Properties

Label 189.2.i
Level 189
Weight 2
Character orbit i
Rep. character \(\chi_{189}(143,\cdot)\)
Character field \(\Q(\zeta_{6})\)
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.i (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 63 \)
Character field: \(\Q(\zeta_{6})\)
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

\(12q \) \(\mathstrut -\mathstrut 10q^{4} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 10q^{4} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 6q^{10} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut -\mathstrut 3q^{13} \) \(\mathstrut -\mathstrut 18q^{14} \) \(\mathstrut +\mathstrut 2q^{16} \) \(\mathstrut -\mathstrut 9q^{17} \) \(\mathstrut -\mathstrut 6q^{19} \) \(\mathstrut -\mathstrut 6q^{20} \) \(\mathstrut +\mathstrut 2q^{22} \) \(\mathstrut +\mathstrut 6q^{23} \) \(\mathstrut +\mathstrut 3q^{25} \) \(\mathstrut +\mathstrut 6q^{26} \) \(\mathstrut -\mathstrut 2q^{28} \) \(\mathstrut +\mathstrut 24q^{29} \) \(\mathstrut +\mathstrut 6q^{34} \) \(\mathstrut -\mathstrut q^{37} \) \(\mathstrut -\mathstrut 27q^{38} \) \(\mathstrut +\mathstrut 24q^{40} \) \(\mathstrut -\mathstrut 6q^{41} \) \(\mathstrut +\mathstrut 2q^{43} \) \(\mathstrut +\mathstrut 27q^{44} \) \(\mathstrut -\mathstrut 4q^{46} \) \(\mathstrut -\mathstrut 30q^{47} \) \(\mathstrut +\mathstrut 6q^{49} \) \(\mathstrut +\mathstrut 9q^{50} \) \(\mathstrut -\mathstrut 15q^{52} \) \(\mathstrut -\mathstrut 24q^{53} \) \(\mathstrut +\mathstrut 24q^{56} \) \(\mathstrut -\mathstrut q^{58} \) \(\mathstrut +\mathstrut 36q^{59} \) \(\mathstrut +\mathstrut 24q^{62} \) \(\mathstrut +\mathstrut 4q^{64} \) \(\mathstrut +\mathstrut 12q^{67} \) \(\mathstrut +\mathstrut 24q^{68} \) \(\mathstrut +\mathstrut 15q^{70} \) \(\mathstrut -\mathstrut 6q^{73} \) \(\mathstrut +\mathstrut 51q^{74} \) \(\mathstrut -\mathstrut 48q^{77} \) \(\mathstrut -\mathstrut 24q^{79} \) \(\mathstrut -\mathstrut 45q^{80} \) \(\mathstrut -\mathstrut 30q^{83} \) \(\mathstrut +\mathstrut 9q^{85} \) \(\mathstrut -\mathstrut 57q^{86} \) \(\mathstrut -\mathstrut 11q^{88} \) \(\mathstrut +\mathstrut 27q^{89} \) \(\mathstrut -\mathstrut 15q^{91} \) \(\mathstrut -\mathstrut 30q^{92} \) \(\mathstrut -\mathstrut 3q^{97} \) \(\mathstrut +\mathstrut 21q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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

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

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