Properties

Label 189.2.f
Level 189
Weight 2
Character orbit f
Rep. character \(\chi_{189}(64,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 12
Newforms 2
Sturm bound 48
Trace bound 2

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Defining parameters

Level: \( N \) = \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 189.f (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newforms: \( 2 \)
Sturm bound: \(48\)
Trace bound: \(2\)
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 12 48
Cusp forms 36 12 24
Eisenstein series 24 0 24

Trace form

\(12q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 6q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 6q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 4q^{11} \) \(\mathstrut +\mathstrut 4q^{14} \) \(\mathstrut -\mathstrut 6q^{16} \) \(\mathstrut +\mathstrut 12q^{17} \) \(\mathstrut -\mathstrut 12q^{19} \) \(\mathstrut -\mathstrut 22q^{20} \) \(\mathstrut +\mathstrut 6q^{22} \) \(\mathstrut +\mathstrut 12q^{23} \) \(\mathstrut +\mathstrut 8q^{26} \) \(\mathstrut +\mathstrut 10q^{29} \) \(\mathstrut +\mathstrut 6q^{31} \) \(\mathstrut -\mathstrut 8q^{32} \) \(\mathstrut -\mathstrut 6q^{34} \) \(\mathstrut -\mathstrut 16q^{35} \) \(\mathstrut -\mathstrut 12q^{37} \) \(\mathstrut +\mathstrut 14q^{38} \) \(\mathstrut -\mathstrut 12q^{40} \) \(\mathstrut -\mathstrut 22q^{41} \) \(\mathstrut +\mathstrut 6q^{43} \) \(\mathstrut -\mathstrut 76q^{44} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut -\mathstrut 6q^{47} \) \(\mathstrut -\mathstrut 6q^{49} \) \(\mathstrut +\mathstrut 4q^{50} \) \(\mathstrut +\mathstrut 18q^{52} \) \(\mathstrut +\mathstrut 24q^{53} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut +\mathstrut 12q^{56} \) \(\mathstrut +\mathstrut 18q^{58} \) \(\mathstrut -\mathstrut 12q^{59} \) \(\mathstrut +\mathstrut 96q^{62} \) \(\mathstrut +\mathstrut 10q^{65} \) \(\mathstrut +\mathstrut 12q^{67} \) \(\mathstrut +\mathstrut 12q^{68} \) \(\mathstrut -\mathstrut 36q^{71} \) \(\mathstrut -\mathstrut 36q^{73} \) \(\mathstrut -\mathstrut 24q^{74} \) \(\mathstrut +\mathstrut 6q^{76} \) \(\mathstrut +\mathstrut 8q^{77} \) \(\mathstrut +\mathstrut 6q^{79} \) \(\mathstrut +\mathstrut 8q^{80} \) \(\mathstrut -\mathstrut 30q^{83} \) \(\mathstrut -\mathstrut 18q^{85} \) \(\mathstrut +\mathstrut 40q^{86} \) \(\mathstrut -\mathstrut 6q^{88} \) \(\mathstrut -\mathstrut 20q^{89} \) \(\mathstrut -\mathstrut 12q^{91} \) \(\mathstrut +\mathstrut 18q^{92} \) \(\mathstrut -\mathstrut 6q^{94} \) \(\mathstrut +\mathstrut 4q^{95} \) \(\mathstrut -\mathstrut 4q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.f.a \(6\) \(1.509\) 6.0.309123.1 None \(-1\) \(0\) \(-5\) \(3\) \(q+(\beta _{1}-\beta _{5})q^{2}+(-1+\beta _{2}+\beta _{4}+\beta _{5})q^{4}+\cdots\)
189.2.f.b \(6\) \(1.509\) \(\Q(\zeta_{18})\) None \(3\) \(0\) \(3\) \(-3\) \(q+(\zeta_{18}-\zeta_{18}^{3}-\zeta_{18}^{4}+\zeta_{18}^{5})q^{2}+\cdots\)

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

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