# Properties

 Label 400.2.bl Level $400$ Weight $2$ Character orbit 400.bl Rep. character $\chi_{400}(29,\cdot)$ Character field $\Q(\zeta_{20})$ Dimension $464$ Newform subspaces $1$ Sturm bound $120$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$400 = 2^{4} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 400.bl (of order $$20$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$400$$ Character field: $$\Q(\zeta_{20})$$ Newform subspaces: $$1$$ Sturm bound: $$120$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(400, [\chi])$$.

Total New Old
Modular forms 496 496 0
Cusp forms 464 464 0
Eisenstein series 32 32 0

## Trace form

 $$464q - 10q^{2} - 10q^{3} - 6q^{4} - 8q^{5} - 6q^{6} - 40q^{8} + O(q^{10})$$ $$464q - 10q^{2} - 10q^{3} - 6q^{4} - 8q^{5} - 6q^{6} - 40q^{8} - 2q^{10} - 6q^{11} - 10q^{12} - 10q^{13} - 18q^{14} - 16q^{15} - 6q^{16} - 20q^{17} - 6q^{19} + 6q^{20} - 24q^{21} - 10q^{22} - 16q^{24} - 36q^{26} - 10q^{27} - 50q^{28} - 6q^{29} + 14q^{30} - 36q^{31} - 20q^{33} - 46q^{34} - 36q^{35} + 38q^{36} - 10q^{37} + 60q^{38} - 84q^{40} - 70q^{42} + 36q^{44} - 24q^{45} + 2q^{46} - 20q^{47} - 140q^{48} + 336q^{49} - 46q^{50} - 28q^{51} + 80q^{52} - 10q^{53} - 30q^{54} - 48q^{56} - 10q^{58} - 6q^{59} + 112q^{60} - 6q^{61} - 10q^{62} - 160q^{63} - 24q^{64} - 48q^{65} - 104q^{66} - 70q^{67} + 6q^{69} - 100q^{70} - 10q^{72} + 28q^{74} - 46q^{75} + 44q^{76} - 80q^{77} - 10q^{78} - 52q^{79} - 2q^{80} + 72q^{81} - 10q^{83} + 28q^{84} - 18q^{85} + 34q^{86} + 100q^{88} + 74q^{90} - 48q^{91} + 80q^{92} - 6q^{94} - 40q^{95} + 54q^{96} - 20q^{97} - 100q^{98} - 64q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(400, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
400.2.bl.a $$464$$ $$3.194$$ None $$-10$$ $$-10$$ $$-8$$ $$0$$