# Properties

 Label 429.2.be Level $429$ Weight $2$ Character orbit 429.be Rep. character $\chi_{429}(89,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $184$ Newform subspaces $1$ Sturm bound $112$ Trace bound $0$

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## Defining parameters

 Level: $$N$$ $$=$$ $$429 = 3 \cdot 11 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 429.be (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$39$$ Character field: $$\Q(\zeta_{12})$$ Newform subspaces: $$1$$ Sturm bound: $$112$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(429, [\chi])$$.

Total New Old
Modular forms 240 184 56
Cusp forms 208 184 24
Eisenstein series 32 0 32

## Trace form

 $$184q - 12q^{6} + 12q^{7} + O(q^{10})$$ $$184q - 12q^{6} + 12q^{7} - 48q^{10} - 16q^{13} + 16q^{15} + 80q^{16} - 8q^{18} - 4q^{19} - 24q^{24} - 48q^{27} - 40q^{28} + 48q^{30} - 20q^{31} + 16q^{34} - 36q^{36} + 44q^{37} + 48q^{39} - 80q^{40} + 20q^{42} - 84q^{43} - 4q^{45} - 64q^{46} + 44q^{48} - 60q^{49} - 200q^{52} - 4q^{54} - 64q^{57} - 48q^{58} - 148q^{60} - 48q^{61} + 40q^{66} + 48q^{67} - 12q^{69} + 24q^{70} - 128q^{72} + 108q^{73} - 60q^{75} - 24q^{76} + 148q^{78} + 32q^{79} + 16q^{81} - 48q^{82} + 116q^{84} + 104q^{85} - 24q^{87} + 72q^{88} + 60q^{91} + 36q^{93} + 16q^{94} - 72q^{96} + 4q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(429, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
429.2.be.a $$184$$ $$3.426$$ None $$0$$ $$0$$ $$0$$ $$12$$

## Decomposition of $$S_{2}^{\mathrm{old}}(429, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(429, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(39, [\chi])$$$$^{\oplus 2}$$