Properties

Label 189.3.d
Level $189$
Weight $3$
Character orbit 189.d
Rep. character $\chi_{189}(55,\cdot)$
Character field $\Q$
Dimension $22$
Newform subspaces $5$
Sturm bound $72$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 189.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(72\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(189, [\chi])\).

Total New Old
Modular forms 54 22 32
Cusp forms 42 22 20
Eisenstein series 12 0 12

Trace form

\( 22 q + 48 q^{4} - 5 q^{7} + O(q^{10}) \) \( 22 q + 48 q^{4} - 5 q^{7} + 128 q^{16} - 44 q^{22} - 122 q^{25} + 6 q^{28} - 130 q^{37} - 196 q^{43} + 100 q^{46} - 131 q^{49} - 284 q^{58} + 280 q^{64} + 218 q^{67} + 150 q^{70} + 890 q^{79} + 468 q^{85} - 652 q^{88} + 345 q^{91} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(189, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
189.3.d.a 189.d 7.b $2$ $5.150$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(0\) \(-7\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}-3q^{4}+(1-2\zeta_{6})q^{5}+(-7+7\zeta_{6})q^{7}+\cdots\)
189.3.d.b 189.d 7.b $2$ $5.150$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(13\) $\mathrm{U}(1)[D_{2}]$ \(q-4q^{4}+(6+\zeta_{6})q^{7}+(-5+10\zeta_{6})q^{13}+\cdots\)
189.3.d.c 189.d 7.b $2$ $5.150$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(0\) \(-7\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}-3q^{4}+(1-2\zeta_{6})q^{5}-7\zeta_{6}q^{7}+\cdots\)
189.3.d.d 189.d 7.b $8$ $5.150$ 8.0.\(\cdots\).6 None \(0\) \(0\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+(3+\beta _{5})q^{4}-\beta _{3}q^{5}+(-2+\cdots)q^{7}+\cdots\)
189.3.d.e 189.d 7.b $8$ $5.150$ 8.0.\(\cdots\).14 None \(0\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}+(5-\beta _{1})q^{4}+\beta _{2}q^{5}+(2+\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(189, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(189, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)