Properties

Label 135.2.p
Level $135$
Weight $2$
Character orbit 135.p
Rep. character $\chi_{135}(4,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $96$
Newform subspaces $1$
Sturm bound $36$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 135 = 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 135.p (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 135 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(36\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(135, [\chi])\).

Total New Old
Modular forms 120 120 0
Cusp forms 96 96 0
Eisenstein series 24 24 0

Trace form

\( 96 q - 12 q^{4} - 9 q^{5} - 6 q^{6} - 18 q^{9} + O(q^{10}) \) \( 96 q - 12 q^{4} - 9 q^{5} - 6 q^{6} - 18 q^{9} - 3 q^{10} - 6 q^{11} - 18 q^{14} - 21 q^{15} - 24 q^{16} - 6 q^{19} - 57 q^{20} + 24 q^{21} - 30 q^{24} + 3 q^{25} + 48 q^{26} - 30 q^{29} - 51 q^{30} - 30 q^{31} - 24 q^{34} - 12 q^{35} + 54 q^{36} - 6 q^{39} - 9 q^{40} - 12 q^{41} + 78 q^{44} + 45 q^{45} - 6 q^{46} - 30 q^{49} + 84 q^{50} - 90 q^{51} + 108 q^{54} - 12 q^{55} - 96 q^{56} + 66 q^{59} + 84 q^{60} + 6 q^{61} + 45 q^{65} - 150 q^{66} + 24 q^{69} - 33 q^{70} - 90 q^{71} + 66 q^{74} + 39 q^{75} + 12 q^{76} + 24 q^{79} + 30 q^{80} - 54 q^{81} + 198 q^{84} - 21 q^{85} + 18 q^{86} + 96 q^{89} + 90 q^{90} - 6 q^{91} + 24 q^{94} + 87 q^{95} + 42 q^{96} + 36 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(135, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
135.2.p.a 135.p 135.p $96$ $1.078$ None 135.2.p.a \(0\) \(0\) \(-9\) \(0\) $\mathrm{SU}(2)[C_{18}]$