Properties

Label 180.3.t
Level $180$
Weight $3$
Character orbit 180.t
Rep. character $\chi_{180}(29,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $24$
Newform subspaces $1$
Sturm bound $108$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 180.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(108\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(180, [\chi])\).

Total New Old
Modular forms 156 24 132
Cusp forms 132 24 108
Eisenstein series 24 0 24

Trace form

\( 24 q - 9 q^{5} + 2 q^{9} + O(q^{10}) \) \( 24 q - 9 q^{5} + 2 q^{9} - 18 q^{11} + 25 q^{15} - 26 q^{21} + 3 q^{25} + 36 q^{29} + 30 q^{31} + 6 q^{39} - 36 q^{41} - 31 q^{45} + 108 q^{49} + 124 q^{51} + 42 q^{55} - 306 q^{59} + 48 q^{61} - 225 q^{65} - 268 q^{69} - 217 q^{75} + 114 q^{79} - 14 q^{81} + 48 q^{85} - 84 q^{91} + 324 q^{95} + 418 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(180, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
180.3.t.a 180.t 45.h $24$ $4.905$ None \(0\) \(0\) \(-9\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{3}^{\mathrm{old}}(180, [\chi])\) into lower level spaces

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