Properties

Label 1008.3
Level 1008
Weight 3
Dimension 23395
Nonzero newspaces 40
Sturm bound 165888
Trace bound 29

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Defining parameters

Level: \( N \) = \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 40 \)
Sturm bound: \(165888\)
Trace bound: \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(1008))\).

Total New Old
Modular forms 56640 23801 32839
Cusp forms 53952 23395 30557
Eisenstein series 2688 406 2282

Trace form

\( 23395q - 24q^{2} - 24q^{3} - 12q^{4} - 15q^{5} - 32q^{6} - 4q^{7} - 72q^{8} + 8q^{9} + O(q^{10}) \) \( 23395q - 24q^{2} - 24q^{3} - 12q^{4} - 15q^{5} - 32q^{6} - 4q^{7} - 72q^{8} + 8q^{9} - 148q^{10} + 11q^{11} - 32q^{12} - 80q^{13} - 76q^{14} - 126q^{15} - 172q^{16} - 285q^{17} - 232q^{18} - 197q^{19} - 196q^{20} - 91q^{21} - 56q^{22} - 89q^{23} + 32q^{24} + 197q^{25} + 164q^{26} - 168q^{27} + 92q^{28} + 140q^{29} + 392q^{30} + 91q^{31} + 676q^{32} + 42q^{33} + 476q^{34} - 267q^{35} + 312q^{36} - 359q^{37} + 900q^{38} - 294q^{39} + 788q^{40} - 48q^{41} + 160q^{42} - 692q^{43} - 68q^{44} + 282q^{45} - 608q^{46} + 279q^{47} - 136q^{48} + 42q^{49} - 1136q^{50} + 604q^{51} - 1192q^{52} + 107q^{53} - 648q^{54} + 796q^{55} - 304q^{56} + 608q^{57} - 1248q^{58} + 1243q^{59} + 1000q^{60} + 77q^{61} + 1152q^{62} + 303q^{63} - 564q^{64} + 292q^{65} + 1168q^{66} + 39q^{67} + 584q^{68} - 526q^{69} + 656q^{70} - 718q^{71} - 256q^{72} - 455q^{73} - 180q^{74} - 776q^{75} + 828q^{76} - 1082q^{77} - 1160q^{78} + 595q^{79} + 348q^{80} - 1592q^{81} + 2980q^{82} + 548q^{83} - 568q^{84} - 418q^{85} + 108q^{86} + 534q^{87} + 1652q^{88} + 3q^{89} - 608q^{90} + 50q^{91} + 1156q^{92} - 234q^{93} + 1356q^{94} - 951q^{95} - 168q^{96} + 72q^{97} + 512q^{98} - 414q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(1008))\)

