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Properties

Label 162.4.c
Level $162$
Weight $4$
Character orbit 162.c
Rep. character $\chi_{162}(55,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $24$
Newform subspaces $10$
Sturm bound $108$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 162.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 10 \)
Sturm bound: \(108\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(162, [\chi])\).

Total New Old
Modular forms 186 24 162
Cusp forms 138 24 114
Eisenstein series 48 0 48

Trace form

\( 24 q - 48 q^{4} - 60 q^{7} + O(q^{10}) \) \( 24 q - 48 q^{4} - 60 q^{7} + 120 q^{13} - 192 q^{16} - 780 q^{19} + 36 q^{22} - 12 q^{25} + 480 q^{28} - 78 q^{31} - 180 q^{34} - 1392 q^{37} - 132 q^{43} - 1008 q^{46} + 1008 q^{49} + 480 q^{52} + 4644 q^{55} - 1260 q^{58} + 84 q^{61} + 1536 q^{64} - 1914 q^{67} - 540 q^{70} - 924 q^{73} + 1560 q^{76} + 4602 q^{79} + 3024 q^{82} + 1026 q^{85} + 144 q^{88} - 5196 q^{91} - 1224 q^{94} + 120 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(162, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
162.4.c.a 162.c 9.c $2$ $9.558$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(-12\) \(7\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{2}-4\zeta_{6}q^{4}-12\zeta_{6}q^{5}+\cdots\)
162.4.c.b 162.c 9.c $2$ $9.558$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(-3\) \(-29\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{2}-4\zeta_{6}q^{4}-3\zeta_{6}q^{5}+\cdots\)
162.4.c.c 162.c 9.c $2$ $9.558$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(6\) \(16\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{2}-4\zeta_{6}q^{4}+6\zeta_{6}q^{5}+\cdots\)
162.4.c.d 162.c 9.c $2$ $9.558$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(21\) \(-8\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{2}-4\zeta_{6}q^{4}+21\zeta_{6}q^{5}+\cdots\)
162.4.c.e 162.c 9.c $2$ $9.558$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(-21\) \(-8\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{2}-4\zeta_{6}q^{4}-21\zeta_{6}q^{5}+\cdots\)
162.4.c.f 162.c 9.c $2$ $9.558$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(-6\) \(16\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{2}-4\zeta_{6}q^{4}-6\zeta_{6}q^{5}+\cdots\)
162.4.c.g 162.c 9.c $2$ $9.558$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(3\) \(-29\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{2}-4\zeta_{6}q^{4}+3\zeta_{6}q^{5}+\cdots\)
162.4.c.h 162.c 9.c $2$ $9.558$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(12\) \(7\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{2}-4\zeta_{6}q^{4}+12\zeta_{6}q^{5}+\cdots\)
162.4.c.i 162.c 9.c $4$ $9.558$ \(\Q(\zeta_{12})\) None \(-4\) \(0\) \(-12\) \(-16\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{12})q^{2}-4\zeta_{12}q^{4}+(-6\zeta_{12}+\cdots)q^{5}+\cdots\)
162.4.c.j 162.c 9.c $4$ $9.558$ \(\Q(\zeta_{12})\) None \(4\) \(0\) \(12\) \(-16\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{12})q^{2}-4\zeta_{12}q^{4}+(6\zeta_{12}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(162, [\chi])\) into lower level spaces

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