Properties

Label 1008.4
Level 1008
Weight 4
Dimension 35195
Nonzero newspaces 40
Sturm bound 221184
Trace bound 29

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Defining parameters

Level: \( N \) = \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 40 \)
Sturm bound: \(221184\)
Trace bound: \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1008))\).

Total New Old
Modular forms 84288 35599 48689
Cusp forms 81600 35195 46405
Eisenstein series 2688 404 2284

Trace form

\( 35195q - 24q^{2} - 24q^{3} - 44q^{4} - 31q^{5} - 32q^{6} - 36q^{7} + 24q^{8} + 32q^{9} + O(q^{10}) \) \( 35195q - 24q^{2} - 24q^{3} - 44q^{4} - 31q^{5} - 32q^{6} - 36q^{7} + 24q^{8} + 32q^{9} + 60q^{10} + 123q^{11} - 32q^{12} + 66q^{13} - 156q^{14} - 18q^{15} + 468q^{16} + 151q^{17} + 248q^{18} - 595q^{19} - 868q^{20} - 349q^{21} - 904q^{22} - 539q^{23} - 1504q^{24} - 855q^{25} - 1676q^{26} + 732q^{27} - 516q^{28} + 784q^{29} + 968q^{30} + 111q^{31} + 1956q^{32} + 18q^{33} + 1884q^{34} + 9q^{35} - 1608q^{36} + 1029q^{37} - 2380q^{38} + 426q^{39} + 1492q^{40} + 234q^{41} + 640q^{42} - 2402q^{43} + 8092q^{44} + 486q^{45} + 5648q^{46} - 7347q^{47} + 4856q^{48} - 4926q^{49} + 5040q^{50} - 3944q^{51} - 744q^{52} - 1145q^{53} + 408q^{54} + 2626q^{55} - 7536q^{56} - 2320q^{57} - 8672q^{58} + 7631q^{59} - 15896q^{60} + 1077q^{61} - 10896q^{62} + 2511q^{63} - 1940q^{64} + 6522q^{65} + 9808q^{66} - 925q^{67} + 12904q^{68} + 11762q^{69} + 3936q^{70} + 5372q^{71} + 15872q^{72} - 9807q^{73} + 8156q^{74} - 164q^{75} - 2468q^{76} - 626q^{77} + 952q^{78} - 5647q^{79} - 13412q^{80} - 6512q^{81} - 6972q^{82} - 10440q^{83} - 9592q^{84} - 1094q^{85} - 17636q^{86} - 7206q^{87} + 9588q^{88} - 9249q^{89} - 2336q^{90} + 7032q^{91} + 21700q^{92} - 1110q^{93} + 10156q^{94} + 25145q^{95} + 12888q^{96} + 1954q^{97} + 6416q^{98} + 14382q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1008))\)

