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Properties

Label 168.4.u
Level $168$
Weight $4$
Character orbit 168.u
Rep. character $\chi_{168}(17,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $48$
Newform subspaces $1$
Sturm bound $128$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 168.u (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(128\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(168, [\chi])\).

Total New Old
Modular forms 208 48 160
Cusp forms 176 48 128
Eisenstein series 32 0 32

Trace form

\( 48 q + 12 q^{7} + 14 q^{9} + O(q^{10}) \) \( 48 q + 12 q^{7} + 14 q^{9} - 88 q^{15} - 270 q^{19} + 50 q^{21} - 438 q^{25} + 216 q^{31} - 372 q^{33} + 66 q^{37} + 242 q^{39} + 900 q^{43} - 294 q^{45} + 60 q^{49} - 138 q^{51} + 1384 q^{57} + 108 q^{61} + 1096 q^{63} + 6 q^{67} - 1206 q^{73} - 594 q^{75} - 588 q^{79} - 54 q^{81} - 240 q^{85} - 3522 q^{87} + 234 q^{91} - 608 q^{93} + 1988 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(168, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
168.4.u.a 168.u 21.g $48$ $9.912$ None \(0\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{4}^{\mathrm{old}}(168, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(168, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 3}\)