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Properties

Label 126.4.e
Level $126$
Weight $4$
Character orbit 126.e
Rep. character $\chi_{126}(25,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $48$
Newform subspaces $2$
Sturm bound $96$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 126.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(96\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(5\)

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

\( 48 q + 192 q^{4} + 20 q^{5} + 8 q^{6} + 12 q^{7} + 4 q^{9} + O(q^{10}) \) \( 48 q + 192 q^{4} + 20 q^{5} + 8 q^{6} + 12 q^{7} + 4 q^{9} - 8 q^{11} + 24 q^{13} + 44 q^{14} - 212 q^{15} + 768 q^{16} + 184 q^{17} + 120 q^{18} - 120 q^{19} + 80 q^{20} + 64 q^{21} + 136 q^{23} + 32 q^{24} - 600 q^{25} + 272 q^{26} - 414 q^{27} + 48 q^{28} - 430 q^{29} - 80 q^{30} + 60 q^{31} + 200 q^{33} - 824 q^{35} + 16 q^{36} + 168 q^{37} + 456 q^{38} - 98 q^{39} + 930 q^{41} + 792 q^{42} + 42 q^{43} - 32 q^{44} - 874 q^{45} + 252 q^{46} - 132 q^{47} - 438 q^{49} + 488 q^{50} - 1336 q^{51} + 96 q^{52} - 156 q^{53} + 1196 q^{54} + 612 q^{55} + 176 q^{56} - 2148 q^{57} - 252 q^{58} - 2416 q^{59} - 848 q^{60} + 1716 q^{61} - 1000 q^{62} - 4302 q^{63} + 3072 q^{64} - 2616 q^{65} - 1984 q^{66} + 1176 q^{67} + 736 q^{68} - 2152 q^{69} - 324 q^{70} + 1024 q^{71} + 480 q^{72} + 672 q^{73} - 420 q^{74} - 3218 q^{75} - 480 q^{76} - 1276 q^{77} + 128 q^{78} + 780 q^{79} + 320 q^{80} - 1736 q^{81} + 940 q^{83} + 256 q^{84} - 720 q^{85} + 552 q^{86} + 6340 q^{87} + 882 q^{89} - 1732 q^{90} - 750 q^{91} + 544 q^{92} + 592 q^{93} - 2448 q^{94} + 7900 q^{95} + 128 q^{96} + 528 q^{97} + 48 q^{98} + 8428 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
126.4.e.a 126.e 63.h $24$ $7.434$ None \(-48\) \(-2\) \(10\) \(-5\) $\mathrm{SU}(2)[C_{3}]$
126.4.e.b 126.e 63.h $24$ $7.434$ None \(48\) \(2\) \(10\) \(17\) $\mathrm{SU}(2)[C_{3}]$

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

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