Properties

Label 135.3.o
Level $135$
Weight $3$
Character orbit 135.o
Rep. character $\chi_{135}(11,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $144$
Newform subspaces $1$
Sturm bound $54$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 135 = 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 135.o (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 27 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(54\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(135, [\chi])\).

Total New Old
Modular forms 228 144 84
Cusp forms 204 144 60
Eisenstein series 24 0 24

Trace form

\( 144 q + 12 q^{6} - 6 q^{9} + O(q^{10}) \) \( 144 q + 12 q^{6} - 6 q^{9} + 18 q^{11} + 18 q^{12} + 54 q^{14} - 96 q^{18} - 96 q^{21} + 72 q^{22} - 108 q^{23} - 354 q^{24} - 24 q^{27} + 216 q^{29} + 120 q^{30} + 432 q^{32} + 336 q^{33} - 144 q^{34} + 84 q^{36} - 36 q^{38} - 96 q^{39} - 360 q^{41} - 660 q^{42} + 180 q^{43} - 648 q^{44} - 180 q^{45} - 432 q^{47} - 894 q^{48} + 72 q^{49} + 90 q^{51} + 54 q^{52} + 372 q^{54} + 396 q^{56} + 660 q^{57} - 270 q^{58} + 594 q^{59} - 144 q^{61} + 1782 q^{62} + 1200 q^{63} + 576 q^{64} - 180 q^{65} - 240 q^{66} - 252 q^{67} + 126 q^{68} - 138 q^{69} - 360 q^{70} - 648 q^{71} - 684 q^{72} + 126 q^{73} - 972 q^{74} - 432 q^{76} - 702 q^{77} - 738 q^{78} - 36 q^{79} + 342 q^{81} - 306 q^{83} - 186 q^{84} + 180 q^{85} + 810 q^{86} - 246 q^{87} + 864 q^{88} - 972 q^{89} + 480 q^{90} - 198 q^{91} - 1368 q^{92} + 774 q^{93} + 1206 q^{94} + 360 q^{95} - 654 q^{96} + 540 q^{97} + 1296 q^{98} - 642 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(135, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
135.3.o.a 135.o 27.f $144$ $3.678$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$

Decomposition of \(S_{3}^{\mathrm{old}}(135, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(135, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 2}\)