# Properties

 Label 230.2.j Level $230$ Weight $2$ Character orbit 230.j Rep. character $\chi_{230}(9,\cdot)$ Character field $\Q(\zeta_{22})$ Dimension $120$ Newform subspaces $1$ Sturm bound $72$ Trace bound $0$

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## Defining parameters

 Level: $$N$$ $$=$$ $$230 = 2 \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 230.j (of order $$22$$ and degree $$10$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$115$$ Character field: $$\Q(\zeta_{22})$$ Newform subspaces: $$1$$ Sturm bound: $$72$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(230, [\chi])$$.

Total New Old
Modular forms 400 120 280
Cusp forms 320 120 200
Eisenstein series 80 0 80

## Trace form

 $$120q + 12q^{4} - 4q^{6} + 8q^{9} + O(q^{10})$$ $$120q + 12q^{4} - 4q^{6} + 8q^{9} + 8q^{11} - 6q^{15} - 12q^{16} - 16q^{19} - 22q^{20} + 4q^{24} - 52q^{25} - 4q^{26} - 8q^{29} - 44q^{30} + 12q^{31} + 16q^{35} - 8q^{36} - 36q^{39} - 28q^{41} - 8q^{44} + 16q^{45} - 4q^{46} - 58q^{49} + 12q^{50} - 24q^{51} - 6q^{54} - 36q^{55} + 22q^{56} - 102q^{59} - 38q^{60} + 72q^{61} + 12q^{64} - 138q^{65} + 80q^{66} - 212q^{69} - 108q^{70} + 176q^{71} - 88q^{74} - 100q^{75} + 16q^{76} - 104q^{79} - 22q^{80} - 28q^{81} - 22q^{84} + 2q^{85} + 62q^{86} + 48q^{89} + 24q^{90} - 56q^{91} + 24q^{94} + 18q^{95} - 4q^{96} + 188q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(230, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
230.2.j.a $$120$$ $$1.837$$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(230, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(230, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(115, [\chi])$$$$^{\oplus 2}$$