# Properties

 Label 312.2.m Level $312$ Weight $2$ Character orbit 312.m Rep. character $\chi_{312}(181,\cdot)$ Character field $\Q$ Dimension $28$ Newform subspaces $3$ Sturm bound $112$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$312 = 2^{3} \cdot 3 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 312.m (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$104$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$112$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(312, [\chi])$$.

Total New Old
Modular forms 60 28 32
Cusp forms 52 28 24
Eisenstein series 8 0 8

## Trace form

 $$28 q - 28 q^{9} + O(q^{10})$$ $$28 q - 28 q^{9} + 4 q^{10} - 4 q^{12} + 16 q^{14} + 12 q^{16} + 8 q^{17} - 28 q^{22} + 36 q^{25} - 12 q^{26} - 4 q^{30} + 40 q^{38} - 4 q^{40} - 32 q^{42} - 16 q^{48} - 44 q^{49} + 4 q^{52} + 48 q^{55} - 32 q^{56} - 88 q^{62} + 24 q^{64} - 24 q^{65} + 12 q^{66} - 8 q^{68} - 4 q^{78} - 40 q^{79} + 28 q^{81} + 76 q^{82} + 24 q^{87} - 44 q^{88} - 4 q^{90} - 40 q^{92} + 76 q^{94} - 80 q^{95} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(312, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
312.2.m.a $2$ $2.491$ $$\Q(\sqrt{-1})$$ None $$-2$$ $$0$$ $$-4$$ $$0$$ $$q+(-1+i)q^{2}-iq^{3}-2iq^{4}-2q^{5}+\cdots$$
312.2.m.b $2$ $2.491$ $$\Q(\sqrt{-1})$$ None $$2$$ $$0$$ $$4$$ $$0$$ $$q+(1+i)q^{2}+iq^{3}+2iq^{4}+2q^{5}+\cdots$$
312.2.m.c $24$ $2.491$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(312, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(312, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(104, [\chi])$$$$^{\oplus 2}$$