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Properties

Label 126.4
Level 126
Weight 4
Dimension 328
Nonzero newspaces 10
Newform subspaces 28
Sturm bound 3456
Trace bound 9

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Defining parameters

Level: \( N \) = \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 10 \)
Newform subspaces: \( 28 \)
Sturm bound: \(3456\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(126))\).

Total New Old
Modular forms 1392 328 1064
Cusp forms 1200 328 872
Eisenstein series 192 0 192

Trace form

\( 328 q - 8 q^{2} - 6 q^{3} + 16 q^{4} - 48 q^{5} + 36 q^{6} - 44 q^{7} + 16 q^{8} + 210 q^{9} + O(q^{10}) \) \( 328 q - 8 q^{2} - 6 q^{3} + 16 q^{4} - 48 q^{5} + 36 q^{6} - 44 q^{7} + 16 q^{8} + 210 q^{9} + 60 q^{10} - 12 q^{11} - 48 q^{12} - 250 q^{13} - 464 q^{14} - 420 q^{15} + 64 q^{16} + 330 q^{17} + 24 q^{18} + 488 q^{19} + 264 q^{20} + 756 q^{21} + 732 q^{22} + 1578 q^{23} + 144 q^{24} + 826 q^{25} + 500 q^{26} - 792 q^{27} - 8 q^{28} - 1164 q^{29} - 264 q^{30} - 1978 q^{31} - 128 q^{32} - 2274 q^{33} - 1092 q^{34} - 1920 q^{35} - 1032 q^{36} + 158 q^{37} - 616 q^{38} + 2424 q^{39} + 240 q^{40} + 3642 q^{41} + 816 q^{42} + 1202 q^{43} + 888 q^{44} + 2796 q^{45} - 504 q^{46} + 1902 q^{47} + 288 q^{48} - 3224 q^{49} + 1408 q^{50} + 3582 q^{51} - 760 q^{52} - 2046 q^{53} - 1188 q^{54} + 900 q^{55} - 224 q^{56} - 5046 q^{57} + 1632 q^{58} - 3930 q^{59} - 2160 q^{60} + 5720 q^{61} + 824 q^{62} - 8622 q^{63} - 512 q^{64} - 7092 q^{65} - 5376 q^{66} - 4648 q^{67} - 3072 q^{68} - 6912 q^{69} - 804 q^{70} - 1608 q^{71} + 48 q^{72} - 3034 q^{73} + 1304 q^{74} + 5214 q^{75} - 256 q^{76} + 8622 q^{77} + 8280 q^{78} + 4382 q^{79} + 960 q^{80} + 294 q^{81} + 5016 q^{82} + 5262 q^{83} - 744 q^{84} + 5424 q^{85} - 4492 q^{86} + 1692 q^{87} - 2352 q^{88} - 4950 q^{89} - 4224 q^{90} - 6970 q^{91} + 528 q^{92} + 2748 q^{93} - 3000 q^{94} + 1374 q^{95} - 384 q^{96} - 2470 q^{97} + 3172 q^{98} + 1032 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(126))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
126.4.a \(\chi_{126}(1, \cdot)\) 126.4.a.a 1 1
126.4.a.b 1
126.4.a.c 1
126.4.a.d 1
126.4.a.e 1
126.4.a.f 1
126.4.a.g 1
126.4.a.h 1
126.4.d \(\chi_{126}(125, \cdot)\) 126.4.d.a 8 1
126.4.e \(\chi_{126}(25, \cdot)\) 126.4.e.a 24 2
126.4.e.b 24
126.4.f \(\chi_{126}(43, \cdot)\) 126.4.f.a 6 2
126.4.f.b 8
126.4.f.c 10
126.4.f.d 12
126.4.g \(\chi_{126}(37, \cdot)\) 126.4.g.a 2 2
126.4.g.b 2
126.4.g.c 2
126.4.g.d 2
126.4.g.e 4
126.4.g.f 4
126.4.g.g 4
126.4.h \(\chi_{126}(67, \cdot)\) 126.4.h.a 24 2
126.4.h.b 24
126.4.k \(\chi_{126}(17, \cdot)\) 126.4.k.a 16 2
126.4.l \(\chi_{126}(5, \cdot)\) 126.4.l.a 48 2
126.4.m \(\chi_{126}(41, \cdot)\) 126.4.m.a 48 2
126.4.t \(\chi_{126}(47, \cdot)\) 126.4.t.a 48 2

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(126))\) into lower level spaces

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