# Properties

 Label 16.9.f Level $16$ Weight $9$ Character orbit 16.f Rep. character $\chi_{16}(3,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $30$ Newform subspaces $1$ Sturm bound $18$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$16 = 2^{4}$$ Weight: $$k$$ $$=$$ $$9$$ Character orbit: $$[\chi]$$ $$=$$ 16.f (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$16$$ Character field: $$\Q(i)$$ Newform subspaces: $$1$$ Sturm bound: $$18$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{9}(16, [\chi])$$.

Total New Old
Modular forms 34 34 0
Cusp forms 30 30 0
Eisenstein series 4 4 0

## Trace form

 $$30 q - 2 q^{2} - 2 q^{3} + 184 q^{4} - 2 q^{5} + 3232 q^{6} - 4 q^{7} - 8732 q^{8} + O(q^{10})$$ $$30 q - 2 q^{2} - 2 q^{3} + 184 q^{4} - 2 q^{5} + 3232 q^{6} - 4 q^{7} - 8732 q^{8} - 1860 q^{10} - 19778 q^{11} + 14068 q^{12} - 2 q^{13} - 58900 q^{14} + 245336 q^{16} - 4 q^{17} - 223730 q^{18} + 167550 q^{19} - 135380 q^{20} - 13124 q^{21} + 985700 q^{22} - 845572 q^{23} - 800592 q^{24} - 184760 q^{26} + 38656 q^{27} + 94136 q^{28} + 1066174 q^{29} + 1881700 q^{30} - 3395192 q^{32} - 4 q^{33} + 1634900 q^{34} + 426620 q^{35} + 1877324 q^{36} + 2360254 q^{37} - 3010352 q^{38} - 7650052 q^{39} + 3256936 q^{40} - 3731304 q^{42} + 6314814 q^{43} - 10360940 q^{44} + 794370 q^{45} + 1510780 q^{46} + 4591848 q^{48} + 14823770 q^{49} + 14752710 q^{50} - 28969860 q^{51} + 4335652 q^{52} + 2679358 q^{53} + 18667040 q^{54} + 46326780 q^{55} - 36346408 q^{56} - 1034696 q^{58} - 46004162 q^{59} - 20687200 q^{60} - 24476034 q^{61} - 64043472 q^{62} + 50827456 q^{64} - 14970820 q^{65} + 65035780 q^{66} + 59474558 q^{67} + 74339312 q^{68} + 8623420 q^{69} + 39082496 q^{70} - 79832068 q^{71} + 929812 q^{72} - 168043460 q^{74} + 88519490 q^{75} - 166219388 q^{76} + 35952572 q^{77} + 5059788 q^{78} - 12904856 q^{80} - 66961570 q^{81} + 261305296 q^{82} - 34471682 q^{83} + 456781480 q^{84} - 107741252 q^{85} + 9841444 q^{86} + 149712636 q^{87} - 173775752 q^{88} - 650366536 q^{90} - 76429060 q^{91} - 449169832 q^{92} + 138269056 q^{93} - 239278032 q^{94} + 378359728 q^{96} - 4 q^{97} + 630040554 q^{98} + 184838270 q^{99} + O(q^{100})$$

## Decomposition of $$S_{9}^{\mathrm{new}}(16, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
16.9.f.a $30$ $6.518$ None $$-2$$ $$-2$$ $$-2$$ $$-4$$