# Properties

 Label 25.4.b Level $25$ Weight $4$ Character orbit 25.b Rep. character $\chi_{25}(24,\cdot)$ Character field $\Q$ Dimension $4$ Newform subspaces $2$ Sturm bound $10$ Trace bound $4$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$25 = 5^{2}$$ Weight: $$k$$ $$=$$ $$4$$ 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: $$10$$ Trace bound: $$4$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(25, [\chi])$$.

Total New Old
Modular forms 10 6 4
Cusp forms 4 4 0
Eisenstein series 6 2 4

## Trace form

 $$4 q - 2 q^{4} - 2 q^{6} + 2 q^{9} + O(q^{10})$$ $$4 q - 2 q^{4} - 2 q^{6} + 2 q^{9} - 22 q^{11} + 36 q^{14} - 46 q^{16} - 130 q^{19} + 108 q^{21} + 210 q^{24} + 248 q^{26} - 220 q^{29} - 132 q^{31} + 26 q^{34} - 676 q^{36} + 544 q^{39} - 362 q^{41} - 1114 q^{44} + 948 q^{46} + 1228 q^{49} + 1378 q^{51} - 730 q^{54} - 180 q^{56} - 440 q^{59} - 2072 q^{61} + 1358 q^{64} - 1114 q^{66} - 1956 q^{69} + 1648 q^{71} + 2756 q^{74} + 2090 q^{76} - 2220 q^{79} - 836 q^{81} + 396 q^{84} - 3352 q^{86} + 2190 q^{89} - 792 q^{91} - 4504 q^{94} + 3278 q^{96} + 3364 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(25, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
25.4.b.a $2$ $1.475$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{2}+iq^{3}-8q^{4}-8q^{6}-3iq^{7}+\cdots$$
25.4.b.b $2$ $1.475$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-7iq^{3}+7q^{4}+7q^{6}+6iq^{7}+\cdots$$