Properties

Label 126.2
Level 126
Weight 2
Dimension 110
Nonzero newspaces 9
Newforms 22
Sturm bound 1728
Trace bound 9

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Defining parameters

Level: \( N \) = \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 9 \)
Newforms: \( 22 \)
Sturm bound: \(1728\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(126))\).

Total New Old
Modular forms 528 110 418
Cusp forms 337 110 227
Eisenstein series 191 0 191

Trace form

\(110q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 6q^{6} \) \(\mathstrut +\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 4q^{8} \) \(\mathstrut -\mathstrut 6q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(110q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 6q^{6} \) \(\mathstrut +\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 4q^{8} \) \(\mathstrut -\mathstrut 6q^{9} \) \(\mathstrut +\mathstrut 6q^{10} \) \(\mathstrut +\mathstrut 6q^{11} \) \(\mathstrut +\mathstrut 6q^{13} \) \(\mathstrut -\mathstrut 16q^{14} \) \(\mathstrut -\mathstrut 24q^{15} \) \(\mathstrut -\mathstrut 4q^{16} \) \(\mathstrut -\mathstrut 36q^{17} \) \(\mathstrut -\mathstrut 12q^{18} \) \(\mathstrut -\mathstrut 30q^{19} \) \(\mathstrut -\mathstrut 18q^{20} \) \(\mathstrut -\mathstrut 42q^{21} \) \(\mathstrut -\mathstrut 42q^{22} \) \(\mathstrut -\mathstrut 60q^{23} \) \(\mathstrut -\mathstrut 6q^{24} \) \(\mathstrut -\mathstrut 40q^{25} \) \(\mathstrut -\mathstrut 38q^{26} \) \(\mathstrut -\mathstrut 36q^{27} \) \(\mathstrut -\mathstrut 4q^{28} \) \(\mathstrut -\mathstrut 12q^{29} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut -\mathstrut 12q^{31} \) \(\mathstrut +\mathstrut 2q^{32} \) \(\mathstrut -\mathstrut 6q^{33} \) \(\mathstrut +\mathstrut 6q^{34} \) \(\mathstrut -\mathstrut 30q^{35} \) \(\mathstrut -\mathstrut 6q^{36} \) \(\mathstrut +\mathstrut 8q^{37} \) \(\mathstrut +\mathstrut 16q^{38} \) \(\mathstrut -\mathstrut 36q^{39} \) \(\mathstrut +\mathstrut 6q^{40} \) \(\mathstrut -\mathstrut 30q^{41} \) \(\mathstrut +\mathstrut 2q^{43} \) \(\mathstrut +\mathstrut 24q^{44} \) \(\mathstrut -\mathstrut 48q^{45} \) \(\mathstrut +\mathstrut 48q^{46} \) \(\mathstrut -\mathstrut 48q^{47} \) \(\mathstrut -\mathstrut 6q^{48} \) \(\mathstrut -\mathstrut 28q^{49} \) \(\mathstrut +\mathstrut 50q^{50} \) \(\mathstrut +\mathstrut 18q^{51} \) \(\mathstrut -\mathstrut 6q^{52} \) \(\mathstrut +\mathstrut 24q^{53} \) \(\mathstrut +\mathstrut 54q^{54} \) \(\mathstrut +\mathstrut 8q^{56} \) \(\mathstrut +\mathstrut 90q^{57} \) \(\mathstrut -\mathstrut 12q^{58} \) \(\mathstrut +\mathstrut 120q^{59} \) \(\mathstrut +\mathstrut 72q^{60} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut +\mathstrut 100q^{62} \) \(\mathstrut +\mathstrut 180q^{63} \) \(\mathstrut -\mathstrut 2q^{64} \) \(\mathstrut +\mathstrut 168q^{65} \) \(\mathstrut +\mathstrut 96q^{66} \) \(\mathstrut -\mathstrut 26q^{67} \) \(\mathstrut +\mathstrut 54q^{68} \) \(\mathstrut +\mathstrut 108q^{69} \) \(\mathstrut -\mathstrut 18q^{70} \) \(\mathstrut +\mathstrut 120q^{71} \) \(\mathstrut -\mathstrut 6q^{72} \) \(\mathstrut -\mathstrut 24q^{73} \) \(\mathstrut +\mathstrut 64q^{74} \) \(\mathstrut +\mathstrut 114q^{75} \) \(\mathstrut +\mathstrut 66q^{77} \) \(\mathstrut +\mathstrut 60q^{78} \) \(\mathstrut +\mathstrut 4q^{79} \) \(\mathstrut +\mathstrut 6q^{80} \) \(\mathstrut +\mathstrut 6q^{81} \) \(\mathstrut +\mathstrut 30q^{83} \) \(\mathstrut +\mathstrut 6q^{84} \) \(\mathstrut +\mathstrut 60q^{85} \) \(\mathstrut +\mathstrut 10q^{86} \) \(\mathstrut -\mathstrut 108q^{87} \) \(\mathstrut -\mathstrut 18q^{88} \) \(\mathstrut -\mathstrut 84q^{89} \) \(\mathstrut -\mathstrut 48q^{90} \) \(\mathstrut -\mathstrut 66q^{91} \) \(\mathstrut -\mathstrut 36q^{92} \) \(\mathstrut -\mathstrut 108q^{93} \) \(\mathstrut -\mathstrut 48q^{94} \) \(\mathstrut -\mathstrut 144q^{95} \) \(\mathstrut -\mathstrut 12q^{96} \) \(\mathstrut -\mathstrut 54q^{97} \) \(\mathstrut -\mathstrut 76q^{98} \) \(\mathstrut -\mathstrut 156q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(126))\)

We only show spaces with even 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
126.2.a \(\chi_{126}(1, \cdot)\) 126.2.a.a 1 1
126.2.a.b 1
126.2.d \(\chi_{126}(125, \cdot)\) None 0 1
126.2.e \(\chi_{126}(25, \cdot)\) 126.2.e.a 2 2
126.2.e.b 2
126.2.e.c 6
126.2.e.d 6
126.2.f \(\chi_{126}(43, \cdot)\) 126.2.f.a 2 2
126.2.f.b 2
126.2.f.c 4
126.2.f.d 4
126.2.g \(\chi_{126}(37, \cdot)\) 126.2.g.a 2 2
126.2.g.b 2
126.2.g.c 2
126.2.g.d 2
126.2.h \(\chi_{126}(67, \cdot)\) 126.2.h.a 2 2
126.2.h.b 2
126.2.h.c 6
126.2.h.d 6
126.2.k \(\chi_{126}(17, \cdot)\) 126.2.k.a 8 2
126.2.l \(\chi_{126}(5, \cdot)\) 126.2.l.a 16 2
126.2.m \(\chi_{126}(41, \cdot)\) 126.2.m.a 16 2
126.2.t \(\chi_{126}(47, \cdot)\) 126.2.t.a 16 2

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(126))\) into lower level spaces

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