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Properties

Label 126.16
Level 126
Weight 16
Dimension 1638
Nonzero newspaces 10
Sturm bound 13824
Trace bound 9

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Defining parameters

Level: \( N \) = \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 16 \)
Nonzero newspaces: \( 10 \)
Sturm bound: \(13824\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_1(126))\).

Total New Old
Modular forms 6576 1638 4938
Cusp forms 6384 1638 4746
Eisenstein series 192 0 192

Trace form

\( 1638 q - 256 q^{2} + 8130 q^{3} + 294912 q^{4} - 353388 q^{5} + 2638080 q^{6} + 1112844 q^{7} + 8388608 q^{8} - 44601846 q^{9} + O(q^{10}) \) \( 1638 q - 256 q^{2} + 8130 q^{3} + 294912 q^{4} - 353388 q^{5} + 2638080 q^{6} + 1112844 q^{7} + 8388608 q^{8} - 44601846 q^{9} + 138205440 q^{10} - 220451988 q^{11} - 125239296 q^{12} + 463807146 q^{13} - 329549824 q^{14} - 3774194340 q^{15} + 4831838208 q^{16} + 2797884774 q^{17} - 4981172736 q^{18} + 13308501576 q^{19} + 9598500864 q^{20} - 7241678388 q^{21} - 24388616448 q^{22} - 95067801222 q^{23} + 43222302720 q^{24} + 101029592676 q^{25} - 3146629376 q^{26} + 376771297032 q^{27} + 43556634624 q^{28} - 402019437864 q^{29} + 430422637056 q^{30} - 302779141362 q^{31} - 68719476736 q^{32} - 588335841402 q^{33} - 170870723328 q^{34} + 2688108358920 q^{35} - 267247583232 q^{36} + 2125079247738 q^{37} - 2747255982080 q^{38} + 6528918938808 q^{39} + 2264357928960 q^{40} + 5762074370046 q^{41} - 2199962689536 q^{42} - 2353631232702 q^{43} - 4597006761984 q^{44} - 4700362421604 q^{45} + 12917078132736 q^{46} + 29395717920726 q^{47} - 130459631616 q^{48} - 75619176007218 q^{49} + 25897420160768 q^{50} - 52073140080906 q^{51} + 14787573940224 q^{52} + 99660945135678 q^{53} + 64372801994496 q^{54} - 41822173708380 q^{55} - 7893529133056 q^{56} - 211263720549774 q^{57} + 15800672779776 q^{58} + 328554419635110 q^{59} + 91727650160640 q^{60} + 85444949119524 q^{61} - 467098229911040 q^{62} - 356031125765838 q^{63} - 184717953466368 q^{64} + 869531805291948 q^{65} + 268791862677504 q^{66} - 113365391408616 q^{67} - 458294825779200 q^{68} - 658686524680368 q^{69} + 38020781581056 q^{70} + 1056225574141464 q^{71} + 105127826423808 q^{72} + 1202847889998618 q^{73} - 1107026745688064 q^{74} - 1723629900634746 q^{75} - 3949757202432 q^{76} + 1260717473408286 q^{77} + 508124059651584 q^{78} + 1607606085613806 q^{79} + 145212844277760 q^{80} + 2276742026218974 q^{81} - 840861357735936 q^{82} - 4237916093610 q^{83} + 373308005646336 q^{84} + 416657861785464 q^{85} - 120890314247936 q^{86} - 1732454240897844 q^{87} - 26190664433664 q^{88} + 6153654173008686 q^{89} + 5316342523017216 q^{90} - 387436431840330 q^{91} - 3332809778724864 q^{92} - 8496109411715652 q^{93} + 2442432087791616 q^{94} - 4367139453697986 q^{95} + 558689345863680 q^{96} - 434760310878114 q^{97} + 330301605774848 q^{98} + 2974222213708776 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_1(126))\)

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
126.16.a \(\chi_{126}(1, \cdot)\) 126.16.a.a 1 1
126.16.a.b 1
126.16.a.c 1
126.16.a.d 1
126.16.a.e 1
126.16.a.f 2
126.16.a.g 2
126.16.a.h 2
126.16.a.i 2
126.16.a.j 2
126.16.a.k 2
126.16.a.l 2
126.16.a.m 3
126.16.a.n 4
126.16.a.o 4
126.16.a.p 4
126.16.a.q 4
126.16.d \(\chi_{126}(125, \cdot)\) 126.16.d.a 40 1
126.16.e \(\chi_{126}(25, \cdot)\) n/a 240 2
126.16.f \(\chi_{126}(43, \cdot)\) n/a 180 2
126.16.g \(\chi_{126}(37, \cdot)\) 126.16.g.a 8 2
126.16.g.b 10
126.16.g.c 10
126.16.g.d 10
126.16.g.e 10
126.16.g.f 12
126.16.g.g 20
126.16.g.h 20
126.16.h \(\chi_{126}(67, \cdot)\) n/a 240 2
126.16.k \(\chi_{126}(17, \cdot)\) 126.16.k.a 80 2
126.16.l \(\chi_{126}(5, \cdot)\) n/a 240 2
126.16.m \(\chi_{126}(41, \cdot)\) n/a 240 2
126.16.t \(\chi_{126}(47, \cdot)\) n/a 240 2

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

Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_1(126))\) into lower level spaces

\( S_{16}^{\mathrm{old}}(\Gamma_1(126)) \cong \) \(S_{16}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 3}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 2}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 1}\)