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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
162.2.c.a \(2\) \(1.294\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-3\) \(4\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-3\zeta_{6}q^{5}+\cdots\)
162.2.c.b \(2\) \(1.294\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(3\) \(1\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+3\zeta_{6}q^{5}+\cdots\)
162.2.c.c \(2\) \(1.294\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-3\) \(1\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-3\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
162.2.c.d \(2\) \(1.294\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(3\) \(4\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+3\zeta_{6}q^{5}+(4+\cdots)q^{7}+\cdots\)

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

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