# Properties

 Label 144.7.e Level $144$ Weight $7$ Character orbit 144.e Rep. character $\chi_{144}(17,\cdot)$ Character field $\Q$ Dimension $12$ Newform subspaces $5$ Sturm bound $168$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$144 = 2^{4} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$7$$ Character orbit: $$[\chi]$$ $$=$$ 144.e (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$3$$ Character field: $$\Q$$ Newform subspaces: $$5$$ Sturm bound: $$168$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$5$$, $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{7}(144, [\chi])$$.

Total New Old
Modular forms 156 12 144
Cusp forms 132 12 120
Eisenstein series 24 0 24

## Trace form

 $$12 q + 720 q^{7} + O(q^{10})$$ $$12 q + 720 q^{7} + 14016 q^{19} - 61356 q^{25} + 42768 q^{31} - 28248 q^{37} + 151584 q^{43} + 112884 q^{49} - 441504 q^{55} + 197016 q^{61} - 284448 q^{67} + 573888 q^{73} - 1294992 q^{79} + 88152 q^{85} + 3293952 q^{91} - 626304 q^{97} + O(q^{100})$$

## Decomposition of $$S_{7}^{\mathrm{new}}(144, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
144.7.e.a $2$ $33.128$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$-1048$$ $$q+5\beta q^{5}-524q^{7}+68\beta q^{11}+344q^{13}+\cdots$$
144.7.e.b $2$ $33.128$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$-120$$ $$q+5\beta q^{5}-60q^{7}-236\beta q^{11}+1192q^{13}+\cdots$$
144.7.e.c $2$ $33.128$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$488$$ $$q+5\beta q^{5}+244q^{7}-188\beta q^{11}-2728q^{13}+\cdots$$
144.7.e.d $2$ $33.128$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$968$$ $$q+41\beta q^{5}+22^{2}q^{7}-316\beta q^{11}+3368q^{13}+\cdots$$
144.7.e.e $4$ $33.128$ $$\Q(\sqrt{-2}, \sqrt{145})$$ None $$0$$ $$0$$ $$0$$ $$432$$ $$q+(-5^{2}\beta _{1}-\beta _{3})q^{5}+(108+\beta _{2})q^{7}+\cdots$$

## Decomposition of $$S_{7}^{\mathrm{old}}(144, [\chi])$$ into lower level spaces

$$S_{7}^{\mathrm{old}}(144, [\chi]) \cong$$ $$S_{7}^{\mathrm{new}}(3, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{7}^{\mathrm{new}}(6, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{7}^{\mathrm{new}}(9, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{7}^{\mathrm{new}}(12, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{7}^{\mathrm{new}}(18, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{7}^{\mathrm{new}}(24, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{7}^{\mathrm{new}}(36, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{7}^{\mathrm{new}}(48, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{7}^{\mathrm{new}}(72, [\chi])$$$$^{\oplus 2}$$