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Properties

Label 1584.2
Level 1584
Weight 2
Dimension 29903
Nonzero newspaces 32
Sturm bound 276480
Trace bound 25

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Defining parameters

Level: \( N \) = \( 1584 = 2^{4} \cdot 3^{2} \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(276480\)
Trace bound: \(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1584))\).

Total New Old
Modular forms 71360 30631 40729
Cusp forms 66881 29903 36978
Eisenstein series 4479 728 3751

Trace form

\( 29903 q - 48 q^{2} - 48 q^{3} - 52 q^{4} - 65 q^{5} - 64 q^{6} - 47 q^{7} - 60 q^{8} - 24 q^{9} + O(q^{10}) \) \( 29903 q - 48 q^{2} - 48 q^{3} - 52 q^{4} - 65 q^{5} - 64 q^{6} - 47 q^{7} - 60 q^{8} - 24 q^{9} - 148 q^{10} - 54 q^{11} - 144 q^{12} - 77 q^{13} - 12 q^{14} - 54 q^{15} - 4 q^{16} - 91 q^{17} - 24 q^{18} - 115 q^{19} + 52 q^{20} - 54 q^{21} - 8 q^{22} - 40 q^{23} + 41 q^{25} + 68 q^{26} - 12 q^{27} - 68 q^{28} - q^{29} - 24 q^{30} - 11 q^{31} + 12 q^{32} - 141 q^{33} - 88 q^{34} + 81 q^{35} - 56 q^{36} - 217 q^{37} - 140 q^{38} + 66 q^{39} - 164 q^{40} - 25 q^{41} - 144 q^{42} + 56 q^{43} - 140 q^{44} - 134 q^{45} - 268 q^{46} + 75 q^{47} - 168 q^{48} - 215 q^{49} - 216 q^{50} + 16 q^{51} - 172 q^{52} - 63 q^{53} - 152 q^{54} - 87 q^{55} - 312 q^{56} - 60 q^{57} - 124 q^{58} + 13 q^{59} - 280 q^{60} - 13 q^{61} - 252 q^{62} - 54 q^{63} - 4 q^{64} - 282 q^{65} - 192 q^{66} - 104 q^{67} - 220 q^{68} - 230 q^{69} + 168 q^{70} - 163 q^{71} - 288 q^{72} + 75 q^{73} - 64 q^{74} - 152 q^{75} + 180 q^{76} - 32 q^{77} - 360 q^{78} - 77 q^{79} - 96 q^{80} - 296 q^{81} + 36 q^{82} - 193 q^{83} - 352 q^{84} + 161 q^{85} - 180 q^{86} - 186 q^{87} + 192 q^{88} + 14 q^{89} - 352 q^{90} - 215 q^{91} - 84 q^{92} + 2 q^{93} - 4 q^{94} - 195 q^{95} - 200 q^{96} + 35 q^{97} - 12 q^{98} - 69 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1584))\)

