# Properties

 Label 425.2.b Level $425$ Weight $2$ Character orbit 425.b Rep. character $\chi_{425}(324,\cdot)$ Character field $\Q$ Dimension $24$ Newform subspaces $6$ Sturm bound $90$ Trace bound $6$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$425 = 5^{2} \cdot 17$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 425.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$6$$ Sturm bound: $$90$$ Trace bound: $$6$$ Distinguishing $$T_p$$: $$2$$, $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(425, [\chi])$$.

Total New Old
Modular forms 52 24 28
Cusp forms 40 24 16
Eisenstein series 12 0 12

## Trace form

 $$24 q - 24 q^{4} - 4 q^{6} - 20 q^{9} + O(q^{10})$$ $$24 q - 24 q^{4} - 4 q^{6} - 20 q^{9} - 4 q^{14} + 40 q^{16} - 28 q^{21} + 16 q^{24} - 20 q^{26} + 4 q^{29} + 36 q^{31} - 4 q^{34} + 4 q^{36} - 56 q^{39} - 4 q^{41} + 24 q^{44} + 28 q^{46} - 4 q^{49} + 8 q^{51} + 80 q^{54} - 8 q^{56} - 8 q^{59} - 16 q^{61} - 104 q^{64} - 96 q^{66} + 56 q^{71} + 68 q^{74} + 32 q^{76} - 68 q^{79} + 24 q^{81} + 140 q^{84} - 64 q^{86} + 56 q^{89} + 64 q^{94} - 156 q^{96} - 12 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(425, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
425.2.b.a $2$ $3.394$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+iq^{3}+q^{4}-q^{6}+iq^{7}+3iq^{8}+\cdots$$
425.2.b.b $2$ $3.394$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+q^{4}-4iq^{7}+3iq^{8}+3q^{9}+\cdots$$
425.2.b.c $2$ $3.394$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-2iq^{3}+q^{4}+2q^{6}-2iq^{7}+\cdots$$
425.2.b.d $4$ $3.394$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}^{2}q^{2}+(-\zeta_{12}-\zeta_{12}^{2})q^{3}-q^{4}+\cdots$$
425.2.b.e $4$ $3.394$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{8}+\zeta_{8}^{2})q^{2}+(-2\zeta_{8}+\zeta_{8}^{2})q^{3}+\cdots$$
425.2.b.f $10$ $3.394$ 10.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{8}q^{2}+\beta _{6}q^{3}+(-2+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(425, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(425, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(85, [\chi])$$$$^{\oplus 2}$$