Properties

Label 168.4.q
Level $168$
Weight $4$
Character orbit 168.q
Rep. character $\chi_{168}(25,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $24$
Newform subspaces $6$
Sturm bound $128$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 168.q (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 6 \)
Sturm bound: \(128\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 208 24 184
Cusp forms 176 24 152
Eisenstein series 32 0 32

Trace form

\( 24q - 6q^{3} + 24q^{7} - 108q^{9} + O(q^{10}) \) \( 24q - 6q^{3} + 24q^{7} - 108q^{9} - 28q^{11} - 140q^{13} - 84q^{15} - 4q^{17} - 250q^{19} - 60q^{21} + 84q^{23} - 138q^{25} + 108q^{27} - 280q^{29} + 168q^{31} + 114q^{33} - 708q^{35} - 318q^{37} - 210q^{39} - 888q^{41} - 116q^{43} + 268q^{49} + 60q^{51} + 1180q^{53} + 3468q^{55} + 612q^{57} - 768q^{59} + 1572q^{61} + 54q^{63} - 992q^{65} - 1014q^{67} - 1704q^{69} - 1072q^{71} + 1550q^{73} - 1362q^{75} - 1140q^{77} + 1268q^{79} - 972q^{81} + 9032q^{83} + 4360q^{85} + 474q^{87} + 2368q^{89} - 450q^{91} - 1146q^{93} - 3392q^{95} - 5860q^{97} + 504q^{99} + O(q^{100}) \)

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.q.a \(2\) \(9.912\) \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(-7\) \(-35\) \(q+3\zeta_{6}q^{3}+(-7+7\zeta_{6})q^{5}+(-14+\cdots)q^{7}+\cdots\)
168.4.q.b \(2\) \(9.912\) \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(-2\) \(35\) \(q+3\zeta_{6}q^{3}+(-2+2\zeta_{6})q^{5}+(21-7\zeta_{6})q^{7}+\cdots\)
168.4.q.c \(2\) \(9.912\) \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(11\) \(7\) \(q+3\zeta_{6}q^{3}+(11-11\zeta_{6})q^{5}+(14-21\zeta_{6})q^{7}+\cdots\)
168.4.q.d \(4\) \(9.912\) \(\Q(\sqrt{-3}, \sqrt{505})\) None \(0\) \(6\) \(-9\) \(0\) \(q+(3-3\beta _{2})q^{3}+(\beta _{1}-5\beta _{2})q^{5}+(8-17\beta _{2}+\cdots)q^{7}+\cdots\)
168.4.q.e \(6\) \(9.912\) 6.0.\(\cdots\).1 None \(0\) \(-9\) \(11\) \(-1\) \(q+(-3+3\beta _{3})q^{3}+(4\beta _{3}-\beta _{4}-\beta _{5})q^{5}+\cdots\)
168.4.q.f \(8\) \(9.912\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(-12\) \(-4\) \(18\) \(q+3\beta _{1}q^{3}+(-1-\beta _{1}+\beta _{6})q^{5}+(2+\cdots)q^{7}+\cdots\)

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

\( S_{4}^{\mathrm{old}}(168, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 2}\)