} + 60 q^{70} - 376 q^{71} + 64 q^{72} - 208 q^{74} - 408 q^{77} + 320 q^{78} + 188 q^{79} + 344 q^{81} - 128 q^{84} + 180 q^{85} + 200 q^{86} - 96 q^{88} - 244 q^{91} - 144 q^{92} - 824 q^{93} - 40 q^{95} + 48 q^{98} - 576 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(70, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
70.3.b.a $8$ $1.907$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $$q+\beta _{6}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+2q^{4}-\beta _{2}q^{5}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(70, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(70, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(7, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 2}$$