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

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

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

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