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Properties

Label 1008.6
Level 1008
Weight 6
Dimension 58793
Nonzero newspaces 40
Sturm bound 331776
Trace bound 29

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Defining parameters

Level: \( N \) = \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 40 \)
Sturm bound: \(331776\)
Trace bound: \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(1008))\).

Total New Old
Modular forms 139584 59197 80387
Cusp forms 136896 58793 78103
Eisenstein series 2688 404 2284

Trace form

\( 58793 q - 24 q^{2} - 24 q^{3} + 20 q^{4} + 5 q^{5} - 32 q^{6} - 12 q^{7} - 552 q^{8} + 80 q^{9} + O(q^{10}) \) \( 58793 q - 24 q^{2} - 24 q^{3} + 20 q^{4} + 5 q^{5} - 32 q^{6} - 12 q^{7} - 552 q^{8} + 80 q^{9} + 796 q^{10} - 381 q^{11} - 32 q^{12} - 618 q^{13} + 324 q^{14} + 3294 q^{15} + 11476 q^{16} - 2861 q^{17} - 16072 q^{18} - 3619 q^{19} - 12580 q^{20} + 2987 q^{21} + 31320 q^{22} + 10597 q^{23} + 32288 q^{24} + 3099 q^{25} - 7724 q^{26} - 12372 q^{27} - 25924 q^{28} - 86180 q^{29} - 62392 q^{30} + 17711 q^{31} + 32676 q^{32} + 41154 q^{33} + 114012 q^{34} + 65745 q^{35} - 60744 q^{36} - 12831 q^{37} + 31124 q^{38} - 116358 q^{39} + 89940 q^{40} - 63114 q^{41} + 30400 q^{42} + 64974 q^{43} - 36644 q^{44} - 17466 q^{45} - 217872 q^{46} + 317517 q^{47} - 224776 q^{48} - 269056 q^{49} - 138000 q^{50} + 114184 q^{51} + 39064 q^{52} - 6773 q^{53} + 230616 q^{54} - 455982 q^{55} + 303888 q^{56} - 373216 q^{57} + 415136 q^{58} - 288313 q^{59} + 468712 q^{60} - 15223 q^{61} + 41808 q^{62} + 143007 q^{63} - 262996 q^{64} + 2250 q^{65} - 7472 q^{66} + 511563 q^{67} - 659672 q^{68} - 278158 q^{69} + 210176 q^{70} - 261316 q^{71} - 1113088 q^{72} + 14541 q^{73} - 692932 q^{74} - 643700 q^{75} + 242204 q^{76} - 10658 q^{77} + 92728 q^{78} - 379983 q^{79} + 1499164 q^{80} + 1328032 q^{81} - 17148 q^{82} + 1586808 q^{83} + 1105928 q^{84} - 393550 q^{85} + 505084 q^{86} + 535530 q^{87} - 255116 q^{88} - 458853 q^{89} - 1229216 q^{90} - 225920 q^{91} - 1852220 q^{92} - 414774 q^{93} - 1503124 q^{94} - 2863111 q^{95} - 1214376 q^{96} - 189666 q^{97} + 488432 q^{98} - 792594 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(1008))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
1008.6.a \(\chi_{1008}(1, \cdot)\) 1008.6.a.a 1 1
1008.6.a.b 1
1008.6.a.c 1
1008.6.a.d 1
1008.6.a.e 1
1008.6.a.f 1
1008.6.a.g 1
1008.6.a.h 1
1008.6.a.i 1
1008.6.a.j 1
1008.6.a.k 1
1008.6.a.l 1
1008.6.a.m 1
1008.6.a.n 1
1008.6.a.o 1
1008.6.a.p 1
1008.6.a.q 1
1008.6.a.r 1
1008.6.a.s 1
1008.6.a.t 1
1008.6.a.u 1
1008.6.a.v 1
1008.6.a.w 1
1008.6.a.x 1
1008.6.a.y 1
1008.6.a.z 1
1008.6.a.ba 1
1008.6.a.bb 1
1008.6.a.bc 1
1008.6.a.bd 2
1008.6.a.be 2
1008.6.a.bf 2
1008.6.a.bg 2
1008.6.a.bh 2
1008.6.a.bi 2
1008.6.a.bj 2
1008.6.a.bk 2
1008.6.a.bl 2
1008.6.a.bm 2
1008.6.a.bn 2
1008.6.a.bo 2
1008.6.a.bp 2
1008.6.a.bq 2
1008.6.a.br 2
1008.6.a.bs 2
1008.6.a.bt 2
1008.6.a.bu 2
1008.6.a.bv 2
1008.6.a.bw 2
1008.6.a.bx 2
1008.6.a.by 4
1008.6.b \(\chi_{1008}(559, \cdot)\) 1008.6.b.a 2 1
1008.6.b.b 2
1008.6.b.c 4
1008.6.b.d 6
1008.6.b.e 6
1008.6.b.f 8
1008.6.b.g 8
1008.6.b.h 12
1008.6.b.i 14
1008.6.b.j 14
1008.6.b.k 24
1008.6.c \(\chi_{1008}(505, \cdot)\) None 0 1
1008.6.h \(\chi_{1008}(575, \cdot)\) 1008.6.h.a 20 1
