# Properties

 Label 402.2.j Level 402 Weight 2 Character orbit j Rep. character $$\chi_{402}(5,\cdot)$$ Character field $$\Q(\zeta_{22})$$ Dimension 240 Newform subspaces 2 Sturm bound 136 Trace bound 2

# Related objects

## Defining parameters

 Level: $$N$$ = $$402 = 2 \cdot 3 \cdot 67$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 402.j (of order $$22$$ and degree $$10$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$201$$ Character field: $$\Q(\zeta_{22})$$ Newform subspaces: $$2$$ Sturm bound: $$136$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(402, [\chi])$$.

Total New Old
Modular forms 720 240 480
Cusp forms 640 240 400
Eisenstein series 80 0 80

## Trace form

 $$240q - 24q^{4} + 2q^{6} - 10q^{9} + O(q^{10})$$ $$240q - 24q^{4} + 2q^{6} - 10q^{9} + 11q^{12} + 8q^{15} - 24q^{16} - 4q^{19} - 22q^{21} + 12q^{22} - 20q^{24} - 48q^{25} - 44q^{31} + 22q^{33} - 10q^{36} + 44q^{37} + 54q^{39} + 44q^{43} - 22q^{45} - 22q^{48} + 4q^{49} - 66q^{52} - 10q^{54} - 72q^{55} - 44q^{58} + 8q^{60} + 44q^{61} - 24q^{64} - 28q^{67} + 44q^{70} - 158q^{73} + 99q^{75} - 4q^{76} - 154q^{79} - 66q^{81} - 38q^{82} - 66q^{87} + 12q^{88} - 4q^{90} + 16q^{91} - 42q^{93} - 44q^{94} + 2q^{96} + 110q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(402, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
402.2.j.a $$120$$ $$3.210$$ None $$-12$$ $$1$$ $$0$$ $$0$$
402.2.j.b $$120$$ $$3.210$$ None $$12$$ $$-1$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(402, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(402, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(201, [\chi])$$$$^{\oplus 2}$$