# Properties

 Label 1260.2.s Level $1260$ Weight $2$ Character orbit 1260.s Rep. character $\chi_{1260}(361,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $28$ Newform subspaces $8$ Sturm bound $576$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1260.s (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$8$$ Sturm bound: $$576$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$11$$, $$13$$

## Dimensions

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

Total New Old
Modular forms 624 28 596
Cusp forms 528 28 500
Eisenstein series 96 0 96

## Trace form

 $$28 q - 2 q^{5} + 2 q^{7} + O(q^{10})$$ $$28 q - 2 q^{5} + 2 q^{7} - 16 q^{13} - 12 q^{17} - 4 q^{19} - 6 q^{23} - 14 q^{25} - 4 q^{29} + 20 q^{37} + 20 q^{41} + 4 q^{43} + 16 q^{47} + 10 q^{49} + 16 q^{53} + 8 q^{55} - 12 q^{59} + 2 q^{61} + 14 q^{67} - 64 q^{71} + 32 q^{77} + 12 q^{79} + 52 q^{83} + 8 q^{85} - 6 q^{89} - 48 q^{91} + 8 q^{95} - 24 q^{97} + O(q^{100})$$

## 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.s.a $$2$$ $$10.061$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-1$$ $$-5$$ $$q-\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+(-4+4\zeta_{6})q^{11}+\cdots$$
1260.2.s.b $$2$$ $$10.061$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-1$$ $$1$$ $$q-\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots$$
1260.2.s.c $$2$$ $$10.061$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-1$$ $$5$$ $$q-\zeta_{6}q^{5}+(3-\zeta_{6})q^{7}+(6-6\zeta_{6})q^{11}+\cdots$$
1260.2.s.d $$2$$ $$10.061$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$1$$ $$5$$ $$q+\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots$$
1260.2.s.e $$4$$ $$10.061$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$-2$$ $$-2$$ $$q+\beta _{1}q^{5}+(\beta _{1}-\beta _{3})q^{7}+(\beta _{2}+\beta _{3})q^{11}+\cdots$$
1260.2.s.f $$4$$ $$10.061$$ $$\Q(\sqrt{-3}, \sqrt{7})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q-\beta _{2}q^{5}+(-\beta _{1}-\beta _{3})q^{7}+(1+\beta _{1}+\cdots)q^{11}+\cdots$$
1260.2.s.g $$6$$ $$10.061$$ 6.0.4406832.1 None $$0$$ $$0$$ $$-3$$ $$-1$$ $$q+(-1+\beta _{3})q^{5}-\beta _{4}q^{7}+(-\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots$$
1260.2.s.h $$6$$ $$10.061$$ 6.0.4406832.1 None $$0$$ $$0$$ $$3$$ $$-1$$ $$q+(1-\beta _{3})q^{5}-\beta _{4}q^{7}+(\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{11}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(1260, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(28, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(42, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(70, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(84, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(105, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(126, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(140, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(210, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(252, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(315, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(420, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(630, [\chi])$$$$^{\oplus 2}$$