# Properties

 Label 3630.2.v Level $3630$ Weight $2$ Character orbit 3630.v Rep. character $\chi_{3630}(403,\cdot)$ Character field $\Q(\zeta_{20})$ Dimension $864$ Sturm bound $1584$

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## Defining parameters

 Level: $$N$$ $$=$$ $$3630 = 2 \cdot 3 \cdot 5 \cdot 11^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3630.v (of order $$20$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$55$$ Character field: $$\Q(\zeta_{20})$$ Sturm bound: $$1584$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(3630, [\chi])$$.

Total New Old
Modular forms 6720 864 5856
Cusp forms 5952 864 5088
Eisenstein series 768 0 768

## Trace form

 $$864q - 16q^{5} - 40q^{7} + O(q^{10})$$ $$864q - 16q^{5} - 40q^{7} - 12q^{15} + 216q^{16} - 40q^{17} + 16q^{23} - 40q^{25} + 16q^{26} - 20q^{28} + 16q^{31} + 216q^{36} + 32q^{37} - 40q^{41} + 12q^{42} + 40q^{46} + 88q^{47} + 80q^{50} + 80q^{51} + 40q^{52} + 72q^{53} - 16q^{56} + 80q^{57} + 12q^{58} + 24q^{60} + 80q^{61} + 80q^{62} + 40q^{63} - 144q^{67} + 40q^{68} - 108q^{70} - 20q^{73} - 24q^{80} + 216q^{81} - 160q^{85} + 32q^{86} + 40q^{91} - 16q^{92} - 24q^{93} + 40q^{95} + 96q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(3630, [\chi])$$ into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

## Decomposition of $$S_{2}^{\mathrm{old}}(3630, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(3630, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(55, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(110, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(165, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(330, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(605, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1210, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1815, [\chi])$$$$^{\oplus 2}$$