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Properties

Label 135.2.j
Level $135$
Weight $2$
Character orbit 135.j
Rep. character $\chi_{135}(19,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $8$
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.j (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{6})\)
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 48 16 32
Cusp forms 24 8 16
Eisenstein series 24 8 16

Trace form

\( 8 q + O(q^{10}) \) \( 8 q - 8 q^{10} + 12 q^{11} + 4 q^{16} - 8 q^{19} - 12 q^{20} - 4 q^{25} - 24 q^{26} - 12 q^{29} + 4 q^{31} - 4 q^{34} + 24 q^{35} - 4 q^{40} + 24 q^{41} + 24 q^{44} - 16 q^{46} - 4 q^{49} - 24 q^{50} + 24 q^{55} + 12 q^{56} - 24 q^{59} - 8 q^{61} + 32 q^{64} + 12 q^{70} - 72 q^{71} + 12 q^{74} - 12 q^{76} + 16 q^{79} + 48 q^{80} + 16 q^{85} + 36 q^{86} + 24 q^{89} - 24 q^{91} + 20 q^{94} - 12 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
135.2.j.a 135.j 45.j $8$ $1.078$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{24}^{6}q^{2}-\zeta_{24}^{3}q^{4}+(\zeta_{24}-\zeta_{24}^{3}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(135, [\chi])\) into lower level spaces

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