# Properties

 Label 72.7.b Level $72$ Weight $7$ Character orbit 72.b Rep. character $\chi_{72}(19,\cdot)$ Character field $\Q$ Dimension $29$ Newform subspaces $4$ Sturm bound $84$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$72 = 2^{3} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$7$$ Character orbit: $$[\chi]$$ $$=$$ 72.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$8$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$84$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

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

Total New Old
Modular forms 76 31 45
Cusp forms 68 29 39
Eisenstein series 8 2 6

## Trace form

 $$29 q - 4 q^{2} - 112 q^{4} - 532 q^{8} + O(q^{10})$$ $$29 q - 4 q^{2} - 112 q^{4} - 532 q^{8} + 1668 q^{10} - 1358 q^{11} + 684 q^{14} - 304 q^{16} + 2446 q^{17} + 3934 q^{19} - 72 q^{20} - 1412 q^{22} - 83275 q^{25} + 5568 q^{26} + 13704 q^{28} - 27784 q^{32} + 29296 q^{34} - 112416 q^{35} + 42652 q^{38} + 129576 q^{40} + 37582 q^{41} - 267986 q^{43} - 116696 q^{44} + 172440 q^{46} - 489523 q^{49} + 267428 q^{50} + 550464 q^{52} + 350376 q^{56} + 68340 q^{58} + 39154 q^{59} - 284316 q^{62} + 431984 q^{64} - 267936 q^{65} - 782978 q^{67} - 344792 q^{68} + 1187304 q^{70} - 663302 q^{73} + 786360 q^{74} + 682984 q^{76} + 1284576 q^{80} + 950344 q^{82} + 288322 q^{83} - 2064884 q^{86} - 2854640 q^{88} - 771362 q^{89} - 302400 q^{91} - 2366304 q^{92} + 2081208 q^{94} - 356630 q^{97} + 3149780 q^{98} + O(q^{100})$$

## 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.b.a $1$ $16.564$ $$\Q$$ $$\Q(\sqrt{-2})$$ $$8$$ $$0$$ $$0$$ $$0$$ $$q+8q^{2}+2^{6}q^{4}+2^{9}q^{8}+2338q^{11}+\cdots$$
72.7.b.b $4$ $16.564$ 4.0.3803625.2 None $$-2$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}+(-11+\beta _{1}+\beta _{2}-\beta _{3})q^{4}+\cdots$$
72.7.b.c $12$ $16.564$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$-10$$ $$0$$ $$0$$ $$0$$ $$q+(-1-\beta _{1})q^{2}+(2+\beta _{1}+\beta _{5})q^{4}+\cdots$$
72.7.b.d $12$ $16.564$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(-13+\beta _{3})q^{4}+(-2\beta _{1}+\cdots)q^{5}+\cdots$$

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

$$S_{7}^{\mathrm{old}}(72, [\chi]) \cong$$ $$S_{7}^{\mathrm{new}}(8, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{7}^{\mathrm{new}}(24, [\chi])$$$$^{\oplus 2}$$