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Properties

Label 180.3.u
Level $180$
Weight $3$
Character orbit 180.u
Rep. character $\chi_{180}(13,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $48$
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.u (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{12})\)
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 312 48 264
Cusp forms 264 48 216
Eisenstein series 48 0 48

Trace form

\( 48 q - 2 q^{3} + O(q^{10}) \) \( 48 q - 2 q^{3} + 12 q^{11} + 22 q^{15} + 36 q^{17} + 52 q^{21} - 12 q^{23} - 6 q^{25} + 46 q^{27} - 14 q^{33} + 72 q^{35} - 84 q^{37} + 72 q^{41} + 110 q^{45} - 78 q^{47} - 4 q^{51} - 312 q^{53} + 132 q^{55} - 338 q^{57} - 96 q^{61} - 242 q^{63} - 132 q^{65} - 78 q^{67} - 312 q^{71} - 274 q^{75} - 240 q^{77} - 364 q^{81} + 132 q^{83} + 96 q^{85} + 172 q^{87} + 168 q^{91} + 364 q^{93} - 168 q^{95} - 90 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.u.a 180.u 45.k $48$ $4.905$ None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$

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

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