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
1584.2.a \(\chi_{1584}(1, \cdot)\) 1584.2.a.a 1 1
1584.2.a.b 1
1584.2.a.c 1
1584.2.a.d 1
1584.2.a.e 1
1584.2.a.f 1
1584.2.a.g 1
1584.2.a.h 1
1584.2.a.i 1
1584.2.a.j 1
1584.2.a.k 1
1584.2.a.l 1
1584.2.a.m 1
1584.2.a.n 1
1584.2.a.o 1
1584.2.a.p 1
1584.2.a.q 1
1584.2.a.r 1
1584.2.a.s 1
1584.2.a.t 2
1584.2.a.u 2
1584.2.a.v 2
1584.2.b \(\chi_{1584}(593, \cdot)\) 1584.2.b.a 2 1
1584.2.b.b 2
1584.2.b.c 2
1584.2.b.d 2
1584.2.b.e 4
1584.2.b.f 6
1584.2.b.g 6
1584.2.d \(\chi_{1584}(287, \cdot)\) 1584.2.d.a 2 1
1584.2.d.b 2
1584.2.d.c 8
1584.2.d.d 8
1584.2.f \(\chi_{1584}(793, \cdot)\) None 0 1
1584.2.h \(\chi_{1584}(1495, \cdot)\) None 0 1
1584.2.k \(\chi_{1584}(1079, \cdot)\) None 0 1
1584.2.m \(\chi_{1584}(1385, \cdot)\) None 0 1
1584.2.o \(\chi_{1584}(703, \cdot)\) 1584.2.o.a 2 1
1584.2.o.b 4
1584.2.o.c 4
1584.2.o.d 4
1584.2.o.e 4
1584.2.o.f 4
1584.2.o.g 8
1584.2.q \(\chi_{1584}(529, \cdot)\) n/a 120 2
1584.2.r \(\chi_{1584}(307, \cdot)\) n/a 236 2
1584.2.u \(\chi_{1584}(397, \cdot)\) n/a 200 2
1584.2.v \(\chi_{1584}(683, \cdot)\) n/a 160 2
1584.2.y \(\chi_{1584}(197, \cdot)\) n/a 192 2
1584.2.z \(\chi_{1584}(289, \cdot)\) n/a 116 4
1584.2.bc \(\chi_{1584}(175, \cdot)\) n/a 144 2
1584.2.be \(\chi_{1584}(329, \cdot)\) None 0 2
1584.2.bg \(\chi_{1584}(23, \cdot)\) None 0 2
1584.2.bh \(\chi_{1584}(439, \cdot)\) None 0 2
1584.2.bj \(\chi_{1584}(265, \cdot)\) None 0 2
1584.2.bl \(\chi_{1584}(815, \cdot)\) n/a 120 2
1584.2.bn \(\chi_{1584}(65, \cdot)\) n/a 140 2
1584.2.bq \(\chi_{1584}(127, \cdot)\) n/a 120 4
1584.2.bs \(\chi_{1584}(233, \cdot)\) None 0 4
1584.2.bu \(\chi_{1584}(71, \cdot)\) None 0 4
1584.2.bx \(\chi_{1584}(343, \cdot)\) None 0 4
1584.2.bz \(\chi_{1584}(361, \cdot)\) None 0 4
1584.2.cb \(\chi_{1584}(575, \cdot)\) 1584.2.cb.a 32 4
1584.2.cb.b 64
1584.2.cd \(\chi_{1584}(17, \cdot)\) 1584.2.cd.a 8 4
1584.2.cd.b 8
1584.2.cd.c 16
1584.2.cd.d 16
1584.2.cd.e 24
1584.2.cd.f 24
1584.2.cf \(\chi_{1584}(155, \cdot)\) n/a 960 4
1584.2.cg \(\chi_{1584}(461, \cdot)\) n/a 1136 4
1584.2.cj \(\chi_{1584}(43, \cdot)\) n/a 1136 4
1584.2.ck \(\chi_{1584}(133, \cdot)\) n/a 960 4
1584.2.cm \(\chi_{1584}(49, \cdot)\) n/a 560 8
1584.2.cn \(\chi_{1584}(413, \cdot)\) n/a 768 8
1584.2.cq \(\chi_{1584}(179, \cdot)\) n/a 768 8
1584.2.cr \(\chi_{1584}(37, \cdot)\) n/a 944 8
1584.2.cu \(\chi_{1584}(19, \cdot)\) n/a 944 8
1584.2.cw \(\chi_{1584}(497, \cdot)\) n/a 560 8
1584.2.cy \(\chi_{1584}(47, \cdot)\) n/a 576 8
1584.2.da \(\chi_{1584}(25, \cdot)\) None 0 8
1584.2.dc \(\chi_{1584}(7, \cdot)\) None 0 8
1584.2.dd \(\chi_{1584}(119, \cdot)\) None 0 8
1584.2.df \(\chi_{1584}(41, \cdot)\) None 0 8
1584.2.dh \(\chi_{1584}(79, \cdot)\) n/a 576 8
1584.2.dl \(\chi_{1584}(157, \cdot)\) n/a 4544 16
1584.2.dm \(\chi_{1584}(139, \cdot)\) n/a 4544 16
1584.2.dp \(\chi_{1584}(29, \cdot)\) n/a 4544 16
1584.2.dq \(\chi_{1584}(59, \cdot)\) n/a 4544 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1584))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1584)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(198))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(264))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(396))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(528))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(792))\)\(^{\oplus 2}\)