Properties

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

Related objects

Downloads

Learn more about

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: \(\Q(\zeta_{6})\)
Newforms: \( 1 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(189, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
189.2.o.a \(12\) \(1.509\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(6\) \(0\) \(0\) \(-2\) \(q+(\beta _{1}-\beta _{3}-\beta _{5})q^{2}+(-\beta _{3}-\beta _{5}-\beta _{8}+\cdots)q^{4}+\cdots\)

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

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