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 $0$

Related objects

Downloads

Learn more about

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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
168.4.u.a \(48\) \(9.912\) None \(0\) \(0\) \(0\) \(12\)

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

\( S_{4}^{\mathrm{old}}(168, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 2}\)