# Properties

 Label 1638.2.bj Level $1638$ Weight $2$ Character orbit 1638.bj Rep. character $\chi_{1638}(127,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $72$ Newform subspaces $9$ Sturm bound $672$ Trace bound $13$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1638.bj (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$9$$ Sturm bound: $$672$$ Trace bound: $$13$$ Distinguishing $$T_p$$: $$5$$, $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1638, [\chi])$$.

Total New Old
Modular forms 704 72 632
Cusp forms 640 72 568
Eisenstein series 64 0 64

## Trace form

 $$72 q + 36 q^{4} + O(q^{10})$$ $$72 q + 36 q^{4} - 12 q^{11} + 20 q^{13} - 8 q^{14} - 36 q^{16} - 4 q^{17} - 4 q^{22} - 8 q^{23} - 88 q^{25} + 4 q^{29} + 8 q^{35} - 32 q^{38} + 60 q^{41} - 12 q^{43} + 12 q^{46} + 36 q^{49} + 12 q^{50} + 4 q^{52} + 8 q^{53} + 28 q^{55} - 4 q^{56} + 12 q^{58} - 96 q^{59} - 4 q^{61} - 12 q^{62} - 72 q^{64} - 36 q^{67} + 4 q^{68} - 24 q^{71} + 8 q^{74} + 32 q^{77} + 8 q^{79} + 20 q^{82} + 4 q^{88} + 72 q^{89} - 4 q^{91} - 16 q^{92} - 16 q^{94} + 12 q^{95} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1638, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1638.2.bj.a $4$ $13.079$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+(1-\zeta_{12}^{2})q^{4}+\cdots$$
1638.2.bj.b $4$ $13.079$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(1-2\zeta_{12}^{2}+\cdots)q^{5}+\cdots$$
1638.2.bj.c $4$ $13.079$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+(1-\zeta_{12}^{2})q^{4}+\cdots$$
1638.2.bj.d $4$ $13.079$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(1-2\zeta_{12}^{2}+\cdots)q^{5}+\cdots$$
1638.2.bj.e $4$ $13.079$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+(1-\zeta_{12}^{2})q^{4}+\cdots$$
1638.2.bj.f $8$ $13.079$ 8.0.195105024.2 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}-\beta _{4}q^{4}+(1-\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots$$
1638.2.bj.g $12$ $13.079$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{6}q^{2}+\beta _{7}q^{4}+(\beta _{1}-\beta _{5}+\beta _{6}-\beta _{7}+\cdots)q^{5}+\cdots$$
1638.2.bj.h $16$ $13.079$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{4}q^{2}+(1-\beta _{5})q^{4}-\beta _{9}q^{5}-\beta _{3}q^{7}+\cdots$$
1638.2.bj.i $16$ $13.079$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{2}+\beta _{5}q^{4}-\beta _{9}q^{5}-\beta _{4}q^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1638, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1638, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(13, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(39, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(78, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(91, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(117, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(182, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(234, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(273, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(546, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(819, [\chi])$$$$^{\oplus 2}$$