Properties

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

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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

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