Properties

Label 3528.2
Level 3528
Weight 2
Dimension 143857
Nonzero newspaces 60
Sturm bound 1354752
Trace bound 25

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 3528 = 2^{3} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 60 \)
Sturm bound: \(1354752\)
Trace bound: \(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3528))\).

Total New Old
Modular forms 344448 145603 198845
Cusp forms 332929 143857 189072
Eisenstein series 11519 1746 9773

Trace form

\( 143857q - 92q^{2} - 123q^{3} - 92q^{4} + 4q^{5} - 128q^{6} - 108q^{7} - 176q^{8} - 249q^{9} + O(q^{10}) \) \( 143857q - 92q^{2} - 123q^{3} - 92q^{4} + 4q^{5} - 128q^{6} - 108q^{7} - 176q^{8} - 249q^{9} - 294q^{10} - 95q^{11} - 134q^{12} + 10q^{13} - 108q^{14} - 240q^{15} - 100q^{16} - 188q^{17} - 120q^{18} - 292q^{19} - 116q^{20} - 208q^{22} - 144q^{23} - 96q^{24} - 224q^{25} - 122q^{26} - 120q^{27} - 372q^{28} + 6q^{29} - 74q^{30} - 190q^{31} - 112q^{32} - 295q^{33} - 176q^{34} - 180q^{35} - 166q^{36} - 78q^{37} - 88q^{38} - 156q^{39} - 140q^{40} - 329q^{41} - 144q^{42} - 233q^{43} - 94q^{45} - 194q^{46} - 228q^{47} - 100q^{48} - 270q^{49} - 176q^{50} - 183q^{51} - 8q^{52} - 122q^{53} - 84q^{54} - 394q^{55} - 66q^{56} - 461q^{57} - 40q^{58} - 161q^{59} - 114q^{60} - 8q^{61} - 46q^{62} - 144q^{63} - 422q^{64} - 214q^{65} - 80q^{66} - 103q^{67} + 66q^{68} + 94q^{69} + 60q^{70} + 62q^{71} + 42q^{72} - 480q^{73} + 304q^{74} + 145q^{75} + 308q^{76} + 126q^{77} + 46q^{78} + 206q^{79} + 498q^{80} - 157q^{81} + 182q^{82} + 266q^{83} + 72q^{84} + 212q^{85} + 508q^{86} + 114q^{87} + 356q^{88} - 110q^{89} + 322q^{90} - 228q^{91} + 408q^{92} + 134q^{93} + 438q^{94} + 250q^{95} + 264q^{96} - 261q^{97} + 132q^{98} - 210q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3528))\)

