# Properties

 Label 72.7.e Level $72$ Weight $7$ Character orbit 72.e Rep. character $\chi_{72}(17,\cdot)$ Character field $\Q$ Dimension $6$ Newform subspaces $2$ Sturm bound $84$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$72 = 2^{3} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$7$$ Character orbit: $$[\chi]$$ $$=$$ 72.e (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$3$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$84$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{7}(72, [\chi])$$.

Total New Old
Modular forms 80 6 74
Cusp forms 64 6 58
Eisenstein series 16 0 16

## Trace form

 $$6 q - 312 q^{7} + O(q^{10})$$ $$6 q - 312 q^{7} - 1968 q^{13} - 10080 q^{19} - 78390 q^{25} + 37608 q^{31} - 215148 q^{37} + 121680 q^{43} - 317958 q^{49} + 1102320 q^{55} - 532980 q^{61} + 1250160 q^{67} - 521184 q^{73} + 1416792 q^{79} - 66180 q^{85} - 1725504 q^{91} + 5472 q^{97} + O(q^{100})$$

## Decomposition of $$S_{7}^{\mathrm{new}}(72, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
72.7.e.a $2$ $16.564$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$120$$ $$q+5\beta q^{5}+60q^{7}+236\beta q^{11}+1192q^{13}+\cdots$$
72.7.e.b $4$ $16.564$ $$\Q(\sqrt{-2}, \sqrt{145})$$ None $$0$$ $$0$$ $$0$$ $$-432$$ $$q+(-5^{2}\beta _{1}-\beta _{3})q^{5}+(-108-\beta _{2}+\cdots)q^{7}+\cdots$$

## Decomposition of $$S_{7}^{\mathrm{old}}(72, [\chi])$$ into lower level spaces

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