Properties

Label 189.2.s
Level $189$
Weight $2$
Character orbit 189.s
Rep. character $\chi_{189}(17,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $12$
Newform subspaces $2$
Sturm bound $48$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 189.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
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

\( 12q + 3q^{2} + 5q^{4} + 6q^{5} - 2q^{7} + O(q^{10}) \) \( 12q + 3q^{2} + 5q^{4} + 6q^{5} - 2q^{7} - 6q^{10} + 3q^{13} - 3q^{14} - q^{16} + 9q^{17} - 6q^{19} + 6q^{20} + 2q^{22} - 6q^{25} - 6q^{26} - 2q^{28} + 24q^{29} - 15q^{31} - 39q^{32} - 6q^{34} - q^{37} - 54q^{38} + 6q^{41} + 2q^{43} - 27q^{44} - 4q^{46} - 15q^{47} - 12q^{49} + 9q^{50} + 24q^{53} + 54q^{56} + 2q^{58} + 18q^{59} + 36q^{61} - 24q^{62} + 4q^{64} - 6q^{65} - 6q^{67} + 48q^{68} - 18q^{70} - 6q^{73} - 48q^{77} + 12q^{79} + 45q^{80} + 30q^{83} + 9q^{85} + 22q^{88} - 27q^{89} - 15q^{91} - 30q^{92} - 3q^{94} - 27q^{95} + 3q^{97} - 21q^{98} + O(q^{100}) \)

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

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

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