Properties

Label 126.3
Level 126
Weight 3
Dimension 216
Nonzero newspaces 10
Newform subspaces 14
Sturm bound 2592
Trace bound 9

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Defining parameters

Level: \( N \) = \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 10 \)
Newform subspaces: \( 14 \)
Sturm bound: \(2592\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(126))\).

Total New Old
Modular forms 960 216 744
Cusp forms 768 216 552
Eisenstein series 192 0 192

Trace form

\( 216q - 4q^{4} + 30q^{5} + 24q^{6} + 14q^{7} - 24q^{9} + O(q^{10}) \) \( 216q - 4q^{4} + 30q^{5} + 24q^{6} + 14q^{7} - 24q^{9} - 18q^{11} - 24q^{12} + 44q^{13} + 72q^{14} + 84q^{15} + 24q^{16} + 186q^{17} + 96q^{18} + 206q^{19} + 72q^{20} + 6q^{21} + 48q^{22} - 222q^{23} - 48q^{24} - 312q^{25} - 264q^{26} - 252q^{27} - 108q^{28} - 420q^{29} - 264q^{30} - 142q^{31} + 84q^{33} - 120q^{34} + 390q^{35} - 24q^{36} + 10q^{37} + 132q^{38} + 276q^{39} + 252q^{41} + 48q^{42} + 148q^{43} + 36q^{44} - 84q^{45} - 12q^{46} - 366q^{47} - 48q^{48} - 66q^{49} - 384q^{50} - 1008q^{51} + 152q^{52} - 1194q^{53} - 648q^{54} - 72q^{55} - 24q^{56} - 768q^{57} + 240q^{58} - 510q^{59} - 72q^{60} - 274q^{61} - 54q^{63} + 128q^{64} - 12q^{65} + 528q^{66} - 210q^{67} + 132q^{68} + 972q^{69} - 240q^{70} + 984q^{71} + 192q^{72} + 350q^{73} + 384q^{74} + 1872q^{75} - 328q^{76} + 1044q^{77} + 480q^{78} + 270q^{79} + 24q^{80} + 528q^{81} - 144q^{82} + 756q^{83} + 144q^{84} - 132q^{85} + 672q^{86} + 576q^{87} + 120q^{88} + 1278q^{89} + 672q^{90} + 476q^{91} + 384q^{92} + 240q^{93} + 300q^{94} + 474q^{95} + 164q^{97} + 744q^{98} - 156q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(126))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
126.3.b \(\chi_{126}(71, \cdot)\) 126.3.b.a 4 1
126.3.c \(\chi_{126}(55, \cdot)\) 126.3.c.a 4 1
126.3.c.b 4
126.3.i \(\chi_{126}(65, \cdot)\) 126.3.i.a 32 2
126.3.j \(\chi_{126}(31, \cdot)\) 126.3.j.a 32 2
126.3.n \(\chi_{126}(19, \cdot)\) 126.3.n.a 4 2
126.3.n.b 4
126.3.n.c 4
126.3.o \(\chi_{126}(13, \cdot)\) 126.3.o.a 32 2
126.3.p \(\chi_{126}(103, \cdot)\) 126.3.p.a 32 2
126.3.q \(\chi_{126}(29, \cdot)\) 126.3.q.a 24 2
126.3.r \(\chi_{126}(11, \cdot)\) 126.3.r.a 32 2
126.3.s \(\chi_{126}(53, \cdot)\) 126.3.s.a 4 2
126.3.s.b 4

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(126))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(126)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 2}\)