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

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