Properties

Label 126.4.m
Level $126$
Weight $4$
Character orbit 126.m
Rep. character $\chi_{126}(41,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $48$
Newform subspaces $1$
Sturm bound $96$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 126.m (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(96\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(126, [\chi])\).

Total New Old
Modular forms 152 48 104
Cusp forms 136 48 88
Eisenstein series 16 0 16

Trace form

\( 48q + 96q^{4} - 12q^{7} - 36q^{9} + O(q^{10}) \) \( 48q + 96q^{4} - 12q^{7} - 36q^{9} + 24q^{11} - 132q^{14} - 120q^{15} - 384q^{16} + 120q^{18} + 180q^{21} + 348q^{23} - 600q^{25} - 96q^{28} - 84q^{29} + 192q^{30} + 96q^{36} - 672q^{37} + 1368q^{39} + 1128q^{42} + 84q^{43} - 1008q^{46} - 42q^{49} + 456q^{50} + 2016q^{51} - 528q^{56} + 732q^{57} + 504q^{58} - 1008q^{60} - 774q^{63} - 3072q^{64} - 6972q^{65} + 1176q^{67} + 216q^{70} - 384q^{72} + 2520q^{74} + 1500q^{77} + 2832q^{78} + 348q^{79} + 2268q^{81} - 1080q^{84} + 720q^{85} + 1200q^{86} + 180q^{91} + 1392q^{92} + 5232q^{93} - 5892q^{95} + 972q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(126, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
126.4.m.a \(48\) \(7.434\) None \(0\) \(0\) \(0\) \(-12\)

Decomposition of \(S_{4}^{\mathrm{old}}(126, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(126, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)