Properties

Label 135.3.h
Level $135$
Weight $3$
Character orbit 135.h
Rep. character $\chi_{135}(44,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $20$
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.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{6})\)
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 84 28 56
Cusp forms 60 20 40
Eisenstein series 24 8 16

Trace form

\( 20 q - 18 q^{4} + 12 q^{5} + O(q^{10}) \) \( 20 q - 18 q^{4} + 12 q^{5} + 4 q^{10} + 24 q^{11} - 30 q^{14} - 26 q^{16} - 8 q^{19} - 144 q^{20} + 2 q^{25} + 114 q^{29} + 28 q^{31} - 4 q^{34} - 34 q^{40} - 102 q^{41} + 116 q^{46} - 40 q^{49} + 408 q^{50} + 36 q^{55} + 618 q^{56} - 120 q^{59} - 50 q^{61} + 140 q^{64} - 492 q^{65} - 54 q^{70} - 504 q^{74} - 96 q^{76} - 128 q^{79} - 74 q^{85} - 1488 q^{86} - 288 q^{91} + 218 q^{94} + 762 q^{95} + O(q^{100}) \)

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.h.a 135.h 45.h $20$ $3.678$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(12\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{2}q^{2}+(-2+\beta _{3}-2\beta _{5})q^{4}+(1+\cdots)q^{5}+\cdots\)

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

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