# Properties

 Label 310.2.b Level $310$ Weight $2$ Character orbit 310.b Rep. character $\chi_{310}(249,\cdot)$ Character field $\Q$ Dimension $16$ Newform subspaces $2$ Sturm bound $96$ Trace bound $6$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$310 = 2 \cdot 5 \cdot 31$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 310.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$96$$ Trace bound: $$6$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(310, [\chi])$$.

Total New Old
Modular forms 52 16 36
Cusp forms 44 16 28
Eisenstein series 8 0 8

## Trace form

 $$16 q - 16 q^{4} - 4 q^{5} - 4 q^{6} - 8 q^{9} + O(q^{10})$$ $$16 q - 16 q^{4} - 4 q^{5} - 4 q^{6} - 8 q^{9} + 4 q^{10} - 4 q^{11} + 4 q^{15} + 16 q^{16} - 16 q^{19} + 4 q^{20} + 8 q^{21} + 4 q^{24} + 8 q^{25} - 12 q^{26} + 20 q^{29} + 8 q^{30} + 8 q^{35} + 8 q^{36} - 32 q^{39} - 4 q^{40} - 8 q^{41} + 4 q^{44} + 12 q^{45} - 16 q^{46} - 32 q^{49} - 56 q^{51} + 40 q^{54} + 20 q^{55} + 8 q^{59} - 4 q^{60} + 4 q^{61} - 16 q^{64} + 12 q^{65} + 24 q^{66} + 4 q^{74} - 32 q^{75} + 16 q^{76} + 56 q^{79} - 4 q^{80} + 56 q^{81} - 8 q^{84} + 12 q^{85} - 36 q^{86} - 28 q^{90} - 48 q^{91} - 16 q^{94} - 4 q^{96} + 44 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(310, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
310.2.b.a $8$ $2.475$ 8.0.619810816.2 None $$0$$ $$0$$ $$-2$$ $$0$$ $$q-\beta _{2}q^{2}+(-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}-\beta _{6}+\cdots)q^{3}+\cdots$$
310.2.b.b $8$ $2.475$ 8.0.2058981376.2 None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+\beta _{4}q^{2}+\beta _{6}q^{3}-q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(310, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(310, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(155, [\chi])$$$$^{\oplus 2}$$