Properties

Label 162.3.b
Level $162$
Weight $3$
Character orbit 162.b
Rep. character $\chi_{162}(161,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $2$
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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
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 66 8 58
Cusp forms 42 8 34
Eisenstein series 24 0 24

Trace form

\( 8 q - 16 q^{4} + 4 q^{7} + O(q^{10}) \) \( 8 q - 16 q^{4} + 4 q^{7} + 12 q^{10} - 44 q^{13} + 32 q^{16} + 16 q^{19} + 24 q^{22} + 20 q^{25} - 8 q^{28} - 44 q^{31} - 108 q^{34} + 52 q^{37} - 24 q^{40} + 4 q^{43} - 24 q^{46} + 276 q^{49} + 88 q^{52} - 324 q^{55} + 132 q^{58} - 176 q^{61} - 64 q^{64} + 172 q^{67} + 24 q^{70} + 16 q^{73} - 32 q^{76} + 76 q^{79} + 120 q^{82} - 396 q^{85} - 48 q^{88} + 500 q^{91} - 264 q^{94} + 4 q^{97} + O(q^{100}) \)

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.b.a 162.b 3.b $4$ $4.414$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-2q^{4}+\beta _{2}q^{5}+(-1+\beta _{3})q^{7}+\cdots\)
162.3.b.b 162.b 3.b $4$ $4.414$ \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-2q^{4}+(\beta _{1}-\beta _{2})q^{5}+(2+2\beta _{3})q^{7}+\cdots\)

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

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