# Properties

 Label 245.2.b Level $245$ Weight $2$ Character orbit 245.b Rep. character $\chi_{245}(99,\cdot)$ Character field $\Q$ Dimension $16$ Newform subspaces $6$ Sturm bound $56$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$245 = 5 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 245.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$6$$ Sturm bound: $$56$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$2$$, $$3$$, $$19$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(245, [\chi])$$.

Total New Old
Modular forms 36 26 10
Cusp forms 20 16 4
Eisenstein series 16 10 6

## Trace form

 $$16 q - 8 q^{4} + 4 q^{5} - 4 q^{6} - 12 q^{9} + O(q^{10})$$ $$16 q - 8 q^{4} + 4 q^{5} - 4 q^{6} - 12 q^{9} - 4 q^{10} + 8 q^{11} - 8 q^{15} + 8 q^{16} - 8 q^{20} - 4 q^{25} - 4 q^{26} - 20 q^{29} + 36 q^{30} - 4 q^{31} + 28 q^{34} - 28 q^{36} - 4 q^{41} - 80 q^{44} + 8 q^{45} + 4 q^{46} + 36 q^{50} + 32 q^{51} - 20 q^{54} - 12 q^{55} + 20 q^{59} + 48 q^{60} + 16 q^{61} + 8 q^{64} + 36 q^{65} + 12 q^{66} + 12 q^{69} + 8 q^{71} - 24 q^{74} - 8 q^{75} - 16 q^{79} - 16 q^{80} - 48 q^{81} - 4 q^{85} + 12 q^{86} - 8 q^{90} - 12 q^{94} - 32 q^{95} + 16 q^{96} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(245, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
245.2.b.a $2$ $1.956$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+2iq^{2}+iq^{3}-2q^{4}+(2+i)q^{5}+\cdots$$
245.2.b.b $2$ $1.956$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+iq^{2}-iq^{3}+q^{4}+(-1+2i)q^{5}+\cdots$$
245.2.b.c $2$ $1.956$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+iq^{2}+iq^{3}+q^{4}+(1-2i)q^{5}-q^{6}+\cdots$$
245.2.b.d $2$ $1.956$ $$\Q(\sqrt{-5})$$ $$\Q(\sqrt{-35})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta q^{3}+2q^{4}+\beta q^{5}-2q^{9}-3q^{11}+\cdots$$
245.2.b.e $4$ $1.956$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{2}+\beta _{2}q^{3}-4q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$$
245.2.b.f $4$ $1.956$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{8}^{2}q^{2}+(2\zeta_{8}+2\zeta_{8}^{3})q^{3}+q^{4}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(245, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(245, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 2}$$