Properties

Label 189.2.h
Level $189$
Weight $2$
Character orbit 189.h
Rep. character $\chi_{189}(37,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $12$
Newform subspaces $2$
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.h (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
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

\( 12q + 2q^{2} + 6q^{4} - 5q^{5} + 12q^{8} + O(q^{10}) \) \( 12q + 2q^{2} + 6q^{4} - 5q^{5} + 12q^{8} - 6q^{10} + q^{11} - 3q^{13} + 16q^{14} - 6q^{16} - 9q^{17} - 4q^{20} - 6q^{22} + 3q^{25} - 16q^{26} - 6q^{28} - 8q^{29} + 6q^{31} - 14q^{32} - 4q^{35} - 3q^{37} - 19q^{38} - 6q^{40} - 10q^{41} - 6q^{43} + 5q^{44} + 54q^{47} - 6q^{49} - 23q^{50} - 15q^{52} + 12q^{53} - 6q^{55} - 6q^{56} - 9q^{58} + 60q^{59} + 12q^{62} - 36q^{64} - 32q^{65} + 12q^{67} - 30q^{68} + 39q^{70} + 30q^{71} + 12q^{73} + 39q^{74} + 6q^{76} + 14q^{77} + 24q^{79} - 19q^{80} - 18q^{83} - 3q^{85} + 7q^{86} - 3q^{88} - 41q^{89} + 21q^{91} - 30q^{92} + 6q^{94} - 26q^{95} - 3q^{97} - 61q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(189, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
189.2.h.a \(2\) \(1.509\) \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(-1\) \(4\) \(q-q^{2}-q^{4}+(-1+\zeta_{6})q^{5}+(3-2\zeta_{6})q^{7}+\cdots\)
189.2.h.b \(10\) \(1.509\) 10.0.\(\cdots\).1 None \(4\) \(0\) \(-4\) \(-4\) \(q+(\beta _{1}-\beta _{5})q^{2}+(1+\beta _{3})q^{4}+(\beta _{6}-\beta _{9})q^{5}+\cdots\)

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

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