## Defining parameters

 Level: $$N$$ = $$3584 = 2^{9} \cdot 7$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$28$$ Sturm bound: $$1572864$$ Trace bound: $$193$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(3584))$$.

Total New Old
Modular forms 397824 213088 184736
Cusp forms 388609 210848 177761
Eisenstein series 9215 2240 6975

## Trace form

 $$210848 q - 256 q^{2} - 192 q^{3} - 256 q^{4} - 256 q^{5} - 256 q^{6} - 240 q^{7} - 640 q^{8} - 320 q^{9} + O(q^{10})$$ $$210848 q - 256 q^{2} - 192 q^{3} - 256 q^{4} - 256 q^{5} - 256 q^{6} - 240 q^{7} - 640 q^{8} - 320 q^{9} - 256 q^{10} - 192 q^{11} - 256 q^{12} - 256 q^{13} - 320 q^{14} - 480 q^{15} - 256 q^{16} - 384 q^{17} - 256 q^{18} - 192 q^{19} - 256 q^{20} - 320 q^{21} - 640 q^{22} - 192 q^{23} - 256 q^{24} - 320 q^{25} - 256 q^{26} - 192 q^{27} - 320 q^{28} - 640 q^{29} - 256 q^{30} - 192 q^{31} - 256 q^{32} - 448 q^{33} - 256 q^{34} - 240 q^{35} - 640 q^{36} - 256 q^{37} - 256 q^{38} - 192 q^{39} - 256 q^{40} - 320 q^{41} - 320 q^{42} - 480 q^{43} - 256 q^{44} - 256 q^{45} - 256 q^{46} - 192 q^{47} - 256 q^{48} - 480 q^{49} - 640 q^{50} - 192 q^{51} - 256 q^{52} - 256 q^{53} - 256 q^{54} - 192 q^{55} - 320 q^{56} - 800 q^{57} - 256 q^{58} - 192 q^{59} - 256 q^{60} - 256 q^{61} - 256 q^{62} - 224 q^{63} - 640 q^{64} - 512 q^{65} - 256 q^{66} - 192 q^{67} - 256 q^{68} - 256 q^{69} - 320 q^{70} - 480 q^{71} - 256 q^{72} - 320 q^{73} - 256 q^{74} - 192 q^{75} - 256 q^{76} - 320 q^{77} - 640 q^{78} - 192 q^{79} - 256 q^{80} - 384 q^{81} - 256 q^{82} - 192 q^{83} - 320 q^{84} - 640 q^{85} - 256 q^{86} - 192 q^{87} - 256 q^{88} - 320 q^{89} - 256 q^{90} - 240 q^{91} - 640 q^{92} - 160 q^{93} - 256 q^{94} - 192 q^{95} - 256 q^{96} - 448 q^{97} - 320 q^{98} - 480 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(3584))$$

