# Properties

 Label 1260.2.c Level $1260$ Weight $2$ Character orbit 1260.c Rep. character $\chi_{1260}(811,\cdot)$ Character field $\Q$ Dimension $80$ Newform subspaces $6$ Sturm bound $576$ Trace bound $10$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1260.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$28$$ Character field: $$\Q$$ Newform subspaces: $$6$$ Sturm bound: $$576$$ Trace bound: $$10$$ Distinguishing $$T_p$$: $$11$$, $$19$$

## Dimensions

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

Total New Old
Modular forms 304 80 224
Cusp forms 272 80 192
Eisenstein series 32 0 32

## Trace form

 $$80 q - 2 q^{2} + 2 q^{4} - 2 q^{8} + O(q^{10})$$ $$80 q - 2 q^{2} + 2 q^{4} - 2 q^{8} + 6 q^{14} - 6 q^{16} - 24 q^{22} - 80 q^{25} + 22 q^{28} - 24 q^{29} + 38 q^{32} + 52 q^{44} + 20 q^{46} - 20 q^{49} + 2 q^{50} + 32 q^{53} - 34 q^{56} + 32 q^{58} + 2 q^{64} + 8 q^{65} - 8 q^{70} + 4 q^{74} + 24 q^{77} - 100 q^{86} - 20 q^{88} - 132 q^{92} + 54 q^{98} + O(q^{100})$$

## 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.c.a $4$ $10.061$ $$\Q(\zeta_{12})$$ None $$2$$ $$0$$ $$0$$ $$0$$ $$q+(1+\zeta_{12}^{3})q^{2}+(\zeta_{12}-2\zeta_{12}^{2}+\zeta_{12}^{3})q^{4}+\cdots$$
1260.2.c.b $4$ $10.061$ $$\Q(\zeta_{12})$$ None $$2$$ $$0$$ $$0$$ $$0$$ $$q+(1+\zeta_{12}^{3})q^{2}+(\zeta_{12}-2\zeta_{12}^{2}+\zeta_{12}^{3})q^{4}+\cdots$$
1260.2.c.c $8$ $10.061$ 8.0.342102016.5 None $$-2$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{4}q^{2}+(-\beta _{3}-\beta _{4}-\beta _{5})q^{4}+\beta _{2}q^{5}+\cdots$$
1260.2.c.d $16$ $10.061$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$-2$$ $$0$$ $$0$$ $$-4$$ $$q+\beta _{4}q^{2}+\beta _{8}q^{4}+\beta _{3}q^{5}+(-\beta _{9}-\beta _{10}+\cdots)q^{7}+\cdots$$
1260.2.c.e $16$ $10.061$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$-2$$ $$0$$ $$0$$ $$4$$ $$q+\beta _{4}q^{2}+\beta _{8}q^{4}-\beta _{3}q^{5}-\beta _{15}q^{7}+\cdots$$
1260.2.c.f $32$ $10.061$ None $$0$$ $$0$$ $$0$$ $$0$$

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

$$S_{2}^{\mathrm{old}}(1260, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(28, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(84, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(140, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(252, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(420, [\chi])$$$$^{\oplus 2}$$