# Properties

 Label 3024.2.t Level $3024$ Weight $2$ Character orbit 3024.t Rep. character $\chi_{3024}(289,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $92$ Newform subspaces $12$ Sturm bound $1152$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$3024 = 2^{4} \cdot 3^{3} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3024.t (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$63$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$12$$ Sturm bound: $$1152$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$5$$, $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(3024, [\chi])$$.

Total New Old
Modular forms 1224 100 1124
Cusp forms 1080 92 988
Eisenstein series 144 8 136

## Trace form

 $$92q + 2q^{5} + q^{7} + O(q^{10})$$ $$92q + 2q^{5} + q^{7} - 2q^{11} - 2q^{13} + 2q^{17} + 2q^{19} - 2q^{23} + 74q^{25} + 6q^{29} - 7q^{31} - 9q^{35} - 2q^{37} + 2q^{41} - 4q^{43} + 21q^{47} - q^{49} + 2q^{53} + 18q^{55} - 35q^{59} + q^{61} + q^{65} - q^{67} - 32q^{71} - 2q^{73} + 21q^{77} - q^{79} - 28q^{83} + 3q^{85} - 2q^{89} - 4q^{91} - 27q^{95} - 2q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(3024, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
3024.2.t.a $$2$$ $$24.147$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-6$$ $$-5$$ $$q-3q^{5}+(-3+\zeta_{6})q^{7}-3q^{11}+(1+\cdots)q^{13}+\cdots$$
3024.2.t.b $$2$$ $$24.147$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-4$$ $$-4$$ $$q-2q^{5}+(-3+2\zeta_{6})q^{7}+4q^{11}+(-3+\cdots)q^{13}+\cdots$$
3024.2.t.c $$2$$ $$24.147$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-2$$ $$5$$ $$q-q^{5}+(3-\zeta_{6})q^{7}-3q^{11}+(-1+\zeta_{6})q^{13}+\cdots$$
3024.2.t.d $$2$$ $$24.147$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$2$$ $$-1$$ $$q+q^{5}+(1-3\zeta_{6})q^{7}+5q^{11}+(5-5\zeta_{6})q^{13}+\cdots$$
3024.2.t.e $$2$$ $$24.147$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$2$$ $$1$$ $$q+q^{5}+(-1+3\zeta_{6})q^{7}+3q^{11}+(-3+\cdots)q^{13}+\cdots$$
3024.2.t.f $$2$$ $$24.147$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$6$$ $$1$$ $$q+3q^{5}+(-1+3\zeta_{6})q^{7}-3q^{11}+(-5+\cdots)q^{13}+\cdots$$
3024.2.t.g $$6$$ $$24.147$$ 6.0.309123.1 None $$0$$ $$0$$ $$-10$$ $$2$$ $$q+(-2-\beta _{1})q^{5}+(\beta _{1}+\beta _{2}+\beta _{4})q^{7}+\cdots$$
3024.2.t.h $$6$$ $$24.147$$ 6.0.309123.1 None $$0$$ $$0$$ $$2$$ $$4$$ $$q-\beta _{3}q^{5}+(1+\beta _{1}-\beta _{2}-\beta _{5})q^{7}-\beta _{3}q^{11}+\cdots$$
3024.2.t.i $$10$$ $$24.147$$ 10.0.$$\cdots$$.1 None $$0$$ $$0$$ $$8$$ $$1$$ $$q+(1-\beta _{2}+\beta _{9})q^{5}+(\beta _{4}-\beta _{5}+\beta _{6}+\cdots)q^{7}+\cdots$$
3024.2.t.j $$14$$ $$24.147$$ $$\mathbb{Q}[x]/(x^{14} - \cdots)$$ None $$0$$ $$0$$ $$-4$$ $$3$$ $$q+(\beta _{3}-\beta _{7})q^{5}+\beta _{5}q^{7}+(-\beta _{9}+\beta _{13})q^{11}+\cdots$$
3024.2.t.k $$22$$ $$24.147$$ None $$0$$ $$0$$ $$2$$ $$1$$
3024.2.t.l $$22$$ $$24.147$$ None $$0$$ $$0$$ $$6$$ $$-7$$

## Decomposition of $$S_{2}^{\mathrm{old}}(3024, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(3024, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(126, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(189, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(252, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(378, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(504, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(756, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1008, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1512, [\chi])$$$$^{\oplus 2}$$