↑

Properties

Label 1088.4
Level 1088
Weight 4
Dimension 61446
Nonzero newspaces 34
Sturm bound 294912
Trace bound 19

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 1088 = 2^{6} \cdot 17 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 34 \)
Sturm bound: \(294912\)
Trace bound: \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1088))\).

Total New Old
Modular forms 111744 62106 49638
Cusp forms 109440 61446 47994
Eisenstein series 2304 660 1644

Trace form

\( 61446 q - 112 q^{2} - 84 q^{3} - 112 q^{4} - 112 q^{5} - 112 q^{6} - 80 q^{7} - 112 q^{8} - 86 q^{9} + O(q^{10}) \) \( 61446 q - 112 q^{2} - 84 q^{3} - 112 q^{4} - 112 q^{5} - 112 q^{6} - 80 q^{7} - 112 q^{8} - 86 q^{9} - 112 q^{10} - 44 q^{11} - 112 q^{12} - 256 q^{13} - 112 q^{14} - 328 q^{15} - 112 q^{16} - 314 q^{17} - 240 q^{18} - 132 q^{19} - 112 q^{20} - 88 q^{21} - 1056 q^{22} - 80 q^{23} - 2112 q^{24} - 242 q^{25} - 32 q^{26} + 288 q^{27} + 1408 q^{28} + 688 q^{29} + 4528 q^{30} + 640 q^{31} + 2368 q^{32} + 1880 q^{33} + 880 q^{34} + 776 q^{35} + 1648 q^{36} + 928 q^{37} - 992 q^{38} - 80 q^{39} - 3392 q^{40} - 2188 q^{41} - 6432 q^{42} - 1756 q^{43} - 2112 q^{44} - 3080 q^{45} - 112 q^{46} - 1968 q^{47} - 112 q^{48} - 2322 q^{49} + 5600 q^{50} - 4564 q^{51} + 6384 q^{52} - 928 q^{53} + 3344 q^{54} - 1232 q^{55} - 896 q^{56} + 2016 q^{57} - 4864 q^{58} + 8836 q^{59} - 9904 q^{60} + 2048 q^{61} - 6096 q^{62} + 15272 q^{63} - 12208 q^{64} + 4240 q^{65} - 11184 q^{66} + 11964 q^{67} - 2184 q^{68} + 1032 q^{69} - 4144 q^{70} + 816 q^{71} + 1184 q^{72} - 2188 q^{73} + 5152 q^{74} - 14820 q^{75} + 11792 q^{76} - 6360 q^{77} + 3872 q^{78} - 20240 q^{79} - 8640 q^{80} - 13834 q^{81} - 14032 q^{82} - 5204 q^{83} - 8400 q^{84} - 1776 q^{85} + 800 q^{86} - 80 q^{87} + 6128 q^{88} + 6996 q^{89} + 18608 q^{90} + 6584 q^{91} + 25120 q^{92} + 16640 q^{93} + 17744 q^{94} + 13704 q^{95} + 25728 q^{96} + 18620 q^{97} + 24096 q^{98} + 9404 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1088))\)

