# Properties

 Label 216.2.v Level 216 Weight 2 Character orbit v Rep. character $$\chi_{216}(11,\cdot)$$ Character field $$\Q(\zeta_{18})$$ Dimension 204 Newform subspaces 2 Sturm bound 72 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ = $$216 = 2^{3} \cdot 3^{3}$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 216.v (of order $$18$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$216$$ Character field: $$\Q(\zeta_{18})$$ Newform subspaces: $$2$$ Sturm bound: $$72$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(216, [\chi])$$.

Total New Old
Modular forms 228 228 0
Cusp forms 204 204 0
Eisenstein series 24 24 0

## Trace form

 $$204q - 6q^{2} - 12q^{3} - 6q^{4} - 6q^{6} - 9q^{8} - 12q^{9} + O(q^{10})$$ $$204q - 6q^{2} - 12q^{3} - 6q^{4} - 6q^{6} - 9q^{8} - 12q^{9} - 3q^{10} - 12q^{11} - 15q^{12} + 9q^{14} - 6q^{16} - 18q^{17} + 15q^{18} - 6q^{19} - 27q^{20} - 6q^{22} - 30q^{24} - 12q^{25} - 12q^{27} - 12q^{28} - 21q^{30} - 36q^{32} - 24q^{33} - 12q^{34} - 18q^{35} - 36q^{36} - 30q^{38} + 9q^{40} - 6q^{42} - 12q^{43} - 81q^{44} - 3q^{46} - 81q^{48} - 12q^{49} + 57q^{50} - 30q^{51} + 21q^{52} + 78q^{54} - 69q^{56} + 6q^{57} - 33q^{58} - 48q^{59} - 54q^{60} + 90q^{62} - 3q^{64} - 12q^{65} + 87q^{66} - 12q^{67} - 9q^{68} - 33q^{70} + 12q^{72} - 6q^{73} + 51q^{74} - 96q^{75} + 6q^{76} + 90q^{78} - 12q^{81} - 12q^{82} - 72q^{83} - 48q^{84} + 78q^{86} - 30q^{88} - 18q^{89} + 120q^{90} - 6q^{91} - 3q^{92} - 33q^{94} + 18q^{96} - 12q^{97} + 162q^{98} - 12q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(216, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
216.2.v.a $$12$$ $$1.725$$ 12.0.$$\cdots$$.1 $$\Q(\sqrt{-2})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{11}q^{2}+(\beta _{5}-\beta _{8}-\beta _{11})q^{3}-2\beta _{4}q^{4}+\cdots$$
216.2.v.b $$192$$ $$1.725$$ None $$-6$$ $$-12$$ $$0$$ $$0$$

## Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ ($$1 - 8 T^{6} + 64 T^{12}$$)
$3$ ($$1 + 10 T^{3} + 73 T^{6} + 270 T^{9} + 729 T^{12}$$)
$5$ ($$( 1 - 125 T^{6} + 15625 T^{12} )^{2}$$)
$7$ ($$( 1 + 343 T^{6} + 117649 T^{12} )^{2}$$)
$11$ ($$( 1 - 6 T + 25 T^{2} - 66 T^{3} + 121 T^{4} )^{3}( 1 + 18 T^{3} - 1007 T^{6} + 23958 T^{9} + 1771561 T^{12} )$$)
$13$ ($$( 1 + 2197 T^{6} + 4826809 T^{12} )^{2}$$)
$17$ ($$( 1 - 90 T^{3} + 3187 T^{6} - 442170 T^{9} + 24137569 T^{12} )( 1 + 90 T^{3} + 3187 T^{6} + 442170 T^{9} + 24137569 T^{12} )$$)
$19$ ($$( 1 - 106 T^{3} + 4377 T^{6} - 727054 T^{9} + 47045881 T^{12} )^{2}$$)
$23$ ($$( 1 - 12167 T^{6} + 148035889 T^{12} )^{2}$$)
$29$ ($$( 1 - 24389 T^{6} + 594823321 T^{12} )^{2}$$)
$31$ ($$( 1 + 29791 T^{6} + 887503681 T^{12} )^{2}$$)
$37$ ($$( 1 + 37 T^{2} + 1369 T^{4} )^{6}$$)
$41$ ($$( 1 + 6 T - 5 T^{2} + 246 T^{3} + 1681 T^{4} )^{3}( 1 + 522 T^{3} + 203563 T^{6} + 35976762 T^{9} + 4750104241 T^{12} )$$)
$43$ ($$( 1 - 10 T + 57 T^{2} - 430 T^{3} + 1849 T^{4} )^{3}( 1 + 290 T^{3} + 4593 T^{6} + 23057030 T^{9} + 6321363049 T^{12} )$$)
$47$ ($$( 1 - 103823 T^{6} + 10779215329 T^{12} )^{2}$$)
$53$ ($$( 1 + 53 T^{2} )^{12}$$)
$59$ ($$( 1 - 6 T + 59 T^{2} )^{6}( 1 + 846 T^{3} + 510337 T^{6} + 173750634 T^{9} + 42180533641 T^{12} )$$)
$61$ ($$( 1 + 226981 T^{6} + 51520374361 T^{12} )^{2}$$)
$67$ ($$( 1 + 14 T + 129 T^{2} + 938 T^{3} + 4489 T^{4} )^{3}( 1 - 70 T^{3} - 295863 T^{6} - 21053410 T^{9} + 90458382169 T^{12} )$$)
$71$ ($$( 1 - 71 T^{2} + 5041 T^{4} )^{6}$$)
$73$ ($$( 1 - 430 T^{3} - 204117 T^{6} - 167277310 T^{9} + 151334226289 T^{12} )^{2}$$)
$79$ ($$( 1 + 493039 T^{6} + 243087455521 T^{12} )^{2}$$)
$83$ ($$( 1 - 1350 T^{3} + 1250713 T^{6} - 771912450 T^{9} + 326940373369 T^{12} )( 1 + 1350 T^{3} + 1250713 T^{6} + 771912450 T^{9} + 326940373369 T^{12} )$$)
$89$ ($$( 1 + 18 T + 89 T^{2} )^{6}( 1 + 18 T + 235 T^{2} + 1602 T^{3} + 7921 T^{4} )^{3}$$)
$97$ ($$( 1 - 10 T + 3 T^{2} - 970 T^{3} + 9409 T^{4} )^{3}( 1 + 1910 T^{3} + 2735427 T^{6} + 1743205430 T^{9} + 832972004929 T^{12} )$$)