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
3528.2.a \(\chi_{3528}(1, \cdot)\) 3528.2.a.a 1 1
3528.2.a.b 1
3528.2.a.c 1
3528.2.a.d 1
3528.2.a.e 1
3528.2.a.f 1
3528.2.a.g 1
3528.2.a.h 1
3528.2.a.i 1
3528.2.a.j 1
3528.2.a.k 1
3528.2.a.l 1
3528.2.a.m 1
3528.2.a.n 1
3528.2.a.o 1
3528.2.a.p 1
3528.2.a.q 1
3528.2.a.r 1
3528.2.a.s 1
3528.2.a.t 1
3528.2.a.u 1
3528.2.a.v 1
3528.2.a.w 1
3528.2.a.x 1
3528.2.a.y 1
3528.2.a.z 1
3528.2.a.ba 1
3528.2.a.bb 2
3528.2.a.bc 2
3528.2.a.bd 2
3528.2.a.be 2
3528.2.a.bf 2
3528.2.a.bg 2
3528.2.a.bh 2
3528.2.a.bi 2
3528.2.a.bj 2
3528.2.a.bk 2
3528.2.a.bl 2
3528.2.a.bm 2
3528.2.b \(\chi_{3528}(1567, \cdot)\) None 0 1
3528.2.c \(\chi_{3528}(1765, \cdot)\) n/a 200 1
3528.2.h \(\chi_{3528}(1079, \cdot)\) None 0 1
3528.2.i \(\chi_{3528}(2645, \cdot)\) n/a 160 1
3528.2.j \(\chi_{3528}(2843, \cdot)\) n/a 164 1
3528.2.k \(\chi_{3528}(881, \cdot)\) 3528.2.k.a 8 1
3528.2.k.b 16
3528.2.k.c 16
3528.2.p \(\chi_{3528}(3331, \cdot)\) n/a 196 1
3528.2.q \(\chi_{3528}(1537, \cdot)\) n/a 240 2
3528.2.r \(\chi_{3528}(1177, \cdot)\) n/a 246 2
3528.2.s \(\chi_{3528}(361, \cdot)\) 3528.2.s.a 2 2
3528.2.s.b 2
3528.2.s.c 2
3528.2.s.d 2
3528.2.s.e 2
3528.2.s.f 2
3528.2.s.g 2
3528.2.s.h 2
3528.2.s.i 2
3528.2.s.j 2
3528.2.s.k 2
3528.2.s.l 2
3528.2.s.m 2
3528.2.s.n 2
3528.2.s.o 2
3528.2.s.p 2
3528.2.s.q 2
3528.2.s.r 2
3528.2.s.s 2
3528.2.s.t 2
3528.2.s.u 2
3528.2.s.v 2
3528.2.s.w 2
3528.2.s.x 2
3528.2.s.y 2
3528.2.s.z 2
3528.2.s.ba 2
3528.2.s.bb 2
3528.2.s.bc 4
3528.2.s.bd 4
3528.2.s.be 4
3528.2.s.bf 4
3528.2.s.bg 4
3528.2.s.bh 4
3528.2.s.bi 4
3528.2.s.bj 4
3528.2.s.bk 4
3528.2.s.bl 4
3528.2.s.bm 4
3528.2.t \(\chi_{3528}(961, \cdot)\) n/a 240 2
3528.2.w \(\chi_{3528}(949, \cdot)\) n/a 944 2
3528.2.x \(\chi_{3528}(31, \cdot)\) None 0 2
3528.2.y \(\chi_{3528}(1685, \cdot)\) n/a 944 2
3528.2.z \(\chi_{3528}(2615, \cdot)\) None 0 2
3528.2.be \(\chi_{3528}(979, \cdot)\) n/a 944 2
3528.2.bf \(\chi_{3528}(619, \cdot)\) n/a 944 2
3528.2.bk \(\chi_{3528}(19, \cdot)\) n/a 392 2
3528.2.bl \(\chi_{3528}(521, \cdot)\) 3528.2.bl.a 16 2
3528.2.bl.b 16
3528.2.bl.c 16
3528.2.bl.d 32
3528.2.bm \(\chi_{3528}(2627, \cdot)\) n/a 320 2
3528.2.br \(\chi_{3528}(491, \cdot)\) n/a 964 2
3528.2.bs \(\chi_{3528}(2273, \cdot)\) n/a 240 2
3528.2.bt \(\chi_{3528}(275, \cdot)\) n/a 944 2
3528.2.bu \(\chi_{3528}(2057, \cdot)\) n/a 240 2
3528.2.bz \(\chi_{3528}(2255, \cdot)\) None 0 2
3528.2.ca \(\chi_{3528}(509, \cdot)\) n/a 944 2
3528.2.cb \(\chi_{3528}(263, \cdot)\) None 0 2
3528.2.cc \(\chi_{3528}(293, \cdot)\) n/a 944 2
3528.2.ch \(\chi_{3528}(2285, \cdot)\) n/a 320 2
3528.2.ci \(\chi_{3528}(863, \cdot)\) None 0 2
3528.2.cj \(\chi_{3528}(1549, \cdot)\) n/a 392 2
3528.2.ck \(\chi_{3528}(1207, \cdot)\) None 0 2
3528.2.cp \(\chi_{3528}(391, \cdot)\) None 0 2
3528.2.cq \(\chi_{3528}(373, \cdot)\) n/a 944 2
