↑

Properties

Label 189.2.o
Level $189$
Weight $2$
Character orbit 189.o
Rep. character $\chi_{189}(62,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $12$
Newform subspaces $1$
Sturm bound $48$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 189.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(48\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(189, [\chi])\).

Total New Old
Modular forms 60 20 40
Cusp forms 36 12 24
Eisenstein series 24 8 16

Trace form

\( 12 q + 6 q^{2} + 2 q^{4} - 2 q^{7} + O(q^{10}) \) \( 12 q + 6 q^{2} + 2 q^{4} - 2 q^{7} + 12 q^{14} + 2 q^{16} - 10 q^{22} - 24 q^{23} - 8 q^{28} - 30 q^{29} + 12 q^{32} - 4 q^{37} - 10 q^{43} - 40 q^{46} + 6 q^{49} + 36 q^{50} - 42 q^{56} + 2 q^{58} + 16 q^{64} + 78 q^{65} + 12 q^{67} + 18 q^{70} + 12 q^{74} + 24 q^{77} - 6 q^{79} - 6 q^{85} - 96 q^{86} + 34 q^{88} - 24 q^{91} - 30 q^{92} - 72 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(189, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
189.2.o.a 189.o 63.o $12$ $1.509$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(6\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{1}-\beta _{3}-\beta _{5})q^{2}+(-\beta _{3}-\beta _{5}-\beta _{8}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(189, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(189, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)