# Properties

 Label 1400.2.bh Level $1400$ Weight $2$ Character orbit 1400.bh Rep. character $\chi_{1400}(249,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $72$ Newform subspaces $10$ Sturm bound $480$ Trace bound $11$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1400 = 2^{3} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1400.bh (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$35$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$10$$ Sturm bound: $$480$$ Trace bound: $$11$$ Distinguishing $$T_p$$: $$3$$, $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1400, [\chi])$$.

Total New Old
Modular forms 528 72 456
Cusp forms 432 72 360
Eisenstein series 96 0 96

## Trace form

 $$72 q + 32 q^{9} + O(q^{10})$$ $$72 q + 32 q^{9} + 4 q^{11} + 8 q^{19} + 20 q^{21} - 24 q^{29} - 4 q^{31} - 32 q^{39} - 16 q^{41} + 48 q^{49} + 12 q^{51} + 52 q^{59} + 24 q^{61} + 88 q^{69} - 32 q^{71} + 12 q^{79} - 60 q^{81} - 36 q^{89} + 16 q^{91} + 88 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1400, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1400.2.bh.a $4$ $11.179$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{3}+(-2\zeta_{12}+3\zeta_{12}^{3})q^{7}+\cdots$$
1400.2.bh.b $4$ $11.179$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{3}+(-\zeta_{12}-2\zeta_{12}^{3})q^{7}-2\zeta_{12}^{2}q^{9}+\cdots$$
1400.2.bh.c $4$ $11.179$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{3}+(3\zeta_{12}-2\zeta_{12}^{3})q^{7}-2\zeta_{12}^{2}q^{9}+\cdots$$
1400.2.bh.d $4$ $11.179$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2\zeta_{12}q^{3}+(3\zeta_{12}-\zeta_{12}^{3})q^{7}+\zeta_{12}^{2}q^{9}+\cdots$$
1400.2.bh.e $4$ $11.179$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2\zeta_{12}q^{3}+(-2\zeta_{12}-\zeta_{12}^{3})q^{7}+\cdots$$
1400.2.bh.f $4$ $11.179$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+3\zeta_{12}q^{3}+(2\zeta_{12}+\zeta_{12}^{3})q^{7}+6\zeta_{12}^{2}q^{9}+\cdots$$
1400.2.bh.g $8$ $11.179$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{24}^{3}q^{3}+(-\zeta_{24}^{2}+\zeta_{24}^{3}-\zeta_{24}^{4}+\cdots)q^{7}+\cdots$$
1400.2.bh.h $12$ $11.179$ $$\Q(\zeta_{36})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{36}+\zeta_{36}^{3}-\zeta_{36}^{7}+\zeta_{36}^{11})q^{3}+\cdots$$
1400.2.bh.i $12$ $11.179$ 12.0.$$\cdots$$.37 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{3}-\beta _{5}+\beta _{7}+\beta _{8})q^{3}+(\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots$$
1400.2.bh.j $16$ $11.179$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{1}-\beta _{9})q^{3}+(\beta _{6}-\beta _{7})q^{7}+(1-\beta _{3}+\cdots)q^{9}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1400, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1400, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(70, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(140, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(175, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(280, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(350, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(700, [\chi])$$$$^{\oplus 2}$$