3528.2.cr \(\chi_{3528}(607, \cdot)\) None 0 2
3528.2.cs \(\chi_{3528}(589, \cdot)\) n/a 964 2
3528.2.cx \(\chi_{3528}(1697, \cdot)\) n/a 240 2
3528.2.cy \(\chi_{3528}(851, \cdot)\) n/a 944 2
3528.2.cz \(\chi_{3528}(1195, \cdot)\) n/a 944 2
3528.2.dc \(\chi_{3528}(505, \cdot)\) n/a 420 6
3528.2.dd \(\chi_{3528}(307, \cdot)\) n/a 1668 6
3528.2.di \(\chi_{3528}(377, \cdot)\) n/a 336 6
3528.2.dj \(\chi_{3528}(323, \cdot)\) n/a 1344 6
3528.2.dk \(\chi_{3528}(125, \cdot)\) n/a 1344 6
3528.2.dl \(\chi_{3528}(71, \cdot)\) None 0 6
3528.2.dq \(\chi_{3528}(253, \cdot)\) n/a 1668 6
3528.2.dr \(\chi_{3528}(55, \cdot)\) None 0 6
3528.2.ds \(\chi_{3528}(193, \cdot)\) n/a 2016 12
3528.2.dt \(\chi_{3528}(289, \cdot)\) n/a 840 12
3528.2.du \(\chi_{3528}(169, \cdot)\) n/a 2016 12
3528.2.dv \(\chi_{3528}(25, \cdot)\) n/a 2016 12
3528.2.dy \(\chi_{3528}(187, \cdot)\) n/a 8016 12
3528.2.dz \(\chi_{3528}(347, \cdot)\) n/a 8016 12
3528.2.ea \(\chi_{3528}(185, \cdot)\) n/a 2016 12
3528.2.ef \(\chi_{3528}(85, \cdot)\) n/a 8016 12
3528.2.eg \(\chi_{3528}(103, \cdot)\) None 0 12
3528.2.eh \(\chi_{3528}(277, \cdot)\) n/a 8016 12
3528.2.ei \(\chi_{3528}(223, \cdot)\) None 0 12
3528.2.en \(\chi_{3528}(199, \cdot)\) None 0 12
3528.2.eo \(\chi_{3528}(37, \cdot)\) n/a 3336 12
3528.2.ep \(\chi_{3528}(359, \cdot)\) None 0 12
3528.2.eq \(\chi_{3528}(269, \cdot)\) n/a 2688 12
3528.2.ev \(\chi_{3528}(461, \cdot)\) n/a 8016 12
3528.2.ew \(\chi_{3528}(23, \cdot)\) None 0 12
3528.2.ex \(\chi_{3528}(5, \cdot)\) n/a 8016 12
3528.2.ey \(\chi_{3528}(239, \cdot)\) None 0 12
3528.2.fd \(\chi_{3528}(41, \cdot)\) n/a 2016 12
3528.2.fe \(\chi_{3528}(11, \cdot)\) n/a 8016 12
3528.2.ff \(\chi_{3528}(257, \cdot)\) n/a 2016 12
3528.2.fg \(\chi_{3528}(155, \cdot)\) n/a 8016 12
3528.2.fl \(\chi_{3528}(107, \cdot)\) n/a 2688 12
3528.2.fm \(\chi_{3528}(17, \cdot)\) n/a 672 12
3528.2.fn \(\chi_{3528}(451, \cdot)\) n/a 3336 12
3528.2.fs \(\chi_{3528}(115, \cdot)\) n/a 8016 12
3528.2.ft \(\chi_{3528}(139, \cdot)\) n/a 8016 12
3528.2.fy \(\chi_{3528}(95, \cdot)\) None 0 12
3528.2.fz \(\chi_{3528}(173, \cdot)\) n/a 8016 12
3528.2.ga \(\chi_{3528}(439, \cdot)\) None 0 12
3528.2.gb \(\chi_{3528}(205, \cdot)\) n/a 8016 12

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3528))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3528)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(252))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(294))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(392))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(441))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(504))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(588))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(882))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1176))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1764))\)\(^{\oplus 2}\)