Properties

Label 126.10
Level 126
Weight 10
Dimension 982
Nonzero newspaces 10
Sturm bound 8640
Trace bound 9

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Defining parameters

Level: \( N \) = \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 10 \)
Sturm bound: \(8640\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(126))\).

Total New Old
Modular forms 3984 982 3002
Cusp forms 3792 982 2810
Eisenstein series 192 0 192

Trace form

\( 982 q + 32 q^{2} - 150 q^{3} + 2560 q^{4} + 4740 q^{5} + 6048 q^{6} - 10628 q^{7} - 16384 q^{8} - 27114 q^{9} + O(q^{10}) \) \( 982 q + 32 q^{2} - 150 q^{3} + 2560 q^{4} + 4740 q^{5} + 6048 q^{6} - 10628 q^{7} - 16384 q^{8} - 27114 q^{9} + 110688 q^{10} + 54636 q^{11} - 150528 q^{12} + 56582 q^{13} + 832256 q^{14} + 516252 q^{15} + 655360 q^{16} + 749682 q^{17} + 552768 q^{18} - 449560 q^{19} - 1230336 q^{20} - 4406220 q^{21} + 1063776 q^{22} + 12456426 q^{23} + 1548288 q^{24} - 1727696 q^{25} - 14167136 q^{26} - 31353624 q^{27} + 644608 q^{28} + 20330736 q^{29} + 33504576 q^{30} + 14517374 q^{31} + 2097152 q^{32} - 83008374 q^{33} - 18204576 q^{34} - 21909288 q^{35} + 625152 q^{36} + 68749814 q^{37} + 12651520 q^{38} + 112055160 q^{39} + 28336128 q^{40} + 35374362 q^{41} - 6302208 q^{42} - 127485814 q^{43} - 117004800 q^{44} - 174472716 q^{45} + 30249984 q^{46} + 450440358 q^{47} + 48365568 q^{48} - 85331810 q^{49} - 315210976 q^{50} - 271206450 q^{51} - 41840128 q^{52} + 52034946 q^{53} - 54935712 q^{54} - 242773884 q^{55} + 91062272 q^{56} + 312807918 q^{57} + 743691072 q^{58} + 924426750 q^{59} + 227902464 q^{60} - 1566870556 q^{61} - 134037440 q^{62} + 1307308914 q^{63} - 436207616 q^{64} + 1108359060 q^{65} + 516189696 q^{66} + 2301920312 q^{67} - 1004497920 q^{68} - 3164474736 q^{69} - 640782624 q^{70} - 3546367080 q^{71} + 35364864 q^{72} + 909876926 q^{73} + 2787569152 q^{74} + 5186203950 q^{75} + 729743360 q^{76} - 1142774502 q^{77} - 3204850752 q^{78} + 1103465198 q^{79} + 445120512 q^{80} - 2957824974 q^{81} - 4356016128 q^{82} - 1926363570 q^{83} + 56787456 q^{84} - 1579988616 q^{85} + 1050114208 q^{86} + 4902196428 q^{87} + 1966989312 q^{88} + 5659127754 q^{89} - 673533696 q^{90} - 5303440210 q^{91} - 3104013312 q^{92} - 5403997644 q^{93} - 4468732416 q^{94} - 6289076034 q^{95} + 994050048 q^{96} + 8249846378 q^{97} + 10066346816 q^{98} + 8347246728 q^{99} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(126))\)

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
126.10.a \(\chi_{126}(1, \cdot)\) 126.10.a.a 1 1
126.10.a.b 1
126.10.a.c 1
126.10.a.d 1
126.10.a.e 1
126.10.a.f 1
126.10.a.g 1
126.10.a.h 1
126.10.a.i 2
126.10.a.j 2
126.10.a.k 2
126.10.a.l 2
126.10.a.m 2
126.10.a.n 2
126.10.a.o 2
126.10.d \(\chi_{126}(125, \cdot)\) 126.10.d.a 24 1
126.10.e \(\chi_{126}(25, \cdot)\) n/a 144 2
126.10.f \(\chi_{126}(43, \cdot)\) n/a 108 2
126.10.g \(\chi_{126}(37, \cdot)\) 126.10.g.a 2 2
126.10.g.b 4
126.10.g.c 4
126.10.g.d 6
126.10.g.e 6
126.10.g.f 6
126.10.g.g 8
126.10.g.h 12
126.10.g.i 12
126.10.h \(\chi_{126}(67, \cdot)\) n/a 144 2
126.10.k \(\chi_{126}(17, \cdot)\) 126.10.k.a 48 2
126.10.l \(\chi_{126}(5, \cdot)\) n/a 144 2
126.10.m \(\chi_{126}(41, \cdot)\) n/a 144 2
126.10.t \(\chi_{126}(47, \cdot)\) n/a 144 2

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(126))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(126)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 2}\)