# Properties

 Label 1064.2 Level 1064 Weight 2 Dimension 18186 Nonzero newspaces 48 Sturm bound 138240 Trace bound 17

## Defining parameters

 Level: $$N$$ = $$1064 = 2^{3} \cdot 7 \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$48$$ Sturm bound: $$138240$$ Trace bound: $$17$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1064))$$.

Total New Old
Modular forms 35856 18866 16990
Cusp forms 33265 18186 15079
Eisenstein series 2591 680 1911

## Trace form

 $$18186 q - 60 q^{2} - 60 q^{3} - 60 q^{4} - 60 q^{6} - 78 q^{7} - 156 q^{8} - 108 q^{9} + O(q^{10})$$ $$18186 q - 60 q^{2} - 60 q^{3} - 60 q^{4} - 60 q^{6} - 78 q^{7} - 156 q^{8} - 108 q^{9} - 60 q^{10} - 48 q^{11} - 60 q^{12} + 12 q^{13} - 78 q^{14} - 132 q^{15} - 60 q^{16} - 108 q^{17} - 96 q^{18} - 66 q^{19} - 168 q^{20} - 216 q^{22} - 96 q^{23} - 132 q^{24} - 156 q^{25} - 120 q^{26} - 102 q^{27} - 174 q^{28} + 36 q^{29} - 156 q^{30} - 60 q^{31} - 120 q^{32} - 24 q^{33} - 132 q^{34} - 42 q^{35} - 216 q^{36} + 48 q^{37} - 84 q^{38} - 36 q^{39} - 120 q^{40} - 36 q^{41} - 6 q^{42} - 84 q^{43} - 12 q^{44} + 120 q^{45} - 60 q^{47} + 60 q^{48} - 150 q^{49} - 72 q^{50} - 126 q^{51} + 48 q^{52} - 12 q^{53} - 24 q^{54} - 120 q^{55} + 6 q^{56} - 360 q^{57} - 72 q^{58} - 132 q^{59} - 36 q^{61} - 132 q^{62} - 222 q^{63} - 360 q^{64} - 228 q^{65} - 300 q^{66} - 312 q^{67} - 312 q^{68} - 24 q^{69} - 342 q^{70} - 336 q^{71} - 636 q^{72} - 246 q^{73} - 516 q^{74} - 468 q^{75} - 498 q^{76} - 90 q^{77} - 684 q^{78} - 348 q^{79} - 576 q^{80} - 330 q^{81} - 744 q^{82} - 240 q^{83} - 510 q^{84} - 528 q^{86} - 360 q^{87} - 492 q^{88} - 240 q^{89} - 504 q^{90} - 126 q^{91} - 492 q^{92} - 48 q^{93} - 204 q^{94} + 12 q^{95} - 180 q^{96} - 144 q^{97} - 126 q^{98} + 114 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1064))$$

