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Properties

Label 162.2.c
Level $162$
Weight $2$
Character orbit 162.c
Rep. character $\chi_{162}(55,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $8$
Newform subspaces $4$
Sturm bound $54$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 162.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 4 \)
Sturm bound: \(54\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(162, [\chi])\).

Total New Old
Modular forms 78 8 70
Cusp forms 30 8 22
Eisenstein series 48 0 48

Trace form

\( 8 q - 4 q^{4} + 10 q^{7} + O(q^{10}) \) \( 8 q - 4 q^{4} + 10 q^{7} + 10 q^{13} - 4 q^{16} - 8 q^{19} - 6 q^{22} - 16 q^{25} - 20 q^{28} - 2 q^{31} - 6 q^{34} + 4 q^{37} + 4 q^{43} + 24 q^{46} - 6 q^{49} + 10 q^{52} - 36 q^{55} + 30 q^{58} - 14 q^{61} + 8 q^{64} - 20 q^{67} + 18 q^{70} + 16 q^{73} + 4 q^{76} + 16 q^{79} - 18 q^{85} - 6 q^{88} + 32 q^{91} - 12 q^{94} - 2 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(162, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
162.2.c.a 162.c 9.c $2$ $1.294$ \(\Q(\sqrt{-3}) \) None 162.2.a.a \(-1\) \(0\) \(-3\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-3\zeta_{6}q^{5}+\cdots\)
162.2.c.b 162.c 9.c $2$ $1.294$ \(\Q(\sqrt{-3}) \) None 54.2.a.a \(-1\) \(0\) \(3\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+3\zeta_{6}q^{5}+\cdots\)
162.2.c.c 162.c 9.c $2$ $1.294$ \(\Q(\sqrt{-3}) \) None 54.2.a.a \(1\) \(0\) \(-3\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-3\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
162.2.c.d 162.c 9.c $2$ $1.294$ \(\Q(\sqrt{-3}) \) None 162.2.a.a \(1\) \(0\) \(3\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+3\zeta_{6}q^{5}+(4+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(162, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(162, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 2}\)