# Properties

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

## 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

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

## 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 available 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

$$S_{2}^{\mathrm{old}}(\Gamma_1(3528)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 36}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 27}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(63))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(84))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(98))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(126))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(147))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(168))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(196))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(252))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(294))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(392))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(441))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(504))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(588))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(882))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1176))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1764))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3528))$$$$^{\oplus 1}$$