Properties

Label 189.2.e
Level 189
Weight 2
Character orbit e
Rep. character \(\chi_{189}(109,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 22
Newform subspaces 6
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.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 6 \)
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 22 38
Cusp forms 36 22 14
Eisenstein series 24 0 24

Trace form

\( 22q - 12q^{4} + 9q^{7} + O(q^{10}) \) \( 22q - 12q^{4} + 9q^{7} - 2q^{10} - 30q^{16} - 9q^{19} + 40q^{22} - 15q^{25} - 20q^{28} + 13q^{31} + 4q^{37} - 70q^{43} - 18q^{46} - 11q^{49} + 20q^{52} + 32q^{55} + 4q^{58} + 15q^{61} + 112q^{64} - 30q^{67} + 152q^{70} + 7q^{73} - 76q^{76} - 22q^{79} - 118q^{82} - 36q^{85} - 54q^{88} - 52q^{91} + 30q^{94} - 14q^{97} + O(q^{100}) \)

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.e.a \(2\) \(1.509\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(4\) \(4\) \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+4\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
189.2.e.b \(2\) \(1.509\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-1\) \(q+(2-2\zeta_{6})q^{4}+(1-3\zeta_{6})q^{7}+2q^{13}+\cdots\)
189.2.e.c \(2\) \(1.509\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-4\) \(4\) \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}-4\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
189.2.e.d \(4\) \(1.509\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(-2\) \(q-\beta _{2}q^{2}+(-4+4\beta _{1})q^{4}-\beta _{2}q^{5}+\cdots\)
189.2.e.e \(6\) \(1.509\) 6.0.309123.1 None \(-2\) \(0\) \(-1\) \(2\) \(q+(-\beta _{1}-\beta _{4}+\beta _{5})q^{2}+(-2+\beta _{2}+\cdots)q^{4}+\cdots\)
189.2.e.f \(6\) \(1.509\) 6.0.309123.1 None \(2\) \(0\) \(1\) \(2\) \(q+(1-\beta _{4}+\beta _{5})q^{2}+(-\beta _{1}-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(189, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)