# Properties

 Label 1536.2 Level 1536 Weight 2 Dimension 27424 Nonzero newspaces 14 Sturm bound 262144 Trace bound 49

## Defining parameters

 Level: $$N$$ = $$1536 = 2^{9} \cdot 3$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$14$$ Sturm bound: $$262144$$ Trace bound: $$49$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1536))$$.

Total New Old
Modular forms 67072 27872 39200
Cusp forms 64001 27424 36577
Eisenstein series 3071 448 2623

## Trace form

 $$27424q - 48q^{3} - 128q^{4} - 64q^{6} - 96q^{7} - 80q^{9} + O(q^{10})$$ $$27424q - 48q^{3} - 128q^{4} - 64q^{6} - 96q^{7} - 80q^{9} - 128q^{10} - 64q^{12} - 128q^{13} - 48q^{15} - 128q^{16} - 64q^{18} - 96q^{19} - 64q^{21} - 128q^{22} - 64q^{24} - 160q^{25} - 48q^{27} - 128q^{28} - 64q^{30} - 96q^{31} - 112q^{33} - 128q^{34} - 64q^{36} - 128q^{37} - 48q^{39} - 128q^{40} - 64q^{42} - 96q^{43} - 64q^{45} - 128q^{46} - 64q^{48} - 192q^{49} - 48q^{51} - 128q^{52} - 64q^{54} - 96q^{55} - 80q^{57} - 128q^{58} - 64q^{60} - 128q^{61} - 32q^{63} - 128q^{64} - 64q^{66} - 96q^{67} - 64q^{69} - 128q^{70} - 64q^{72} - 160q^{73} - 48q^{75} - 128q^{76} - 64q^{78} - 96q^{79} - 96q^{81} - 128q^{82} - 64q^{84} - 128q^{85} - 48q^{87} - 128q^{88} - 64q^{90} - 96q^{91} - 16q^{93} - 128q^{94} - 64q^{96} - 224q^{97} - 48q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1536))$$

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
1536.2.a $$\chi_{1536}(1, \cdot)$$ 1536.2.a.a 2 1
1536.2.a.b 2
1536.2.a.c 2
1536.2.a.d 2
1536.2.a.e 2
1536.2.a.f 2
1536.2.a.g 2
1536.2.a.h 2
1536.2.a.i 2
1536.2.a.j 2
1536.2.a.k 2
1536.2.a.l 2
1536.2.a.m 4
1536.2.a.n 4
1536.2.c $$\chi_{1536}(1535, \cdot)$$ 1536.2.c.a 2 1
1536.2.c.b 2
1536.2.c.c 2
1536.2.c.d 2
1536.2.c.e 4
1536.2.c.f 4
1536.2.c.g 4
1536.2.c.h 4
1536.2.c.i 4
1536.2.c.j 4
1536.2.c.k 8
1536.2.c.l 8
1536.2.c.m 16
1536.2.d $$\chi_{1536}(769, \cdot)$$ 1536.2.d.a 4 1
1536.2.d.b 4
1536.2.d.c 4
1536.2.d.d 4
1536.2.d.e 4
1536.2.d.f 4
1536.2.d.g 8
1536.2.f $$\chi_{1536}(767, \cdot)$$ 1536.2.f.a 4 1
1536.2.f.b 4
1536.2.f.c 4
1536.2.f.d 4
1536.2.f.e 4
1536.2.f.f 4
1536.2.f.g 4
1536.2.f.h 4
1536.2.f.i 4
1536.2.f.j 4
1536.2.f.k 8
1536.2.f.l 16
1536.2.j $$\chi_{1536}(385, \cdot)$$ 1536.2.j.a 4 2
1536.2.j.b 4
1536.2.j.c 4
1536.2.j.d 4
1536.2.j.e 8
1536.2.j.f 8
1536.2.j.g 8
1536.2.j.h 8
1536.2.j.i 8
1536.2.j.j 8
1536.2.k $$\chi_{1536}(383, \cdot)$$ n/a 128 2
1536.2.n $$\chi_{1536}(193, \cdot)$$ n/a 128 4
1536.2.o $$\chi_{1536}(191, \cdot)$$ n/a 224 4
1536.2.r $$\chi_{1536}(97, \cdot)$$ n/a 256 8
1536.2.s $$\chi_{1536}(95, \cdot)$$ n/a 480 8
1536.2.v $$\chi_{1536}(49, \cdot)$$ n/a 512 16
1536.2.w $$\chi_{1536}(47, \cdot)$$ n/a 992 16
1536.2.z $$\chi_{1536}(25, \cdot)$$ None 0 32
1536.2.ba $$\chi_{1536}(23, \cdot)$$ None 0 32
1536.2.bd $$\chi_{1536}(13, \cdot)$$ n/a 8192 64
1536.2.be $$\chi_{1536}(11, \cdot)$$ n/a 16256 64

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1536))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1536)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 7}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(96))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(128))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(192))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(256))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(384))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(512))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(768))$$$$^{\oplus 2}$$