We only show spaces with odd 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
1008.3.d \(\chi_{1008}(449, \cdot)\) 1008.3.d.a 4 1
1008.3.d.b 4
1008.3.d.c 4
1008.3.d.d 4
1008.3.d.e 8
1008.3.e \(\chi_{1008}(503, \cdot)\) None 0 1
1008.3.f \(\chi_{1008}(433, \cdot)\) 1008.3.f.a 1 1
1008.3.f.b 2
1008.3.f.c 2
1008.3.f.d 2
1008.3.f.e 2
1008.3.f.f 2
1008.3.f.g 4
1008.3.f.h 4
1008.3.f.i 4
1008.3.f.j 8
1008.3.f.k 8
1008.3.g \(\chi_{1008}(631, \cdot)\) None 0 1
1008.3.l \(\chi_{1008}(937, \cdot)\) None 0 1
1008.3.m \(\chi_{1008}(127, \cdot)\) 1008.3.m.a 2 1
1008.3.m.b 4
1008.3.m.c 4
1008.3.m.d 4
1008.3.m.e 4
1008.3.m.f 4
1008.3.m.g 8
1008.3.n \(\chi_{1008}(953, \cdot)\) None 0 1
1008.3.o \(\chi_{1008}(1007, \cdot)\) 1008.3.o.a 8 1
1008.3.o.b 24
1008.3.u \(\chi_{1008}(181, \cdot)\) n/a 316 2
1008.3.w \(\chi_{1008}(197, \cdot)\) n/a 192 2
1008.3.y \(\chi_{1008}(251, \cdot)\) n/a 256 2
1008.3.ba \(\chi_{1008}(379, \cdot)\) n/a 240 2
1008.3.bc \(\chi_{1008}(311, \cdot)\) None 0 2
1008.3.bd \(\chi_{1008}(65, \cdot)\) n/a 188 2
1008.3.bi \(\chi_{1008}(583, \cdot)\) None 0 2
1008.3.bj \(\chi_{1008}(817, \cdot)\) n/a 188 2
1008.3.bk \(\chi_{1008}(143, \cdot)\) 1008.3.bk.a 20 2
1008.3.bk.b 20
1008.3.bk.c 24
1008.3.bl \(\chi_{1008}(233, \cdot)\) None 0 2
1008.3.bo \(\chi_{1008}(281, \cdot)\) None 0 2
1008.3.bp \(\chi_{1008}(383, \cdot)\) n/a 192 2
1008.3.bq \(\chi_{1008}(137, \cdot)\) None 0 2
1008.3.br \(\chi_{1008}(335, \cdot)\) n/a 192 2
1008.3.bv \(\chi_{1008}(265, \cdot)\) None 0 2
1008.3.bw \(\chi_{1008}(655, \cdot)\) n/a 192 2
1008.3.bx \(\chi_{1008}(745, \cdot)\) None 0 2
1008.3.by \(\chi_{1008}(463, \cdot)\) n/a 144 2
1008.3.cd \(\chi_{1008}(415, \cdot)\) 1008.3.cd.a 2 2
1008.3.cd.b 2
1008.3.cd.c 2
1008.3.cd.d 2
1008.3.cd.e 4
1008.3.cd.f 4
1008.3.cd.g 4
1008.3.cd.h 6
1008.3.cd.i 6
1008.3.cd.j 6
1008.3.cd.k 6
1008.3.cd.l 6
1008.3.cd.m 6
1008.3.cd.n 8
1008.3.cd.o 8
1008.3.cd.p 8
1008.3.ce \(\chi_{1008}(73, \cdot)\) None 0 2
1008.3.cf \(\chi_{1008}(487, \cdot)\) None 0 2
1008.3.cg \(\chi_{1008}(145, \cdot)\) 1008.3.cg.a 2 2
1008.3.cg.b 2
1008.3.cg.c 2
1008.3.cg.d 2
1008.3.cg.e 2
1008.3.cg.f 2
1008.3.cg.g 2
1008.3.cg.h 4
1008.3.cg.i 4
1008.3.cg.j 4
1008.3.cg.k 4
1008.3.cg.l 4
1008.3.cg.m 4
1008.3.cg.n 8
1008.3.cg.o 8
1008.3.cg.p 8
1008.3.cg.q 16
1008.3.cl \(\chi_{1008}(97, \cdot)\) n/a 188 2
1008.3.cm \(\chi_{1008}(151, \cdot)\) None 0 2
1008.3.cn \(\chi_{1008}(241, \cdot)\) n/a 188 2
1008.3.co \(\chi_{1008}(295, \cdot)\) None 0 2
1008.3.ct \(\chi_{1008}(113, \cdot)\) n/a 144 2
1008.3.cu \(\chi_{1008}(887, \cdot)\) None 0 2
1008.3.cv \(\chi_{1008}(401, \cdot)\) n/a 188 2
1008.3.cw \(\chi_{1008}(167, \cdot)\) None 0 2
1008.3.db \(\chi_{1008}(215, \cdot)\) None 0 2
1008.3.dc \(\chi_{1008}(305, \cdot)\) 1008.3.dc.a 4 2
1008.3.dc.b 4
1008.3.dc.c 4
1008.3.dc.d 8
1008.3.dc.e 12
1008.3.dc.f 16
1008.3.dc.g 16
1008.3.dd \(\chi_{1008}(79, \cdot)\) n/a 192 2
1008.3.de \(\chi_{1008}(313, \cdot)\) None 0 2
1008.3.di \(\chi_{1008}(47, \cdot)\) n/a 192 2
1008.3.dj \(\chi_{1008}(473, \cdot)\) None 0 2
1008.3.dl \(\chi_{1008}(29, \cdot)\) n/a 1152 4
1008.3.dn \(\chi_{1008}(13, \cdot)\) n/a 1520 4
1008.3.dp \(\chi_{1008}(59, \cdot)\) n/a 1520 4
1008.3.dq \(\chi_{1008}(403, \cdot)\) n/a 1520 4
1008.3.dt \(\chi_{1008}(163, \cdot)\) n/a 632 4
1008.3.dv \(\chi_{1008}(395, \cdot)\) n/a 512 4
1008.3.dw \(\chi_{1008}(131, \cdot)\) n/a 1520 4
1008.3.dz \(\chi_{1008}(67, \cdot)\) n/a 1520 4
1008.3.eb \(\chi_{1008}(61, \cdot)\) n/a 1520 4
1008.3.ed \(\chi_{1008}(53, \cdot)\) n/a 512 4
1008.3.ee \(\chi_{1008}(149, \cdot)\) n/a 1520 4
1008.3.eg \(\chi_{1008}(229, \cdot)\) n/a 1520 4
1008.3.ej \(\chi_{1008}(325, \cdot)\) n/a 632 4
1008.3.el \(\chi_{1008}(221, \cdot)\) n/a 1520 4
1008.3.en \(\chi_{1008}(43, \cdot)\) n/a 1152 4
1008.3.ep \(\chi_{1008}(83, \cdot)\) n/a 1520 4

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(1008))\) into lower level spaces

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