Properties

Label 126.4.g
Level $126$
Weight $4$
Character orbit 126.g
Rep. character $\chi_{126}(37,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $20$
Newform subspaces $7$
Sturm bound $96$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 126.g (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 7 \)
Sturm bound: \(96\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 160 20 140
Cusp forms 128 20 108
Eisenstein series 32 0 32

Trace form

\( 20q - 40q^{4} - 18q^{5} - 8q^{7} + O(q^{10}) \) \( 20q - 40q^{4} - 18q^{5} - 8q^{7} + 8q^{10} + 6q^{11} - 192q^{13} - 72q^{14} - 160q^{16} - 150q^{17} + 46q^{19} + 144q^{20} + 256q^{22} + 210q^{23} - 68q^{25} - 120q^{26} + 40q^{28} - 336q^{29} - 138q^{31} - 512q^{34} - 426q^{35} - 242q^{37} - 192q^{38} + 32q^{40} + 2016q^{41} + 1288q^{43} + 24q^{44} + 40q^{46} + 102q^{47} + 1412q^{49} - 1824q^{50} + 384q^{52} - 1182q^{53} - 1916q^{55} + 288q^{56} - 136q^{58} + 90q^{59} - 294q^{61} + 3744q^{62} + 1280q^{64} + 1524q^{65} + 1226q^{67} - 600q^{68} - 1520q^{70} - 672q^{71} + 1142q^{73} - 312q^{74} - 368q^{76} - 2226q^{77} + 1266q^{79} - 288q^{80} + 1200q^{82} + 2568q^{83} - 4892q^{85} - 984q^{86} - 512q^{88} - 2754q^{89} + 2100q^{91} - 1680q^{92} - 216q^{94} - 1974q^{95} - 160q^{97} + 2880q^{98} + O(q^{100}) \)

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.g.a \(2\) \(7.434\) \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(-15\) \(35\) \(q+(-2+2\zeta_{6})q^{2}-4\zeta_{6}q^{4}+(-15+\cdots)q^{5}+\cdots\)
126.4.g.b \(2\) \(7.434\) \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(-6\) \(-7\) \(q+(-2+2\zeta_{6})q^{2}-4\zeta_{6}q^{4}+(-6+6\zeta_{6})q^{5}+\cdots\)
126.4.g.c \(2\) \(7.434\) \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(7\) \(-20\) \(q+(-2+2\zeta_{6})q^{2}-4\zeta_{6}q^{4}+(7-7\zeta_{6})q^{5}+\cdots\)
126.4.g.d \(2\) \(7.434\) \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(-9\) \(-28\) \(q+(2-2\zeta_{6})q^{2}-4\zeta_{6}q^{4}+(-9+9\zeta_{6})q^{5}+\cdots\)
126.4.g.e \(4\) \(7.434\) \(\Q(\sqrt{-3}, \sqrt{193})\) None \(-4\) \(0\) \(7\) \(6\) \(q-2\beta _{2}q^{2}+(-4+4\beta _{2})q^{4}+(\beta _{1}+3\beta _{2}+\cdots)q^{5}+\cdots\)
126.4.g.f \(4\) \(7.434\) \(\Q(\sqrt{-3}, \sqrt{193})\) None \(4\) \(0\) \(-7\) \(6\) \(q+2\beta _{2}q^{2}+(-4+4\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
126.4.g.g \(4\) \(7.434\) \(\Q(\sqrt{-3}, \sqrt{1345})\) None \(4\) \(0\) \(5\) \(0\) \(q+2\beta _{2}q^{2}+(-4+4\beta _{2})q^{4}+(\beta _{1}+2\beta _{2}+\cdots)q^{5}+\cdots\)

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

\( S_{4}^{\mathrm{old}}(126, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)