1008.6.h.b 40
1008.6.i \(\chi_{1008}(377, \cdot)\) None 0 1
1008.6.j \(\chi_{1008}(71, \cdot)\) None 0 1
1008.6.k \(\chi_{1008}(881, \cdot)\) 1008.6.k.a 4 1
1008.6.k.b 8
1008.6.k.c 12
1008.6.k.d 16
1008.6.k.e 40
1008.6.p \(\chi_{1008}(55, \cdot)\) None 0 1
1008.6.q \(\chi_{1008}(529, \cdot)\) n/a 476 2
1008.6.r \(\chi_{1008}(337, \cdot)\) n/a 360 2
1008.6.s \(\chi_{1008}(289, \cdot)\) n/a 198 2
1008.6.t \(\chi_{1008}(193, \cdot)\) n/a 476 2
1008.6.v \(\chi_{1008}(323, \cdot)\) n/a 480 2
1008.6.x \(\chi_{1008}(307, \cdot)\) n/a 796 2
1008.6.z \(\chi_{1008}(253, \cdot)\) n/a 600 2
1008.6.bb \(\chi_{1008}(125, \cdot)\) n/a 640 2
1008.6.be \(\chi_{1008}(457, \cdot)\) None 0 2
1008.6.bf \(\chi_{1008}(31, \cdot)\) n/a 480 2
1008.6.bg \(\chi_{1008}(185, \cdot)\) None 0 2
1008.6.bh \(\chi_{1008}(95, \cdot)\) n/a 480 2
1008.6.bm \(\chi_{1008}(391, \cdot)\) None 0 2
1008.6.bn \(\chi_{1008}(103, \cdot)\) None 0 2
1008.6.bs \(\chi_{1008}(199, \cdot)\) None 0 2
1008.6.bt \(\chi_{1008}(17, \cdot)\) n/a 160 2
1008.6.bu \(\chi_{1008}(359, \cdot)\) None 0 2
1008.6.bz \(\chi_{1008}(407, \cdot)\) None 0 2
1008.6.ca \(\chi_{1008}(257, \cdot)\) n/a 476 2
1008.6.cb \(\chi_{1008}(23, \cdot)\) None 0 2
1008.6.cc \(\chi_{1008}(209, \cdot)\) n/a 476 2
1008.6.ch \(\chi_{1008}(239, \cdot)\) n/a 360 2
1008.6.ci \(\chi_{1008}(761, \cdot)\) None 0 2
1008.6.cj \(\chi_{1008}(527, \cdot)\) n/a 480 2
1008.6.ck \(\chi_{1008}(41, \cdot)\) None 0 2
1008.6.cp \(\chi_{1008}(89, \cdot)\) None 0 2
1008.6.cq \(\chi_{1008}(431, \cdot)\) n/a 160 2
1008.6.cr \(\chi_{1008}(361, \cdot)\) None 0 2
1008.6.cs \(\chi_{1008}(271, \cdot)\) n/a 200 2
1008.6.cx \(\chi_{1008}(223, \cdot)\) n/a 480 2
1008.6.cy \(\chi_{1008}(25, \cdot)\) None 0 2
1008.6.cz \(\chi_{1008}(367, \cdot)\) n/a 480 2
1008.6.da \(\chi_{1008}(169, \cdot)\) None 0 2
1008.6.df \(\chi_{1008}(689, \cdot)\) n/a 476 2
1008.6.dg \(\chi_{1008}(599, \cdot)\) None 0 2
1008.6.dh \(\chi_{1008}(439, \cdot)\) None 0 2
1008.6.dk \(\chi_{1008}(139, \cdot)\) n/a 3824 4
1008.6.dm \(\chi_{1008}(155, \cdot)\) n/a 2880 4
1008.6.do \(\chi_{1008}(205, \cdot)\) n/a 3824 4
1008.6.dr \(\chi_{1008}(5, \cdot)\) n/a 3824 4
1008.6.ds \(\chi_{1008}(269, \cdot)\) n/a 1280 4
1008.6.du \(\chi_{1008}(37, \cdot)\) n/a 1592 4
1008.6.dx \(\chi_{1008}(277, \cdot)\) n/a 3824 4
1008.6.dy \(\chi_{1008}(173, \cdot)\) n/a 3824 4
1008.6.ea \(\chi_{1008}(347, \cdot)\) n/a 3824 4
1008.6.ec \(\chi_{1008}(19, \cdot)\) n/a 1592 4
1008.6.ef \(\chi_{1008}(115, \cdot)\) n/a 3824 4
1008.6.eh \(\chi_{1008}(11, \cdot)\) n/a 3824 4
1008.6.ei \(\chi_{1008}(107, \cdot)\) n/a 1280 4
1008.6.ek \(\chi_{1008}(187, \cdot)\) n/a 3824 4
1008.6.em \(\chi_{1008}(293, \cdot)\) n/a 3824 4
1008.6.eo \(\chi_{1008}(85, \cdot)\) n/a 2880 4

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(1008))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(1008)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 20}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 18}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 15}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 9}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(252))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(336))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(504))\)\(^{\oplus 2}\)