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Properties

Label 135.3.l
Level $135$
Weight $3$
Character orbit 135.l
Rep. character $\chi_{135}(37,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $40$
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.l (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{12})\)
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 168 56 112
Cusp forms 120 40 80
Eisenstein series 48 16 32

Trace form

\( 40 q + 2 q^{2} + 2 q^{5} - 2 q^{7} + 24 q^{8} - 8 q^{10} - 8 q^{11} - 2 q^{13} + 28 q^{16} - 28 q^{17} + 114 q^{20} + 14 q^{22} - 82 q^{23} - 8 q^{25} + 112 q^{26} - 88 q^{28} - 4 q^{31} + 14 q^{32} - 352 q^{35}+ \cdots + 1876 q^{98}+O(q^{100}) \) Copy content Toggle raw display

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
135.3.l.a 135.l 45.k $40$ $3.678$ None 45.3.k.a \(2\) \(0\) \(2\) \(-2\) $\mathrm{SU}(2)[C_{12}]$

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

\( S_{3}^{\mathrm{old}}(135, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)