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Properties

Label 342.3.z
Level $342$
Weight $3$
Character orbit 342.z
Rep. character $\chi_{342}(91,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $96$
Newform subspaces $4$
Sturm bound $180$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 342.z (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 4 \)
Sturm bound: \(180\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(342, [\chi])\).

Total New Old
Modular forms 768 96 672
Cusp forms 672 96 576
Eisenstein series 96 0 96

Trace form

\( 96 q - 18 q^{7} + O(q^{10}) \) \( 96 q - 18 q^{7} + 30 q^{11} - 30 q^{13} - 48 q^{14} - 90 q^{17} - 72 q^{19} + 24 q^{20} + 132 q^{22} - 24 q^{23} - 180 q^{25} + 48 q^{26} - 48 q^{28} - 102 q^{29} - 108 q^{31} + 24 q^{34} + 258 q^{35} + 12 q^{38} + 18 q^{41} + 102 q^{43} + 96 q^{44} + 360 q^{46} + 402 q^{47} - 150 q^{49} + 432 q^{50} + 84 q^{52} + 114 q^{53} + 150 q^{55} - 48 q^{58} - 312 q^{59} + 12 q^{61} - 228 q^{62} + 384 q^{64} - 990 q^{65} - 204 q^{67} - 120 q^{68} - 240 q^{70} - 216 q^{71} - 204 q^{73} - 144 q^{74} + 72 q^{76} - 144 q^{77} - 126 q^{79} - 480 q^{82} + 18 q^{83} - 180 q^{85} - 12 q^{86} - 444 q^{89} - 132 q^{91} + 156 q^{92} - 138 q^{95} + 216 q^{97} - 48 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(342, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
342.3.z.a 342.z 19.f $12$ $9.319$ 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(18\) $\mathrm{SU}(2)[C_{18}]$ \(q+(-\beta _{1}+\beta _{7})q^{2}-2\beta _{8}q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots\)
342.3.z.b 342.z 19.f $24$ $9.319$ None \(0\) \(0\) \(0\) \(-18\) $\mathrm{SU}(2)[C_{18}]$
342.3.z.c 342.z 19.f $24$ $9.319$ None \(0\) \(0\) \(0\) \(18\) $\mathrm{SU}(2)[C_{18}]$
342.3.z.d 342.z 19.f $36$ $9.319$ None \(0\) \(0\) \(0\) \(-36\) $\mathrm{SU}(2)[C_{18}]$

Decomposition of \(S_{3}^{\mathrm{old}}(342, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(342, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 2}\)