Properties

Label 189.2.g
Level 189
Weight 2
Character orbit g
Rep. character \(\chi_{189}(100,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 12
Newforms 2
Sturm bound 48
Trace bound 1

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Defining parameters

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

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

\(12q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 3q^{4} \) \(\mathstrut +\mathstrut 10q^{5} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 3q^{4} \) \(\mathstrut +\mathstrut 10q^{5} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut -\mathstrut 6q^{10} \) \(\mathstrut -\mathstrut 2q^{11} \) \(\mathstrut -\mathstrut 3q^{13} \) \(\mathstrut -\mathstrut 11q^{14} \) \(\mathstrut +\mathstrut 3q^{16} \) \(\mathstrut -\mathstrut 9q^{17} \) \(\mathstrut -\mathstrut 4q^{20} \) \(\mathstrut -\mathstrut 6q^{22} \) \(\mathstrut -\mathstrut 6q^{25} \) \(\mathstrut -\mathstrut 16q^{26} \) \(\mathstrut -\mathstrut 6q^{28} \) \(\mathstrut -\mathstrut 8q^{29} \) \(\mathstrut -\mathstrut 3q^{31} \) \(\mathstrut +\mathstrut 7q^{32} \) \(\mathstrut -\mathstrut 4q^{35} \) \(\mathstrut -\mathstrut 3q^{37} \) \(\mathstrut +\mathstrut 38q^{38} \) \(\mathstrut +\mathstrut 12q^{40} \) \(\mathstrut -\mathstrut 10q^{41} \) \(\mathstrut -\mathstrut 6q^{43} \) \(\mathstrut +\mathstrut 5q^{44} \) \(\mathstrut -\mathstrut 27q^{47} \) \(\mathstrut +\mathstrut 12q^{49} \) \(\mathstrut -\mathstrut 23q^{50} \) \(\mathstrut +\mathstrut 30q^{52} \) \(\mathstrut +\mathstrut 12q^{53} \) \(\mathstrut -\mathstrut 6q^{55} \) \(\mathstrut +\mathstrut 48q^{56} \) \(\mathstrut +\mathstrut 18q^{58} \) \(\mathstrut -\mathstrut 30q^{59} \) \(\mathstrut +\mathstrut 12q^{62} \) \(\mathstrut -\mathstrut 36q^{64} \) \(\mathstrut +\mathstrut 16q^{65} \) \(\mathstrut -\mathstrut 6q^{67} \) \(\mathstrut +\mathstrut 60q^{68} \) \(\mathstrut -\mathstrut 24q^{70} \) \(\mathstrut +\mathstrut 30q^{71} \) \(\mathstrut +\mathstrut 12q^{73} \) \(\mathstrut -\mathstrut 78q^{74} \) \(\mathstrut +\mathstrut 6q^{76} \) \(\mathstrut +\mathstrut 26q^{77} \) \(\mathstrut -\mathstrut 12q^{79} \) \(\mathstrut -\mathstrut 19q^{80} \) \(\mathstrut -\mathstrut 18q^{83} \) \(\mathstrut -\mathstrut 3q^{85} \) \(\mathstrut -\mathstrut 14q^{86} \) \(\mathstrut +\mathstrut 6q^{88} \) \(\mathstrut -\mathstrut 41q^{89} \) \(\mathstrut +\mathstrut 21q^{91} \) \(\mathstrut -\mathstrut 30q^{92} \) \(\mathstrut -\mathstrut 3q^{94} \) \(\mathstrut +\mathstrut 13q^{95} \) \(\mathstrut -\mathstrut 3q^{97} \) \(\mathstrut -\mathstrut 61q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.g.a \(2\) \(1.509\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(2\) \(1\) \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+q^{5}+(-1+3\zeta_{6})q^{7}+\cdots\)
189.2.g.b \(10\) \(1.509\) 10.0.\(\cdots\).1 None \(-2\) \(0\) \(8\) \(-1\) \(q-\beta _{1}q^{2}+(-\beta _{3}+\beta _{6}+\beta _{7})q^{4}+(1+\cdots)q^{5}+\cdots\)

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

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