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
3584.2.a $$\chi_{3584}(1, \cdot)$$ 3584.2.a.a 2 1
3584.2.a.b 2
3584.2.a.c 4
3584.2.a.d 4
3584.2.a.e 6
3584.2.a.f 6
3584.2.a.g 6
3584.2.a.h 6
3584.2.a.i 6
3584.2.a.j 6
3584.2.a.k 6
3584.2.a.l 6
3584.2.a.m 8
3584.2.a.n 8
3584.2.a.o 10
3584.2.a.p 10
3584.2.b $$\chi_{3584}(1793, \cdot)$$ 3584.2.b.a 2 1
3584.2.b.b 2
3584.2.b.c 4
3584.2.b.d 4
3584.2.b.e 8
3584.2.b.f 8
3584.2.b.g 10
3584.2.b.h 10
3584.2.b.i 12
3584.2.b.j 12
3584.2.b.k 12
3584.2.b.l 12
3584.2.e $$\chi_{3584}(1791, \cdot)$$ n/a 128 1
3584.2.f $$\chi_{3584}(3583, \cdot)$$ n/a 128 1
3584.2.i $$\chi_{3584}(513, \cdot)$$ n/a 256 2
3584.2.j $$\chi_{3584}(895, \cdot)$$ n/a 256 2
3584.2.m $$\chi_{3584}(897, \cdot)$$ 3584.2.m.a 2 2
3584.2.m.b 2
3584.2.m.c 2
3584.2.m.d 2
3584.2.m.e 2
3584.2.m.f 2
3584.2.m.g 2
3584.2.m.h 2
3584.2.m.i 2
3584.2.m.j 2
3584.2.m.k 2
3584.2.m.l 2
3584.2.m.m 2
3584.2.m.n 2
3584.2.m.o 2
3584.2.m.p 2
3584.2.m.q 2
3584.2.m.r 2
3584.2.m.s 2
3584.2.m.t 2
3584.2.m.u 2
3584.2.m.v 2
3584.2.m.w 2
3584.2.m.x 2
3584.2.m.y 2
3584.2.m.z 2
3584.2.m.ba 2
3584.2.m.bb 2
3584.2.m.bc 4
3584.2.m.bd 4
3584.2.m.be 4
3584.2.m.bf 4
3584.2.m.bg 6
3584.2.m.bh 6
3584.2.m.bi 6
3584.2.m.bj 6
3584.2.m.bk 24
3584.2.m.bl 24
3584.2.m.bm 24
3584.2.m.bn 24
3584.2.p $$\chi_{3584}(2047, \cdot)$$ n/a 256 2
3584.2.q $$\chi_{3584}(255, \cdot)$$ n/a 256 2
3584.2.t $$\chi_{3584}(2305, \cdot)$$ n/a 256 2
3584.2.u $$\chi_{3584}(449, \cdot)$$ n/a 384 4
3584.2.x $$\chi_{3584}(447, \cdot)$$ n/a 480 4
3584.2.z $$\chi_{3584}(383, \cdot)$$ n/a 512 4
3584.2.ba $$\chi_{3584}(641, \cdot)$$ n/a 512 4
3584.2.bc $$\chi_{3584}(225, \cdot)$$ n/a 768 8
3584.2.bd $$\chi_{3584}(223, \cdot)$$ n/a 992 8
3584.2.bh $$\chi_{3584}(65, \cdot)$$ n/a 960 8
3584.2.bi $$\chi_{3584}(703, \cdot)$$ n/a 960 8
3584.2.bk $$\chi_{3584}(111, \cdot)$$ n/a 2016 16
3584.2.bn $$\chi_{3584}(113, \cdot)$$ n/a 1536 16
3584.2.bq $$\chi_{3584}(31, \cdot)$$ n/a 1984 16
3584.2.br $$\chi_{3584}(289, \cdot)$$ n/a 1984 16
3584.2.bs $$\chi_{3584}(57, \cdot)$$ None 0 32
3584.2.bv $$\chi_{3584}(55, \cdot)$$ None 0 32
3584.2.bx $$\chi_{3584}(47, \cdot)$$ n/a 4032 32
3584.2.by $$\chi_{3584}(81, \cdot)$$ n/a 4032 32
3584.2.ca $$\chi_{3584}(29, \cdot)$$ n/a 24576 64
3584.2.cb $$\chi_{3584}(27, \cdot)$$ n/a 32640 64
3584.2.cf $$\chi_{3584}(9, \cdot)$$ None 0 64
3584.2.cg $$\chi_{3584}(87, \cdot)$$ None 0 64
3584.2.ck $$\chi_{3584}(3, \cdot)$$ n/a 65280 128
3584.2.cl $$\chi_{3584}(37, \cdot)$$ n/a 65280 128

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(3584))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(3584)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 7}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(112))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(128))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(224))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(256))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(448))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(512))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(896))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1792))$$$$^{\oplus 2}$$