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
1008.4.a \(\chi_{1008}(1, \cdot)\) 1008.4.a.a 1 1
1008.4.a.b 1
1008.4.a.c 1
1008.4.a.d 1
1008.4.a.e 1
1008.4.a.f 1
1008.4.a.g 1
1008.4.a.h 1
1008.4.a.i 1
1008.4.a.j 1
1008.4.a.k 1
1008.4.a.l 1
1008.4.a.m 1
1008.4.a.n 1
1008.4.a.o 1
1008.4.a.p 1
1008.4.a.q 1
1008.4.a.r 1
1008.4.a.s 1
1008.4.a.t 1
1008.4.a.u 1
1008.4.a.v 1
1008.4.a.w 1
1008.4.a.x 2
1008.4.a.y 2
1008.4.a.z 2
1008.4.a.ba 2
1008.4.a.bb 2
1008.4.a.bc 2
1008.4.a.bd 2
1008.4.a.be 2
1008.4.a.bf 2
1008.4.a.bg 2
1008.4.a.bh 2
1008.4.b \(\chi_{1008}(559, \cdot)\) 1008.4.b.a 2 1
1008.4.b.b 2
1008.4.b.c 2
1008.4.b.d 2
1008.4.b.e 2
1008.4.b.f 2
1008.4.b.g 4
1008.4.b.h 4
1008.4.b.i 8
1008.4.b.j 8
1008.4.b.k 8
1008.4.b.l 16
1008.4.c \(\chi_{1008}(505, \cdot)\) None 0 1
1008.4.h \(\chi_{1008}(575, \cdot)\) 1008.4.h.a 12 1
1008.4.h.b 24
1008.4.i \(\chi_{1008}(377, \cdot)\) None 0 1
1008.4.j \(\chi_{1008}(71, \cdot)\) None 0 1
1008.4.k \(\chi_{1008}(881, \cdot)\) 1008.4.k.a 4 1
1008.4.k.b 4
1008.4.k.c 8
1008.4.k.d 8
1008.4.k.e 24
1008.4.p \(\chi_{1008}(55, \cdot)\) None 0 1
1008.4.q \(\chi_{1008}(529, \cdot)\) n/a 284 2
1008.4.r \(\chi_{1008}(337, \cdot)\) n/a 216 2
1008.4.s \(\chi_{1008}(289, \cdot)\) n/a 118 2
1008.4.t \(\chi_{1008}(193, \cdot)\) n/a 284 2
1008.4.v \(\chi_{1008}(323, \cdot)\) n/a 288 2
1008.4.x \(\chi_{1008}(307, \cdot)\) n/a 476 2
1008.4.z \(\chi_{1008}(253, \cdot)\) n/a 360 2
1008.4.bb \(\chi_{1008}(125, \cdot)\) n/a 384 2
1008.4.be \(\chi_{1008}(457, \cdot)\) None 0 2
1008.4.bf \(\chi_{1008}(31, \cdot)\) n/a 288 2
1008.4.bg \(\chi_{1008}(185, \cdot)\) None 0 2
1008.4.bh \(\chi_{1008}(95, \cdot)\) n/a 288 2
1008.4.bm \(\chi_{1008}(391, \cdot)\) None 0 2
1008.4.bn \(\chi_{1008}(103, \cdot)\) None 0 2
1008.4.bs \(\chi_{1008}(199, \cdot)\) None 0 2
1008.4.bt \(\chi_{1008}(17, \cdot)\) 1008.4.bt.a 16 2
1008.4.bt.b 16
1008.4.bt.c 16
1008.4.bt.d 48
1008.4.bu \(\chi_{1008}(359, \cdot)\) None 0 2
1008.4.bz \(\chi_{1008}(407, \cdot)\) None 0 2
1008.4.ca \(\chi_{1008}(257, \cdot)\) n/a 284 2
1008.4.cb \(\chi_{1008}(23, \cdot)\) None 0 2
1008.4.cc \(\chi_{1008}(209, \cdot)\) n/a 284 2
1008.4.ch \(\chi_{1008}(239, \cdot)\) n/a 216 2
1008.4.ci \(\chi_{1008}(761, \cdot)\) None 0 2
1008.4.cj \(\chi_{1008}(527, \cdot)\) n/a 288 2
1008.4.ck \(\chi_{1008}(41, \cdot)\) None 0 2
1008.4.cp \(\chi_{1008}(89, \cdot)\) None 0 2
1008.4.cq \(\chi_{1008}(431, \cdot)\) 1008.4.cq.a 32 2
1008.4.cq.b 32
1008.4.cq.c 32
1008.4.cr \(\chi_{1008}(361, \cdot)\) None 0 2
1008.4.cs \(\chi_{1008}(271, \cdot)\) n/a 120 2
1008.4.cx \(\chi_{1008}(223, \cdot)\) n/a 288 2
1008.4.cy \(\chi_{1008}(25, \cdot)\) None 0 2
1008.4.cz \(\chi_{1008}(367, \cdot)\) n/a 288 2
1008.4.da \(\chi_{1008}(169, \cdot)\) None 0 2
1008.4.df \(\chi_{1008}(689, \cdot)\) n/a 284 2
1008.4.dg \(\chi_{1008}(599, \cdot)\) None 0 2
1008.4.dh \(\chi_{1008}(439, \cdot)\) None 0 2
1008.4.dk \(\chi_{1008}(139, \cdot)\) n/a 2288 4
1008.4.dm \(\chi_{1008}(155, \cdot)\) n/a 1728 4
1008.4.do \(\chi_{1008}(205, \cdot)\) n/a 2288 4
1008.4.dr \(\chi_{1008}(5, \cdot)\) n/a 2288 4
1008.4.ds \(\chi_{1008}(269, \cdot)\) n/a 768 4
1008.4.du \(\chi_{1008}(37, \cdot)\) n/a 952 4
1008.4.dx \(\chi_{1008}(277, \cdot)\) n/a 2288 4
1008.4.dy \(\chi_{1008}(173, \cdot)\) n/a 2288 4
1008.4.ea \(\chi_{1008}(347, \cdot)\) n/a 2288 4
1008.4.ec \(\chi_{1008}(19, \cdot)\) n/a 952 4
1008.4.ef \(\chi_{1008}(115, \cdot)\) n/a 2288 4
1008.4.eh \(\chi_{1008}(11, \cdot)\) n/a 2288 4
1008.4.ei \(\chi_{1008}(107, \cdot)\) n/a 768 4
1008.4.ek \(\chi_{1008}(187, \cdot)\) n/a 2288 4
1008.4.em \(\chi_{1008}(293, \cdot)\) n/a 2288 4
1008.4.eo \(\chi_{1008}(85, \cdot)\) n/a 1728 4

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1008))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1008)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 15}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(252))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(336))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(504))\)\(^{\oplus 2}\)