Properties

Label 540.3.t
Level $540$
Weight $3$
Character orbit 540.t
Rep. character $\chi_{540}(89,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $24$
Newform subspaces $1$
Sturm bound $324$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 540 = 2^{2} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 540.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(324\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(540, [\chi])\).

Total New Old
Modular forms 468 24 444
Cusp forms 396 24 372
Eisenstein series 72 0 72

Trace form

\( 24 q + 9 q^{5} + O(q^{10}) \) \( 24 q + 9 q^{5} + 18 q^{11} + 3 q^{25} - 36 q^{29} + 30 q^{31} + 36 q^{41} + 108 q^{49} + 42 q^{55} + 306 q^{59} + 48 q^{61} + 225 q^{65} + 114 q^{79} + 48 q^{85} - 84 q^{91} - 324 q^{95} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(540, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
540.3.t.a 540.t 45.h $24$ $14.714$ None \(0\) \(0\) \(9\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{3}^{\mathrm{old}}(540, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(540, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 2}\)