# Properties

 Label 7168.2 Level 7168 Weight 2 Dimension 845472 Nonzero newspaces 32 Sturm bound 6291456

## Defining parameters

 Level: $$N$$ = $$7168 = 2^{10} \cdot 7$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$32$$ Sturm bound: $$6291456$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(7168))$$.

Total New Old
Modular forms 1582848 850272 732576
Cusp forms 1562881 845472 717409
Eisenstein series 19967 4800 15167

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(7168))$$

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
7168.2.a $$\chi_{7168}(1, \cdot)$$ 7168.2.a.a 2 1
7168.2.a.b 2
7168.2.a.c 2
7168.2.a.d 2
7168.2.a.e 2
7168.2.a.f 2
7168.2.a.g 2
7168.2.a.h 2
7168.2.a.i 2
7168.2.a.j 2
7168.2.a.k 2
7168.2.a.l 2
7168.2.a.m 2
7168.2.a.n 2
7168.2.a.o 2
7168.2.a.p 2
7168.2.a.q 2
7168.2.a.r 2
7168.2.a.s 4
7168.2.a.t 4
7168.2.a.u 4
7168.2.a.v 4
7168.2.a.w 4
7168.2.a.x 4
7168.2.a.y 6
7168.2.a.z 6
7168.2.a.ba 8
7168.2.a.bb 8
7168.2.a.bc 8
7168.2.a.bd 8
7168.2.a.be 8
7168.2.a.bf 8
7168.2.a.bg 12
7168.2.a.bh 12
7168.2.a.bi 12
7168.2.a.bj 12
7168.2.a.bk 12
7168.2.a.bl 12
7168.2.b $$\chi_{7168}(3585, \cdot)$$ n/a 192 1
7168.2.e $$\chi_{7168}(3583, \cdot)$$ n/a 248 1
7168.2.f $$\chi_{7168}(7167, \cdot)$$ n/a 248 1
7168.2.i $$\chi_{7168}(4097, \cdot)$$ n/a 496 2
7168.2.j $$\chi_{7168}(1791, \cdot)$$ n/a 496 2
7168.2.m $$\chi_{7168}(1793, \cdot)$$ n/a 384 2
7168.2.p $$\chi_{7168}(2047, \cdot)$$ n/a 496 2
7168.2.q $$\chi_{7168}(5631, \cdot)$$ n/a 496 2
7168.2.t $$\chi_{7168}(513, \cdot)$$ n/a 496 2
7168.2.u $$\chi_{7168}(897, \cdot)$$ n/a 768 4
7168.2.x $$\chi_{7168}(895, \cdot)$$ n/a 1024 4
7168.2.z $$\chi_{7168}(255, \cdot)$$ n/a 992 4
7168.2.ba $$\chi_{7168}(2305, \cdot)$$ n/a 992 4
7168.2.bc $$\chi_{7168}(449, \cdot)$$ n/a 1536 8
7168.2.bd $$\chi_{7168}(447, \cdot)$$ n/a 1984 8
7168.2.bh $$\chi_{7168}(641, \cdot)$$ n/a 2048 8
7168.2.bi $$\chi_{7168}(383, \cdot)$$ n/a 2048 8
7168.2.bk $$\chi_{7168}(223, \cdot)$$ n/a 4032 16
7168.2.bn $$\chi_{7168}(225, \cdot)$$ n/a 3072 16
7168.2.bq $$\chi_{7168}(703, \cdot)$$ n/a 3968 16
7168.2.br $$\chi_{7168}(65, \cdot)$$ n/a 3968 16
7168.2.bs $$\chi_{7168}(113, \cdot)$$ n/a 6144 32
7168.2.bv $$\chi_{7168}(111, \cdot)$$ n/a 8128 32
7168.2.bx $$\chi_{7168}(31, \cdot)$$ n/a 8064 32
7168.2.by $$\chi_{7168}(289, \cdot)$$ n/a 8064 32
7168.2.ca $$\chi_{7168}(57, \cdot)$$ None 0 64
7168.2.cb $$\chi_{7168}(55, \cdot)$$ None 0 64
7168.2.cf $$\chi_{7168}(81, \cdot)$$ n/a 16256 64
7168.2.cg $$\chi_{7168}(47, \cdot)$$ n/a 16256 64
7168.2.ci $$\chi_{7168}(27, \cdot)$$ n/a 130816 128
7168.2.cl $$\chi_{7168}(29, \cdot)$$ n/a 98304 128
7168.2.co $$\chi_{7168}(87, \cdot)$$ None 0 128
7168.2.cp $$\chi_{7168}(9, \cdot)$$ None 0 128
7168.2.cr $$\chi_{7168}(3, \cdot)$$ n/a 261632 256
7168.2.cs $$\chi_{7168}(37, \cdot)$$ n/a 261632 256

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(7168))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(7168)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 14}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(112))$$$$^{\oplus 7}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(128))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(224))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(256))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(448))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(512))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(896))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1024))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1792))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3584))$$$$^{\oplus 2}$$