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Properties

Label 180.2.r
Level $180$
Weight $2$
Character orbit 180.r
Rep. character $\chi_{180}(49,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $12$
Newform subspaces $1$
Sturm bound $72$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 180.r (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(72\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(180, [\chi])\).

Total New Old
Modular forms 84 12 72
Cusp forms 60 12 48
Eisenstein series 24 0 24

Trace form

\( 12 q + q^{5} + 8 q^{9} + O(q^{10}) \) \( 12 q + q^{5} + 8 q^{9} + 2 q^{11} - 5 q^{15} + 10 q^{21} - 3 q^{25} - 18 q^{29} + 6 q^{31} - 34 q^{35} - 42 q^{39} + 14 q^{41} - 31 q^{45} + 16 q^{51} - 6 q^{55} - 34 q^{59} + 6 q^{61} + 15 q^{65} + 14 q^{69} + 41 q^{75} - 6 q^{79} - 8 q^{81} - 12 q^{85} + 112 q^{89} + 12 q^{91} + 36 q^{95} + 82 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(180, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
180.2.r.a 180.r 45.j $12$ $1.437$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(1\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{3}+\beta _{9}q^{5}+(-\beta _{3}+\beta _{6}-\beta _{7}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(180, [\chi])\) into lower level spaces

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