# Properties

 Label 18.9.d Level $18$ Weight $9$ Character orbit 18.d Rep. character $\chi_{18}(5,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $16$ Newform subspaces $1$ Sturm bound $27$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$18 = 2 \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$9$$ Character orbit: $$[\chi]$$ $$=$$ 18.d (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$9$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$1$$ Sturm bound: $$27$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{9}(18, [\chi])$$.

Total New Old
Modular forms 52 16 36
Cusp forms 44 16 28
Eisenstein series 8 0 8

## Trace form

 $$16 q + 126 q^{3} + 1024 q^{4} - 882 q^{5} + 384 q^{6} - 1846 q^{7} - 28662 q^{9} + O(q^{10})$$ $$16 q + 126 q^{3} + 1024 q^{4} - 882 q^{5} + 384 q^{6} - 1846 q^{7} - 28662 q^{9} + 45756 q^{11} + 5376 q^{12} - 3370 q^{13} - 94464 q^{14} + 128754 q^{15} - 131072 q^{16} - 236544 q^{18} + 362180 q^{19} - 112896 q^{20} - 299166 q^{21} - 61824 q^{22} + 1311138 q^{23} - 147456 q^{24} + 963394 q^{25} - 208656 q^{27} - 472576 q^{28} - 2851290 q^{29} - 1253376 q^{30} + 542438 q^{31} + 3875796 q^{33} + 220416 q^{34} - 3655680 q^{36} + 3343328 q^{37} - 1314432 q^{38} - 5896002 q^{39} + 9218592 q^{41} + 14237952 q^{42} + 339512 q^{43} - 32740578 q^{45} + 7417344 q^{46} - 34980606 q^{47} - 1376256 q^{48} - 2364654 q^{49} + 27744768 q^{50} + 50877810 q^{51} + 431360 q^{52} - 5648256 q^{54} - 4584276 q^{55} - 12091392 q^{56} - 34049898 q^{57} - 7852800 q^{58} + 93924216 q^{59} + 18604800 q^{60} - 841954 q^{61} - 14043234 q^{63} - 33554432 q^{64} - 126568134 q^{65} - 35179776 q^{66} + 29946644 q^{67} - 5476608 q^{68} + 70499610 q^{69} - 34359552 q^{70} - 11894784 q^{72} - 7547764 q^{73} + 35124480 q^{74} + 114494910 q^{75} + 23179520 q^{76} + 9309294 q^{77} + 23014656 q^{78} + 33813002 q^{79} - 46018134 q^{81} - 137346048 q^{82} + 114200226 q^{83} - 15040512 q^{84} - 125696772 q^{85} - 171379584 q^{86} - 159599970 q^{87} + 7913472 q^{88} + 129745152 q^{90} + 268578316 q^{91} + 167825664 q^{92} + 120711534 q^{93} - 11832576 q^{94} - 143949240 q^{95} - 25165824 q^{96} - 89415484 q^{97} + 366888330 q^{99} + O(q^{100})$$

## Decomposition of $$S_{9}^{\mathrm{new}}(18, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
18.9.d.a $16$ $7.333$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$126$$ $$-882$$ $$-1846$$ $$q+\beta _{4}q^{2}+(7+2\beta _{1}+\beta _{3}+\beta _{4})q^{3}+\cdots$$

## Decomposition of $$S_{9}^{\mathrm{old}}(18, [\chi])$$ into lower level spaces

$$S_{9}^{\mathrm{old}}(18, [\chi]) \simeq$$ $$S_{9}^{\mathrm{new}}(9, [\chi])$$$$^{\oplus 2}$$