# Properties

 Label 96.8.n Level $96$ Weight $8$ Character orbit 96.n Rep. character $\chi_{96}(13,\cdot)$ Character field $\Q(\zeta_{8})$ Dimension $224$ Newform subspaces $1$ Sturm bound $128$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$96 = 2^{5} \cdot 3$$ Weight: $$k$$ $$=$$ $$8$$ Character orbit: $$[\chi]$$ $$=$$ 96.n (of order $$8$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$32$$ Character field: $$\Q(\zeta_{8})$$ Newform subspaces: $$1$$ Sturm bound: $$128$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{8}(96, [\chi])$$.

Total New Old
Modular forms 456 224 232
Cusp forms 440 224 216
Eisenstein series 16 0 16

## Trace form

 $$224 q + O(q^{10})$$ $$224 q + 13000 q^{10} - 30672 q^{12} + 52384 q^{14} + 21112 q^{16} - 40824 q^{18} - 164000 q^{20} + 511464 q^{22} + 286832 q^{23} - 81864 q^{24} + 727960 q^{26} + 390920 q^{28} + 1429968 q^{31} - 1071320 q^{32} + 403160 q^{34} - 1633008 q^{35} + 1244920 q^{38} - 4089528 q^{40} - 732368 q^{43} + 3370472 q^{44} + 2715808 q^{46} + 2317416 q^{50} - 2993328 q^{51} - 8882216 q^{52} + 3631264 q^{53} + 157464 q^{54} + 4191008 q^{55} + 10737272 q^{56} + 7269664 q^{58} + 3671872 q^{59} - 2168208 q^{60} + 4559776 q^{61} - 10347504 q^{62} - 4000752 q^{63} - 22412520 q^{64} - 3757104 q^{66} + 776272 q^{67} + 17922136 q^{68} - 9580896 q^{69} - 1696200 q^{70} + 24697408 q^{71} - 21862880 q^{74} - 11260512 q^{75} + 5188008 q^{76} + 23828896 q^{77} - 14742648 q^{78} + 69474376 q^{80} - 6997080 q^{82} - 39909568 q^{86} - 37691824 q^{88} + 3406992 q^{91} - 684560 q^{92} + 50770592 q^{94} + 54100440 q^{96} - 52426160 q^{98} + O(q^{100})$$

## Decomposition of $$S_{8}^{\mathrm{new}}(96, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
96.8.n.a $224$ $29.989$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{8}^{\mathrm{old}}(96, [\chi])$$ into lower level spaces

$$S_{8}^{\mathrm{old}}(96, [\chi]) \cong$$ $$S_{8}^{\mathrm{new}}(32, [\chi])$$$$^{\oplus 2}$$