# Properties

 Label 245.2.e Level $245$ Weight $2$ Character orbit 245.e Rep. character $\chi_{245}(116,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $28$ Newform subspaces $9$ Sturm bound $56$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$245 = 5 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 245.e (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$9$$ Sturm bound: $$56$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$2$$, $$3$$

## Dimensions

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

Total New Old
Modular forms 72 28 44
Cusp forms 40 28 12
Eisenstein series 32 0 32

## Trace form

 $$28 q + 4 q^{2} + 2 q^{3} - 12 q^{4} + 2 q^{5} + 4 q^{6} - 24 q^{8} - 14 q^{9} + O(q^{10})$$ $$28 q + 4 q^{2} + 2 q^{3} - 12 q^{4} + 2 q^{5} + 4 q^{6} - 24 q^{8} - 14 q^{9} + 2 q^{10} + 10 q^{11} - 6 q^{12} + 8 q^{13} - 8 q^{15} + 4 q^{16} + 4 q^{17} + 2 q^{18} - 4 q^{20} - 16 q^{22} + 2 q^{23} + 2 q^{24} - 14 q^{25} - 12 q^{26} - 4 q^{27} - 16 q^{29} - 2 q^{30} - 12 q^{31} + 8 q^{32} + 12 q^{33} - 24 q^{34} + 28 q^{36} - 20 q^{37} + 8 q^{38} - 14 q^{39} + 6 q^{40} + 20 q^{41} + 12 q^{43} + 8 q^{44} + 22 q^{46} + 4 q^{47} - 12 q^{48} - 8 q^{50} + 22 q^{51} - 20 q^{52} + 8 q^{53} + 6 q^{54} - 8 q^{55} + 56 q^{57} + 18 q^{58} - 8 q^{59} + 2 q^{60} - 6 q^{61} + 24 q^{62} - 2 q^{65} - 4 q^{66} + 22 q^{67} + 20 q^{68} + 12 q^{69} - 32 q^{71} + 50 q^{72} + 4 q^{73} + 36 q^{74} + 2 q^{75} - 32 q^{76} - 112 q^{78} + 26 q^{79} + 6 q^{80} + 14 q^{81} - 18 q^{82} - 4 q^{83} - 20 q^{85} - 54 q^{86} - 2 q^{87} - 44 q^{88} - 6 q^{89} + 16 q^{90} + 76 q^{92} - 16 q^{93} + 4 q^{94} + 4 q^{95} - 10 q^{96} - 24 q^{97} + 56 q^{99} + O(q^{100})$$

## 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.e.a $2$ $1.956$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$1$$ $$0$$ $$q+(-1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+\zeta_{6}q^{5}+\cdots$$
245.2.e.b $2$ $1.956$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$-1$$ $$0$$ $$q+(1-\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}-\zeta_{6}q^{5}+\cdots$$
245.2.e.c $2$ $1.956$ $$\Q(\sqrt{-3})$$ None $$2$$ $$-3$$ $$1$$ $$0$$ $$q+2\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots$$
245.2.e.d $2$ $1.956$ $$\Q(\sqrt{-3})$$ None $$2$$ $$3$$ $$-1$$ $$0$$ $$q+2\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots$$
245.2.e.e $4$ $1.956$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$-2$$ $$2$$ $$2$$ $$0$$ $$q+(-1+\beta _{1}-\beta _{2})q^{2}+(-\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots$$
245.2.e.f $4$ $1.956$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$-2$$ $$-2$$ $$0$$ $$q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2}-\beta _{3})q^{3}+(-1+\cdots)q^{5}+\cdots$$
245.2.e.g $4$ $1.956$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$2$$ $$2$$ $$0$$ $$q+\beta _{1}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{5}+\cdots$$
245.2.e.h $4$ $1.956$ $$\Q(\sqrt{-3}, \sqrt{17})$$ None $$1$$ $$-1$$ $$2$$ $$0$$ $$q+\beta _{1}q^{2}+(-1-\beta _{1}+\beta _{2}-\beta _{3})q^{3}+\cdots$$
245.2.e.i $4$ $1.956$ $$\Q(\sqrt{-3}, \sqrt{17})$$ None $$1$$ $$1$$ $$-2$$ $$0$$ $$q+\beta _{1}q^{2}+(1+\beta _{1}-\beta _{2}+\beta _{3})q^{3}+(-2+\cdots)q^{4}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(245, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(49, [\chi])$$$$^{\oplus 2}$$