Properties

Label 189.2.e
Level $189$
Weight $2$
Character orbit 189.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

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

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
189.2.e.a 189.e 7.c $2$ $1.509$ \(\Q(\sqrt{-3}) \) None 189.2.e.a \(-1\) \(0\) \(4\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+4\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
189.2.e.b 189.e 7.c $2$ $1.509$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) 189.2.e.b \(0\) \(0\) \(0\) \(-1\) $\mathrm{U}(1)[D_{3}]$ \(q+(2-2\zeta_{6})q^{4}+(1-3\zeta_{6})q^{7}+2q^{13}+\cdots\)
189.2.e.c 189.e 7.c $2$ $1.509$ \(\Q(\sqrt{-3}) \) None 189.2.e.a \(1\) \(0\) \(-4\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}-4\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
189.2.e.d 189.e 7.c $4$ $1.509$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None 189.2.e.d \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{2}+(-4+4\beta _{1})q^{4}-\beta _{2}q^{5}+\cdots\)
189.2.e.e 189.e 7.c $6$ $1.509$ 6.0.309123.1 None 189.2.e.e \(-2\) \(0\) \(-1\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}-\beta _{4}+\beta _{5})q^{2}+(-2+\beta _{2}+\cdots)q^{4}+\cdots\)
189.2.e.f 189.e 7.c $6$ $1.509$ 6.0.309123.1 None 189.2.e.e \(2\) \(0\) \(1\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{4}+\beta _{5})q^{2}+(-\beta _{1}-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)

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

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