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
1088.4.a \(\chi_{1088}(1, \cdot)\) 1088.4.a.a 1 1
1088.4.a.b 1
1088.4.a.c 1
1088.4.a.d 1
1088.4.a.e 1
1088.4.a.f 1
1088.4.a.g 1
1088.4.a.h 1
1088.4.a.i 1
1088.4.a.j 1
1088.4.a.k 1
1088.4.a.l 1
1088.4.a.m 2
1088.4.a.n 2
1088.4.a.o 2
1088.4.a.p 2
1088.4.a.q 2
1088.4.a.r 3
1088.4.a.s 3
1088.4.a.t 3
1088.4.a.u 3
1088.4.a.v 3
1088.4.a.w 3
1088.4.a.x 3
1088.4.a.y 3
1088.4.a.z 3
1088.4.a.ba 3
1088.4.a.bb 4
1088.4.a.bc 4
1088.4.a.bd 4
1088.4.a.be 4
1088.4.a.bf 6
1088.4.a.bg 7
1088.4.a.bh 7
1088.4.a.bi 8
1088.4.b \(\chi_{1088}(577, \cdot)\) n/a 106 1
1088.4.c \(\chi_{1088}(545, \cdot)\) 1088.4.c.a 16 1
1088.4.c.b 16
1088.4.c.c 32
1088.4.c.d 32
1088.4.h \(\chi_{1088}(33, \cdot)\) n/a 108 1
1088.4.j \(\chi_{1088}(81, \cdot)\) n/a 212 2
1088.4.l \(\chi_{1088}(273, \cdot)\) n/a 192 2
1088.4.m \(\chi_{1088}(225, \cdot)\) n/a 216 2
1088.4.o \(\chi_{1088}(769, \cdot)\) n/a 212 2
1088.4.r \(\chi_{1088}(305, \cdot)\) n/a 212 2
1088.4.s \(\chi_{1088}(625, \cdot)\) n/a 212 2
1088.4.v \(\chi_{1088}(281, \cdot)\) None 0 4
1088.4.x \(\chi_{1088}(185, \cdot)\) None 0 4
1088.4.z \(\chi_{1088}(89, \cdot)\) None 0 4
1088.4.bb \(\chi_{1088}(257, \cdot)\) n/a 424 4
1088.4.bc \(\chi_{1088}(169, \cdot)\) None 0 4
1088.4.bd \(\chi_{1088}(137, \cdot)\) None 0 4
1088.4.be \(\chi_{1088}(433, \cdot)\) n/a 424 4
1088.4.bg \(\chi_{1088}(49, \cdot)\) n/a 424 4
1088.4.bk \(\chi_{1088}(161, \cdot)\) n/a 432 4
1088.4.bn \(\chi_{1088}(217, \cdot)\) None 0 4
1088.4.bp \(\chi_{1088}(9, \cdot)\) None 0 4
1088.4.bq \(\chi_{1088}(25, \cdot)\) None 0 4
1088.4.bs \(\chi_{1088}(139, \cdot)\) n/a 3440 8
1088.4.bv \(\chi_{1088}(3, \cdot)\) n/a 3440 8
1088.4.bx \(\chi_{1088}(189, \cdot)\) n/a 3440 8
1088.4.by \(\chi_{1088}(147, \cdot)\) n/a 3440 8
1088.4.ca \(\chi_{1088}(107, \cdot)\) n/a 3440 8
1088.4.cd \(\chi_{1088}(79, \cdot)\) n/a 848 8
1088.4.ce \(\chi_{1088}(53, \cdot)\) n/a 3440 8
1088.4.cf \(\chi_{1088}(77, \cdot)\) n/a 3440 8
1088.4.cg \(\chi_{1088}(7, \cdot)\) None 0 8
1088.4.cj \(\chi_{1088}(75, \cdot)\) n/a 3440 8
1088.4.cl \(\chi_{1088}(91, \cdot)\) n/a 3440 8
1088.4.cn \(\chi_{1088}(69, \cdot)\) n/a 3072 8
1088.4.cp \(\chi_{1088}(63, \cdot)\) n/a 848 8
1088.4.cr \(\chi_{1088}(23, \cdot)\) None 0 8
1088.4.cs \(\chi_{1088}(13, \cdot)\) n/a 3440 8
1088.4.cv \(\chi_{1088}(149, \cdot)\) n/a 3440 8
1088.4.cx \(\chi_{1088}(39, \cdot)\) None 0 8
1088.4.cy \(\chi_{1088}(31, \cdot)\) n/a 864 8
1088.4.da \(\chi_{1088}(101, \cdot)\) n/a 3440 8
1088.4.dc \(\chi_{1088}(231, \cdot)\) None 0 8
1088.4.dh \(\chi_{1088}(207, \cdot)\) n/a 848 8
1088.4.dj \(\chi_{1088}(253, \cdot)\) n/a 3440 8
1088.4.dl \(\chi_{1088}(347, \cdot)\) n/a 3440 8
1088.4.dm \(\chi_{1088}(379, \cdot)\) n/a 3440 8

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1088))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1088)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 7}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(136))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(272))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(544))\)\(^{\oplus 2}\)