# Properties

 Label 864.2.bh Level 864 Weight 2 Character orbit bh Rep. character $$\chi_{864}(47,\cdot)$$ Character field $$\Q(\zeta_{18})$$ Dimension 204 Newform subspaces 2 Sturm bound 288 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ = $$864 = 2^{5} \cdot 3^{3}$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 864.bh (of order $$18$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$216$$ Character field: $$\Q(\zeta_{18})$$ Newform subspaces: $$2$$ Sturm bound: $$288$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(864, [\chi])$$.

Total New Old
Modular forms 912 228 684
Cusp forms 816 204 612
Eisenstein series 96 24 72

## Trace form

 $$204q + 12q^{3} - 12q^{9} + O(q^{10})$$ $$204q + 12q^{3} - 12q^{9} + 12q^{11} - 18q^{17} + 6q^{19} - 12q^{25} + 12q^{27} - 24q^{33} + 18q^{35} + 12q^{43} - 12q^{49} + 30q^{51} + 6q^{57} + 48q^{59} - 12q^{65} + 12q^{67} - 6q^{73} + 96q^{75} - 12q^{81} + 72q^{83} - 18q^{89} + 6q^{91} - 12q^{97} + 12q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(864, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
864.2.bh.a $$12$$ $$6.899$$ 12.0.$$\cdots$$.1 $$\Q(\sqrt{-2})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{4}-\beta _{7}+\beta _{10})q^{3}+(-\beta _{2}+2\beta _{5}+\cdots)q^{9}+\cdots$$
864.2.bh.b $$192$$ $$6.899$$ None $$0$$ $$12$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(864, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(864, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(216, [\chi])$$$$^{\oplus 3}$$

## Hecke Characteristic Polynomials

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