Properties

Label 189.2.c
Level $189$
Weight $2$
Character orbit 189.c
Rep. character $\chi_{189}(188,\cdot)$
Character field $\Q$
Dimension $10$
Newform subspaces $3$
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.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
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 30 10 20
Cusp forms 18 10 8
Eisenstein series 12 0 12

Trace form

\( 10 q - 8 q^{4} - 3 q^{7} + O(q^{10}) \) \( 10 q - 8 q^{4} - 3 q^{7} - 12 q^{16} - 28 q^{22} + 22 q^{25} + 26 q^{28} - 6 q^{37} + 12 q^{43} - 4 q^{46} - 29 q^{49} + 80 q^{58} + 36 q^{64} - 22 q^{67} - 36 q^{70} - 10 q^{79} - 36 q^{85} + 4 q^{88} + 27 q^{91} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
189.2.c.a 189.c 21.c $2$ $1.509$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(1\) $\mathrm{U}(1)[D_{2}]$ \(q+2q^{4}+\zeta_{6}q^{7}+(1-2\zeta_{6})q^{13}+4q^{16}+\cdots\)
189.2.c.b 189.c 21.c $4$ $1.509$ \(\Q(\sqrt{-3}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-3q^{4}-\beta _{3}q^{5}+(-2+\beta _{2}+\cdots)q^{7}+\cdots\)
189.2.c.c 189.c 21.c $4$ $1.509$ \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-\beta _{2}q^{5}+(1-\beta _{3})q^{7}-2\beta _{1}q^{8}+\cdots\)

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

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