# Properties

 Label 3072.2 Level 3072 Weight 2 Dimension 110112 Nonzero newspaces 16 Sturm bound 1048576 Trace bound 233

## Defining parameters

 Level: $$N$$ = $$3072 = 2^{10} \cdot 3$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$16$$ Sturm bound: $$1048576$$ Trace bound: $$233$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(3072))$$.

Total New Old
Modular forms 265472 111072 154400
Cusp forms 258817 110112 148705
Eisenstein series 6655 960 5695

## Trace form

 $$110112 q - 96 q^{3} - 256 q^{4} - 128 q^{6} - 192 q^{7} - 160 q^{9} + O(q^{10})$$ $$110112 q - 96 q^{3} - 256 q^{4} - 128 q^{6} - 192 q^{7} - 160 q^{9} - 256 q^{10} - 128 q^{12} - 256 q^{13} - 96 q^{15} - 256 q^{16} - 128 q^{18} - 192 q^{19} - 128 q^{21} - 256 q^{22} - 128 q^{24} - 320 q^{25} - 96 q^{27} - 256 q^{28} - 128 q^{30} - 192 q^{31} - 224 q^{33} - 256 q^{34} - 128 q^{36} - 256 q^{37} - 96 q^{39} - 256 q^{40} - 128 q^{42} - 192 q^{43} - 128 q^{45} - 256 q^{46} - 128 q^{48} - 384 q^{49} - 96 q^{51} - 256 q^{52} - 128 q^{54} - 192 q^{55} - 160 q^{57} - 256 q^{58} - 128 q^{60} - 256 q^{61} - 96 q^{63} - 256 q^{64} - 128 q^{66} - 192 q^{67} - 128 q^{69} - 256 q^{70} - 128 q^{72} - 320 q^{73} - 96 q^{75} - 256 q^{76} - 128 q^{78} - 192 q^{79} - 192 q^{81} - 256 q^{82} - 128 q^{84} - 256 q^{85} - 96 q^{87} - 256 q^{88} - 128 q^{90} - 192 q^{91} - 128 q^{93} - 256 q^{94} - 128 q^{96} - 448 q^{97} - 96 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(3072))$$

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
3072.2.a $$\chi_{3072}(1, \cdot)$$ 3072.2.a.a 2 1
3072.2.a.b 2
3072.2.a.c 2
3072.2.a.d 2
3072.2.a.e 2
3072.2.a.f 2
3072.2.a.g 2
3072.2.a.h 2
3072.2.a.i 4
3072.2.a.j 4
3072.2.a.k 4
3072.2.a.l 4
3072.2.a.m 4
3072.2.a.n 4
3072.2.a.o 4
3072.2.a.p 4
3072.2.a.q 4
3072.2.a.r 4
3072.2.a.s 4
3072.2.a.t 4
3072.2.c $$\chi_{3072}(3071, \cdot)$$ n/a 120 1
3072.2.d $$\chi_{3072}(1537, \cdot)$$ 3072.2.d.a 4 1
3072.2.d.b 4
3072.2.d.c 4
3072.2.d.d 4
3072.2.d.e 8
3072.2.d.f 8
3072.2.d.g 8
3072.2.d.h 8
3072.2.d.i 8
3072.2.d.j 8
3072.2.f $$\chi_{3072}(1535, \cdot)$$ n/a 120 1
3072.2.j $$\chi_{3072}(769, \cdot)$$ n/a 128 2
3072.2.k $$\chi_{3072}(767, \cdot)$$ n/a 240 2
3072.2.n $$\chi_{3072}(385, \cdot)$$ n/a 256 4
3072.2.o $$\chi_{3072}(383, \cdot)$$ n/a 512 4
3072.2.r $$\chi_{3072}(193, \cdot)$$ n/a 512 8
3072.2.s $$\chi_{3072}(191, \cdot)$$ n/a 960 8
3072.2.v $$\chi_{3072}(97, \cdot)$$ n/a 1024 16
3072.2.w $$\chi_{3072}(95, \cdot)$$ n/a 1984 16
3072.2.z $$\chi_{3072}(49, \cdot)$$ n/a 2048 32
3072.2.ba $$\chi_{3072}(47, \cdot)$$ n/a 4032 32
3072.2.bd $$\chi_{3072}(25, \cdot)$$ None 0 64
3072.2.be $$\chi_{3072}(23, \cdot)$$ None 0 64
3072.2.bh $$\chi_{3072}(13, \cdot)$$ n/a 32768 128
3072.2.bi $$\chi_{3072}(11, \cdot)$$ n/a 65280 128

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(3072))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(3072)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 14}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 7}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(96))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(128))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(192))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(256))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(384))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(512))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(768))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1024))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1536))$$$$^{\oplus 2}$$