# Properties

 Label 1260.2.bm Level $1260$ Weight $2$ Character orbit 1260.bm Rep. character $\chi_{1260}(109,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $40$ Newform subspaces $4$ Sturm bound $576$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1260.bm (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$35$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$4$$ Sturm bound: $$576$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$11$$, $$17$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1260, [\chi])$$.

Total New Old
Modular forms 624 40 584
Cusp forms 528 40 488
Eisenstein series 96 0 96

## Trace form

 $$40 q - q^{5} + O(q^{10})$$ $$40 q - q^{5} + 2 q^{11} - 10 q^{19} + 3 q^{25} - 20 q^{29} - 6 q^{31} - 15 q^{35} + 12 q^{41} + 2 q^{49} + 14 q^{55} + 26 q^{59} + 16 q^{61} + 10 q^{65} + 32 q^{71} + 14 q^{79} - 58 q^{85} + 44 q^{89} - 4 q^{91} + 7 q^{95} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1260, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1260.2.bm.a $4$ $10.061$ $$\Q(\sqrt{-3}, \sqrt{-19})$$ None $$0$$ $$0$$ $$-1$$ $$-3$$ $$q+(-\beta _{2}-\beta _{3})q^{5}+(-2+\beta _{1}+2\beta _{2}+\cdots)q^{7}+\cdots$$
1260.2.bm.b $4$ $10.061$ $$\Q(\sqrt{-3}, \sqrt{-19})$$ None $$0$$ $$0$$ $$2$$ $$3$$ $$q+(\beta _{1}-\beta _{3})q^{5}+(2-\beta _{1}-2\beta _{2})q^{7}+\cdots$$
1260.2.bm.c $16$ $10.061$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+(-\beta _{8}-\beta _{12}-\beta _{14})q^{5}+(-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$$
1260.2.bm.d $16$ $10.061$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{4}q^{5}+(\beta _{5}-\beta _{6}+\beta _{14})q^{7}-\beta _{15}q^{11}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1260, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1260, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(70, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(105, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(140, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(210, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(315, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(420, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(630, [\chi])$$$$^{\oplus 2}$$