# Properties

 Label 3584.1 Level 3584 Weight 1 Dimension 136 Nonzero newspaces 6 Newform subspaces 14 Sturm bound 786432 Trace bound 109

## Defining parameters

 Level: $$N$$ = $$3584 = 2^{9} \cdot 7$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$6$$ Newform subspaces: $$14$$ Sturm bound: $$786432$$ Trace bound: $$109$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(3584))$$.

Total New Old
Modular forms 5098 1256 3842
Cusp forms 490 136 354
Eisenstein series 4608 1120 3488

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 136 0 0 0

## Trace form

 $$136 q + O(q^{10})$$ $$136 q + 8 q^{49} - 16 q^{65} + 24 q^{81} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(3584))$$

We only show spaces with odd 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
3584.1.c $$\chi_{3584}(2561, \cdot)$$ 3584.1.c.a 4 1
3584.1.c.b 4
3584.1.c.c 4
3584.1.d $$\chi_{3584}(1023, \cdot)$$ None 0 1
3584.1.g $$\chi_{3584}(2815, \cdot)$$ None 0 1
3584.1.h $$\chi_{3584}(769, \cdot)$$ 3584.1.h.a 4 1
3584.1.h.b 4
3584.1.h.c 4
3584.1.k $$\chi_{3584}(127, \cdot)$$ None 0 2
3584.1.l $$\chi_{3584}(1665, \cdot)$$ None 0 2
3584.1.n $$\chi_{3584}(257, \cdot)$$ None 0 2
3584.1.o $$\chi_{3584}(767, \cdot)$$ None 0 2
3584.1.r $$\chi_{3584}(1535, \cdot)$$ None 0 2
3584.1.s $$\chi_{3584}(1025, \cdot)$$ None 0 2
3584.1.v $$\chi_{3584}(321, \cdot)$$ 3584.1.v.a 4 4
3584.1.v.b 4
3584.1.v.c 4
3584.1.v.d 4
3584.1.w $$\chi_{3584}(575, \cdot)$$ None 0 4
3584.1.y $$\chi_{3584}(639, \cdot)$$ None 0 4
3584.1.bb $$\chi_{3584}(129, \cdot)$$ None 0 4
3584.1.be $$\chi_{3584}(351, \cdot)$$ None 0 8
3584.1.bf $$\chi_{3584}(97, \cdot)$$ 3584.1.bf.a 8 8
3584.1.bf.b 8
3584.1.bg $$\chi_{3584}(577, \cdot)$$ None 0 8
3584.1.bj $$\chi_{3584}(191, \cdot)$$ None 0 8
3584.1.bl $$\chi_{3584}(15, \cdot)$$ None 0 16
3584.1.bm $$\chi_{3584}(209, \cdot)$$ 3584.1.bm.a 16 16
3584.1.bo $$\chi_{3584}(33, \cdot)$$ None 0 16
3584.1.bp $$\chi_{3584}(95, \cdot)$$ None 0 16
3584.1.bt $$\chi_{3584}(41, \cdot)$$ None 0 32
3584.1.bu $$\chi_{3584}(71, \cdot)$$ None 0 32
3584.1.bw $$\chi_{3584}(79, \cdot)$$ None 0 32
3584.1.bz $$\chi_{3584}(17, \cdot)$$ None 0 32
3584.1.cc $$\chi_{3584}(43, \cdot)$$ None 0 64
3584.1.cd $$\chi_{3584}(13, \cdot)$$ 3584.1.cd.a 64 64
3584.1.ce $$\chi_{3584}(73, \cdot)$$ None 0 64
3584.1.ch $$\chi_{3584}(23, \cdot)$$ None 0 64
3584.1.ci $$\chi_{3584}(5, \cdot)$$ None 0 128
3584.1.cj $$\chi_{3584}(11, \cdot)$$ None 0 128

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(3584))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(3584)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 7}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(112))$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(128))$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(224))$$$$^{\oplus 5}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(256))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(448))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(512))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(896))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(1792))$$$$^{\oplus 2}$$