# Properties

 Label 25.6.b Level $25$ Weight $6$ Character orbit 25.b Rep. character $\chi_{25}(24,\cdot)$ Character field $\Q$ Dimension $6$ Newform subspaces $2$ Sturm bound $15$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$25 = 5^{2}$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 25.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$15$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(25, [\chi])$$.

Total New Old
Modular forms 16 8 8
Cusp forms 10 6 4
Eisenstein series 6 2 4

## Trace form

 $$6 q - 82 q^{4} - 398 q^{6} + 62 q^{9} + O(q^{10})$$ $$6 q - 82 q^{4} - 398 q^{6} + 62 q^{9} - 688 q^{11} - 804 q^{14} + 3586 q^{16} + 4240 q^{19} + 4392 q^{21} - 6030 q^{24} - 8368 q^{26} + 14660 q^{29} - 7088 q^{31} - 33514 q^{34} - 21964 q^{36} - 5936 q^{39} + 36712 q^{41} + 65486 q^{44} + 16812 q^{46} - 16742 q^{49} - 22328 q^{51} - 14710 q^{54} + 62460 q^{56} + 16120 q^{59} + 15812 q^{61} - 65922 q^{64} - 20446 q^{66} - 13176 q^{69} - 239888 q^{71} + 81716 q^{74} - 194430 q^{76} - 64240 q^{79} + 187846 q^{81} + 41676 q^{84} + 492872 q^{86} - 57120 q^{89} + 68672 q^{91} + 291656 q^{94} - 197698 q^{96} - 510776 q^{99} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(25, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
25.6.b.a $2$ $4.010$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+2iq^{3}+28q^{4}-8q^{6}+96iq^{7}+\cdots$$
25.6.b.b $4$ $4.010$ $$\Q(i, \sqrt{241})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{1}+\beta _{2})q^{2}+(-2\beta _{1}-\beta _{2})q^{3}+\cdots$$

## Decomposition of $$S_{6}^{\mathrm{old}}(25, [\chi])$$ into lower level spaces

$$S_{6}^{\mathrm{old}}(25, [\chi]) \cong$$ $$S_{6}^{\mathrm{new}}(5, [\chi])$$$$^{\oplus 2}$$