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Properties

Label 162.3.d
Level $162$
Weight $3$
Character orbit 162.d
Rep. character $\chi_{162}(53,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $16$
Newform subspaces $3$
Sturm bound $81$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 162.d (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(81\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(162, [\chi])\).

Total New Old
Modular forms 132 16 116
Cusp forms 84 16 68
Eisenstein series 48 0 48

Trace form

\( 16 q + 16 q^{4} - 10 q^{7} + O(q^{10}) \) \( 16 q + 16 q^{4} - 10 q^{7} + 50 q^{13} - 32 q^{16} + 164 q^{19} + 24 q^{22} + 52 q^{25} - 40 q^{28} - 100 q^{31} - 48 q^{34} - 388 q^{37} + 140 q^{43} + 48 q^{46} - 138 q^{49} - 100 q^{52} + 144 q^{55} - 120 q^{58} - 94 q^{61} - 128 q^{64} + 62 q^{67} + 360 q^{70} - 4 q^{73} + 164 q^{76} - 106 q^{79} - 216 q^{82} - 144 q^{85} - 48 q^{88} + 28 q^{91} - 168 q^{94} - 286 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(162, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
162.3.d.a 162.d 9.d $4$ $4.414$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(-10\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+2\beta _{2}q^{4}+(-6\beta _{1}+6\beta _{3})q^{5}+\cdots\)
162.3.d.b 162.d 9.d $4$ $4.414$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+2\beta _{2}q^{4}+(3\beta _{1}-3\beta _{3})q^{5}+\cdots\)
162.3.d.c 162.d 9.d $8$ $4.414$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{24}^{5}q^{2}+2\zeta_{24}q^{4}+(2\zeta_{24}^{3}-\zeta_{24}^{6}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(162, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(162, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 2}\)