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Properties

Label 135.4.j
Level $135$
Weight $4$
Character orbit 135.j
Rep. character $\chi_{135}(19,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $32$
Newform subspaces $1$
Sturm bound $72$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 135 = 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 135.j (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(72\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(135, [\chi])\).

Total New Old
Modular forms 120 40 80
Cusp forms 96 32 64
Eisenstein series 24 8 16

Trace form

\( 32 q + 54 q^{4} - 3 q^{5} + O(q^{10}) \) \( 32 q + 54 q^{4} - 3 q^{5} - 20 q^{10} - 90 q^{11} + 102 q^{14} - 146 q^{16} - 8 q^{19} + 6 q^{20} + 71 q^{25} + 936 q^{26} + 516 q^{29} - 38 q^{31} + 212 q^{34} + 534 q^{35} + 44 q^{40} - 576 q^{41} - 3288 q^{44} - 580 q^{46} - 4 q^{49} - 558 q^{50} + 30 q^{55} - 2430 q^{56} + 2202 q^{59} - 20 q^{61} + 644 q^{64} - 339 q^{65} + 636 q^{70} + 5904 q^{71} + 4080 q^{74} + 396 q^{76} - 218 q^{79} - 2532 q^{80} - 704 q^{85} - 6108 q^{86} - 8148 q^{89} - 1884 q^{91} - 1078 q^{94} + 1692 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(135, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
135.4.j.a 135.j 45.j $32$ $7.965$ None \(0\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{4}^{\mathrm{old}}(135, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(135, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)