# Properties

 Label 7.9.d Level $7$ Weight $9$ Character orbit 7.d Rep. character $\chi_{7}(3,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $8$ Newform subspaces $1$ Sturm bound $6$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$7$$ Weight: $$k$$ $$=$$ $$9$$ Character orbit: $$[\chi]$$ $$=$$ 7.d (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$1$$ Sturm bound: $$6$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{9}(7, [\chi])$$.

Total New Old
Modular forms 12 12 0
Cusp forms 8 8 0
Eisenstein series 4 4 0

## Trace form

 $$8 q - 4 q^{2} - 84 q^{3} - 164 q^{4} - 840 q^{5} - 140 q^{7} + 6544 q^{8} + 396 q^{9} + O(q^{10})$$ $$8 q - 4 q^{2} - 84 q^{3} - 164 q^{4} - 840 q^{5} - 140 q^{7} + 6544 q^{8} + 396 q^{9} + 5796 q^{10} + 1784 q^{11} - 40908 q^{12} - 9856 q^{14} + 131808 q^{15} - 8584 q^{16} - 141456 q^{17} - 121944 q^{18} - 257544 q^{19} + 474012 q^{21} + 1706256 q^{22} - 348940 q^{23} - 895104 q^{24} - 557752 q^{25} - 2913120 q^{26} + 1485092 q^{28} + 4983176 q^{29} - 551112 q^{30} - 2376696 q^{31} - 332016 q^{32} - 5719140 q^{33} + 2491272 q^{35} + 13269408 q^{36} + 492740 q^{37} - 7088088 q^{38} - 2850372 q^{39} - 7601832 q^{40} + 3586128 q^{42} + 4448432 q^{43} - 3678804 q^{44} + 3328164 q^{45} - 226560 q^{46} + 2704128 q^{47} - 3811024 q^{49} - 15628912 q^{50} - 350856 q^{51} + 11135208 q^{52} + 2281460 q^{53} + 24553368 q^{54} - 6573392 q^{56} - 43638408 q^{57} + 11442696 q^{58} + 25291140 q^{59} + 17679564 q^{60} + 59368764 q^{61} - 60081756 q^{63} - 114153056 q^{64} + 16923396 q^{65} + 463428 q^{66} - 107108 q^{67} + 44316972 q^{68} + 19120080 q^{70} - 82809760 q^{71} + 13297584 q^{72} + 116758404 q^{73} + 72690340 q^{74} + 79832424 q^{75} - 58244200 q^{77} - 44122512 q^{78} - 50628092 q^{79} - 93591624 q^{80} - 96868872 q^{81} - 91061712 q^{82} + 154096572 q^{84} + 119231208 q^{85} + 39093088 q^{86} + 26702676 q^{87} + 41392848 q^{88} - 2322516 q^{89} - 151794552 q^{91} + 253819128 q^{92} - 57693204 q^{93} - 345566088 q^{94} - 172787052 q^{95} - 416455200 q^{96} + 373659692 q^{98} + 672244008 q^{99} + O(q^{100})$$

## Decomposition of $$S_{9}^{\mathrm{new}}(7, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
7.9.d.a $8$ $2.852$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None $$-4$$ $$-84$$ $$-840$$ $$-140$$ $$q+(-\beta _{1}+\beta _{2}+\beta _{3})q^{2}+(-7+7\beta _{2}+\cdots)q^{3}+\cdots$$