Properties

Label 189.2.p
Level $189$
Weight $2$
Character orbit 189.p
Rep. character $\chi_{189}(26,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $22$
Newform subspaces $4$
Sturm bound $48$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 189.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
Sturm bound: \(48\)
Trace bound: \(4\)
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

\( 22q + 12q^{4} - 5q^{7} + O(q^{10}) \) \( 22q + 12q^{4} - 5q^{7} + 6q^{10} + 2q^{16} - 3q^{19} - 32q^{22} - 11q^{25} - 12q^{28} - 39q^{31} - 4q^{37} - 12q^{40} - 10q^{43} - 26q^{46} + 37q^{49} + 36q^{52} + 4q^{58} + 15q^{61} + 64q^{64} + 50q^{67} - 84q^{70} + 51q^{73} - 46q^{79} + 18q^{82} + 12q^{85} - 22q^{88} - 54q^{91} - 138q^{94} + O(q^{100}) \)

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.p.a \(2\) \(1.509\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(1\) \(q+(-2+2\zeta_{6})q^{4}+(-1+3\zeta_{6})q^{7}+\cdots\)
189.2.p.b \(4\) \(1.509\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(10\) \(q+\beta _{1}q^{2}+(\beta _{1}-2\beta _{3})q^{5}+(2+\beta _{2})q^{7}+\cdots\)
189.2.p.c \(4\) \(1.509\) \(\Q(\sqrt{-3}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(-8\) \(q+\beta _{1}q^{2}+3\beta _{2}q^{4}+(-3+2\beta _{2})q^{7}+\cdots\)
189.2.p.d \(12\) \(1.509\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(-8\) \(q-\beta _{1}q^{2}+(1-\beta _{3}-\beta _{7}+\beta _{9})q^{4}+(\beta _{5}+\cdots)q^{5}+\cdots\)

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

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