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
1064.2.a $$\chi_{1064}(1, \cdot)$$ 1064.2.a.a 2 1
1064.2.a.b 2
1064.2.a.c 2
1064.2.a.d 2
1064.2.a.e 2
1064.2.a.f 3
1064.2.a.g 4
1064.2.a.h 4
1064.2.a.i 5
1064.2.b $$\chi_{1064}(533, \cdot)$$ n/a 108 1
1064.2.e $$\chi_{1064}(379, \cdot)$$ n/a 120 1
1064.2.f $$\chi_{1064}(797, \cdot)$$ n/a 156 1
1064.2.i $$\chi_{1064}(419, \cdot)$$ n/a 144 1
1064.2.j $$\chi_{1064}(951, \cdot)$$ None 0 1
1064.2.m $$\chi_{1064}(265, \cdot)$$ 1064.2.m.a 16 1
1064.2.m.b 24
1064.2.n $$\chi_{1064}(911, \cdot)$$ None 0 1
1064.2.q $$\chi_{1064}(305, \cdot)$$ 1064.2.q.a 2 2
1064.2.q.b 2
1064.2.q.c 2
1064.2.q.d 2
1064.2.q.e 2
1064.2.q.f 2
1064.2.q.g 2
1064.2.q.h 2
1064.2.q.i 2
1064.2.q.j 2
1064.2.q.k 4
1064.2.q.l 4
1064.2.q.m 6
1064.2.q.n 16
1064.2.q.o 22
1064.2.r $$\chi_{1064}(505, \cdot)$$ 1064.2.r.a 2 2
1064.2.r.b 2
1064.2.r.c 2
1064.2.r.d 2
1064.2.r.e 2
1064.2.r.f 4
1064.2.r.g 8
1064.2.r.h 8
1064.2.r.i 14
1064.2.r.j 16
1064.2.s $$\chi_{1064}(121, \cdot)$$ 1064.2.s.a 2 2
1064.2.s.b 2
1064.2.s.c 4
1064.2.s.d 32
1064.2.s.e 40
1064.2.t $$\chi_{1064}(961, \cdot)$$ 1064.2.t.a 2 2
1064.2.t.b 2
1064.2.t.c 4
1064.2.t.d 32
1064.2.t.e 40
1064.2.u $$\chi_{1064}(467, \cdot)$$ n/a 312 2
1064.2.x $$\chi_{1064}(829, \cdot)$$ n/a 312 2
1064.2.y $$\chi_{1064}(331, \cdot)$$ n/a 312 2
1064.2.bb $$\chi_{1064}(429, \cdot)$$ n/a 312 2
1064.2.bc $$\chi_{1064}(145, \cdot)$$ 1064.2.bc.a 80 2
1064.2.bf $$\chi_{1064}(87, \cdot)$$ None 0 2
1064.2.bh $$\chi_{1064}(183, \cdot)$$ None 0 2
1064.2.bj $$\chi_{1064}(151, \cdot)$$ None 0 2
1064.2.bn $$\chi_{1064}(391, \cdot)$$ None 0 2
1064.2.bp $$\chi_{1064}(873, \cdot)$$ 1064.2.bp.a 80 2
1064.2.bq $$\chi_{1064}(495, \cdot)$$ None 0 2
1064.2.bs $$\chi_{1064}(601, \cdot)$$ 1064.2.bs.a 80 2
1064.2.bw $$\chi_{1064}(639, \cdot)$$ None 0 2
1064.2.bx $$\chi_{1064}(107, \cdot)$$ n/a 312 2
1064.2.ca $$\chi_{1064}(277, \cdot)$$ n/a 312 2
1064.2.cc $$\chi_{1064}(69, \cdot)$$ n/a 312 2
1064.2.ce $$\chi_{1064}(115, \cdot)$$ n/a 288 2
1064.2.cf $$\chi_{1064}(341, \cdot)$$ n/a 312 2
1064.2.ch $$\chi_{1064}(83, \cdot)$$ n/a 312 2
1064.2.ck $$\chi_{1064}(197, \cdot)$$ n/a 240 2
1064.2.cm $$\chi_{1064}(683, \cdot)$$ n/a 312 2
1064.2.cn $$\chi_{1064}(837, \cdot)$$ n/a 288 2
1064.2.cp $$\chi_{1064}(715, \cdot)$$ n/a 240 2
1064.2.cr $$\chi_{1064}(619, \cdot)$$ n/a 312 2
1064.2.cu $$\chi_{1064}(677, \cdot)$$ n/a 312 2
1064.2.cx $$\chi_{1064}(487, \cdot)$$ None 0 2
1064.2.cy $$\chi_{1064}(297, \cdot)$$ 1064.2.cy.a 80 2
1064.2.db $$\chi_{1064}(311, \cdot)$$ None 0 2
1064.2.dc $$\chi_{1064}(169, \cdot)$$ n/a 180 6
1064.2.dd $$\chi_{1064}(9, \cdot)$$ n/a 240 6
1064.2.de $$\chi_{1064}(25, \cdot)$$ n/a 240 6
1064.2.df $$\chi_{1064}(199, \cdot)$$ None 0 6
1064.2.dg $$\chi_{1064}(79, \cdot)$$ None 0 6
1064.2.dj $$\chi_{1064}(117, \cdot)$$ n/a 936 6
1064.2.dk $$\chi_{1064}(93, \cdot)$$ n/a 936 6
1064.2.dp $$\chi_{1064}(41, \cdot)$$ n/a 240 6
1064.2.ds $$\chi_{1064}(89, \cdot)$$ n/a 240 6
1064.2.dv $$\chi_{1064}(139, \cdot)$$ n/a 936 6
1064.2.dw $$\chi_{1064}(155, \cdot)$$ n/a 720 6
1064.2.dz $$\chi_{1064}(51, \cdot)$$ n/a 936 6
1064.2.ea $$\chi_{1064}(283, \cdot)$$ n/a 936 6
1064.2.ed $$\chi_{1064}(15, \cdot)$$ None 0 6
1064.2.ee $$\chi_{1064}(55, \cdot)$$ None 0 6
1064.2.eh $$\chi_{1064}(47, \cdot)$$ None 0 6
1064.2.ei $$\chi_{1064}(375, \cdot)$$ None 0 6
1064.2.el $$\chi_{1064}(85, \cdot)$$ n/a 720 6
1064.2.em $$\chi_{1064}(13, \cdot)$$ n/a 936 6
1064.2.ep $$\chi_{1064}(269, \cdot)$$ n/a 936 6
1064.2.eq $$\chi_{1064}(541, \cdot)$$ n/a 936 6
1064.2.er $$\chi_{1064}(33, \cdot)$$ n/a 240 6
1064.2.eu $$\chi_{1064}(67, \cdot)$$ n/a 936 6
1064.2.ev $$\chi_{1064}(131, \cdot)$$ n/a 936 6

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1064))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1064)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(133))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(152))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(266))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(532))$$$$^{\oplus 2}$$