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Properties

Label 162.6.c
Level $162$
Weight $6$
Character orbit 162.c
Rep. character $\chi_{162}(55,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $40$
Newform subspaces $16$
Sturm bound $162$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 162.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 16 \)
Sturm bound: \(162\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(162, [\chi])\).

Total New Old
Modular forms 294 40 254
Cusp forms 246 40 206
Eisenstein series 48 0 48

Trace form

\( 40 q - 320 q^{4} + 290 q^{7} + O(q^{10}) \) \( 40 q - 320 q^{4} + 290 q^{7} - 1810 q^{13} - 5120 q^{16} + 2408 q^{19} + 1896 q^{22} - 19112 q^{25} - 9280 q^{28} + 6158 q^{31} + 7656 q^{34} - 91636 q^{37} - 16804 q^{43} + 37920 q^{46} + 9510 q^{49} - 28960 q^{52} - 198036 q^{55} + 25080 q^{58} + 39662 q^{61} + 163840 q^{64} - 10204 q^{67} - 60120 q^{70} + 41624 q^{73} - 19264 q^{76} - 155200 q^{79} + 42336 q^{82} - 14994 q^{85} + 30336 q^{88} - 248384 q^{91} + 96240 q^{94} + 268250 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(162, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
162.6.c.a 162.c 9.c $2$ $25.982$ \(\Q(\sqrt{-3}) \) None \(-4\) \(0\) \(-96\) \(148\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-4+4\zeta_{6})q^{2}-2^{4}\zeta_{6}q^{4}-96\zeta_{6}q^{5}+\cdots\)
162.6.c.b 162.c 9.c $2$ $25.982$ \(\Q(\sqrt{-3}) \) None \(-4\) \(0\) \(-33\) \(-59\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-4+4\zeta_{6})q^{2}-2^{4}\zeta_{6}q^{4}-33\zeta_{6}q^{5}+\cdots\)
162.6.c.c 162.c 9.c $2$ $25.982$ \(\Q(\sqrt{-3}) \) None \(-4\) \(0\) \(-24\) \(-77\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-4+4\zeta_{6})q^{2}-2^{4}\zeta_{6}q^{4}-24\zeta_{6}q^{5}+\cdots\)
162.6.c.d 162.c 9.c $2$ $25.982$ \(\Q(\sqrt{-3}) \) None \(-4\) \(0\) \(-21\) \(-74\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-4+4\zeta_{6})q^{2}-2^{4}\zeta_{6}q^{4}-21\zeta_{6}q^{5}+\cdots\)
162.6.c.e 162.c 9.c $2$ $25.982$ \(\Q(\sqrt{-3}) \) None \(-4\) \(0\) \(66\) \(-176\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-4+4\zeta_{6})q^{2}-2^{4}\zeta_{6}q^{4}+66\zeta_{6}q^{5}+\cdots\)
162.6.c.f 162.c 9.c $2$ $25.982$ \(\Q(\sqrt{-3}) \) None \(-4\) \(0\) \(84\) \(193\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-4+4\zeta_{6})q^{2}-2^{4}\zeta_{6}q^{4}+84\zeta_{6}q^{5}+\cdots\)
162.6.c.g 162.c 9.c $2$ $25.982$ \(\Q(\sqrt{-3}) \) None \(4\) \(0\) \(-84\) \(193\) $\mathrm{SU}(2)[C_{3}]$ \(q+(4-4\zeta_{6})q^{2}-2^{4}\zeta_{6}q^{4}-84\zeta_{6}q^{5}+\cdots\)
162.6.c.h 162.c 9.c $2$ $25.982$ \(\Q(\sqrt{-3}) \) None \(4\) \(0\) \(-66\) \(-176\) $\mathrm{SU}(2)[C_{3}]$ \(q+(4-4\zeta_{6})q^{2}-2^{4}\zeta_{6}q^{4}-66\zeta_{6}q^{5}+\cdots\)
162.6.c.i 162.c 9.c $2$ $25.982$ \(\Q(\sqrt{-3}) \) None \(4\) \(0\) \(21\) \(-74\) $\mathrm{SU}(2)[C_{3}]$ \(q+(4-4\zeta_{6})q^{2}-2^{4}\zeta_{6}q^{4}+21\zeta_{6}q^{5}+\cdots\)
162.6.c.j 162.c 9.c $2$ $25.982$ \(\Q(\sqrt{-3}) \) None \(4\) \(0\) \(24\) \(-77\) $\mathrm{SU}(2)[C_{3}]$ \(q+(4-4\zeta_{6})q^{2}-2^{4}\zeta_{6}q^{4}+24\zeta_{6}q^{5}+\cdots\)
162.6.c.k 162.c 9.c $2$ $25.982$ \(\Q(\sqrt{-3}) \) None \(4\) \(0\) \(33\) \(-59\) $\mathrm{SU}(2)[C_{3}]$ \(q+(4-4\zeta_{6})q^{2}-2^{4}\zeta_{6}q^{4}+33\zeta_{6}q^{5}+\cdots\)
162.6.c.l 162.c 9.c $2$ $25.982$ \(\Q(\sqrt{-3}) \) None \(4\) \(0\) \(96\) \(148\) $\mathrm{SU}(2)[C_{3}]$ \(q+(4-4\zeta_{6})q^{2}-2^{4}\zeta_{6}q^{4}+96\zeta_{6}q^{5}+\cdots\)
162.6.c.m 162.c 9.c $4$ $25.982$ \(\Q(\sqrt{-3}, \sqrt{-307})\) None \(-8\) \(0\) \(12\) \(14\) $\mathrm{SU}(2)[C_{3}]$ \(q+4\beta _{1}q^{2}+(-2^{4}-2^{4}\beta _{1})q^{4}+(6+6\beta _{1}+\cdots)q^{5}+\cdots\)
162.6.c.n 162.c 9.c $4$ $25.982$ \(\Q(\zeta_{12})\) None \(-8\) \(0\) \(12\) \(176\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-4+4\zeta_{12})q^{2}-2^{4}\zeta_{12}q^{4}+(6\zeta_{12}+\cdots)q^{5}+\cdots\)
162.6.c.o 162.c 9.c $4$ $25.982$ \(\Q(\sqrt{-3}, \sqrt{-307})\) None \(8\) \(0\) \(-12\) \(14\) $\mathrm{SU}(2)[C_{3}]$ \(q-4\beta _{1}q^{2}+(-2^{4}-2^{4}\beta _{1})q^{4}+(-6+\cdots)q^{5}+\cdots\)
162.6.c.p 162.c 9.c $4$ $25.982$ \(\Q(\zeta_{12})\) None \(8\) \(0\) \(-12\) \(176\) $\mathrm{SU}(2)[C_{3}]$ \(q+(4-4\zeta_{12})q^{2}-2^{4}\zeta_{12}q^{4}+(-6\zeta_{12}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(162, [\chi])\) into lower level spaces

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