# Properties

 Label 100.9.k Level $100$ Weight $9$ Character orbit 100.k Rep. character $\chi_{100}(13,\cdot)$ Character field $\Q(\zeta_{20})$ Dimension $160$ Newform subspaces $1$ Sturm bound $135$ Trace bound $0$

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## Defining parameters

 Level: $$N$$ $$=$$ $$100 = 2^{2} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$9$$ Character orbit: $$[\chi]$$ $$=$$ 100.k (of order $$20$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$25$$ Character field: $$\Q(\zeta_{20})$$ Newform subspaces: $$1$$ Sturm bound: $$135$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{9}(100, [\chi])$$.

Total New Old
Modular forms 984 160 824
Cusp forms 936 160 776
Eisenstein series 48 0 48

## Trace form

 $$160 q + 70 q^{3} - 894 q^{5} + 2030 q^{7} + O(q^{10})$$ $$160 q + 70 q^{3} - 894 q^{5} + 2030 q^{7} - 33180 q^{13} + 48478 q^{15} - 414270 q^{17} + 718900 q^{19} - 207030 q^{23} + 1528574 q^{25} + 720310 q^{27} - 1956900 q^{29} + 6217120 q^{33} - 3418728 q^{35} - 14424480 q^{37} + 22510400 q^{39} + 4374720 q^{41} - 4033290 q^{43} + 13482846 q^{45} + 7278150 q^{47} - 15887760 q^{53} - 11288940 q^{55} + 39717680 q^{57} + 119809950 q^{59} + 18369120 q^{61} - 19887500 q^{63} + 136188762 q^{65} - 58954530 q^{67} - 128418850 q^{69} + 60703860 q^{71} + 33399920 q^{73} + 54011742 q^{75} + 184811940 q^{77} + 138506200 q^{79} + 196903220 q^{81} - 176936400 q^{83} - 186109196 q^{85} - 418946050 q^{87} + 442507050 q^{89} - 205667130 q^{93} + 256003896 q^{95} + 310913960 q^{97} + O(q^{100})$$

## Decomposition of $$S_{9}^{\mathrm{new}}(100, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
100.9.k.a $160$ $40.738$ None $$0$$ $$70$$ $$-894$$ $$2030$$

## Decomposition of $$S_{9}^{\mathrm{old}}(100, [\chi])$$ into lower level spaces

$$S_{9}^{\mathrm{old}}(100, [\chi]) \simeq$$ $$S_{9}^{\mathrm{new}}(25, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{9}^{\mathrm{new}}(50, [\chi])$$$$^{\oplus 2}$$