# Properties

 Label 6592.2 Level 6592 Weight 2 Dimension 761410 Nonzero newspaces 32 Sturm bound 5431296

## Defining parameters

 Level: $$N$$ = $$6592 = 2^{6} \cdot 103$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$32$$ Sturm bound: $$5431296$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(6592))$$.

Total New Old
Modular forms 1365168 765854 599314
Cusp forms 1350481 761410 589071
Eisenstein series 14687 4444 10243

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(6592))$$

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 available newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
6592.2.a $$\chi_{6592}(1, \cdot)$$ 6592.2.a.a 1 1
6592.2.a.b 1
6592.2.a.c 2
6592.2.a.d 2
6592.2.a.e 2
6592.2.a.f 2
6592.2.a.g 2
6592.2.a.h 2
6592.2.a.i 2
6592.2.a.j 2
6592.2.a.k 2
6592.2.a.l 2
6592.2.a.m 2
6592.2.a.n 2
6592.2.a.o 2
6592.2.a.p 2
6592.2.a.q 2
6592.2.a.r 2
6592.2.a.s 2
6592.2.a.t 2
6592.2.a.u 2
6592.2.a.v 2
6592.2.a.w 4
6592.2.a.x 4
6592.2.a.y 4
6592.2.a.z 4
6592.2.a.ba 5
6592.2.a.bb 5
6592.2.a.bc 6
6592.2.a.bd 6
6592.2.a.be 6
6592.2.a.bf 6
6592.2.a.bg 8
6592.2.a.bh 8
6592.2.a.bi 8
6592.2.a.bj 8
6592.2.a.bk 9
6592.2.a.bl 9
6592.2.a.bm 9
6592.2.a.bn 9
6592.2.a.bo 10
6592.2.a.bp 10
6592.2.a.bq 12
6592.2.a.br 12
6592.2.b $$\chi_{6592}(3297, \cdot)$$ n/a 204 1
6592.2.d $$\chi_{6592}(3295, \cdot)$$ n/a 208 1
6592.2.g $$\chi_{6592}(6591, \cdot)$$ n/a 206 1
6592.2.i $$\chi_{6592}(1601, \cdot)$$ n/a 412 2
6592.2.k $$\chi_{6592}(1649, \cdot)$$ n/a 408 2
6592.2.m $$\chi_{6592}(1647, \cdot)$$ n/a 412 2
6592.2.n $$\chi_{6592}(1695, \cdot)$$ n/a 416 2
6592.2.p $$\chi_{6592}(2209, \cdot)$$ n/a 416 2
6592.2.t $$\chi_{6592}(1087, \cdot)$$ n/a 412 2
6592.2.v $$\chi_{6592}(825, \cdot)$$ None 0 4
6592.2.x $$\chi_{6592}(823, \cdot)$$ None 0 4
6592.2.z $$\chi_{6592}(47, \cdot)$$ n/a 824 4
6592.2.bb $$\chi_{6592}(561, \cdot)$$ n/a 824 4
6592.2.bc $$\chi_{6592}(411, \cdot)$$ n/a 6640 8
6592.2.bd $$\chi_{6592}(413, \cdot)$$ n/a 6528 8
6592.2.bg $$\chi_{6592}(385, \cdot)$$ n/a 3296 16
6592.2.bi $$\chi_{6592}(263, \cdot)$$ None 0 8
6592.2.bk $$\chi_{6592}(777, \cdot)$$ None 0 8
6592.2.bm $$\chi_{6592}(127, \cdot)$$ n/a 3296 16
6592.2.bp $$\chi_{6592}(31, \cdot)$$ n/a 3328 16
6592.2.br $$\chi_{6592}(545, \cdot)$$ n/a 3328 16
6592.2.bs $$\chi_{6592}(149, \cdot)$$ n/a 13280 16
6592.2.bt $$\chi_{6592}(459, \cdot)$$ n/a 13280 16
6592.2.bw $$\chi_{6592}(129, \cdot)$$ n/a 6592 32
6592.2.bx $$\chi_{6592}(399, \cdot)$$ n/a 6592 32
6592.2.bz $$\chi_{6592}(81, \cdot)$$ n/a 6592 32
6592.2.cb $$\chi_{6592}(191, \cdot)$$ n/a 6592 32
6592.2.cf $$\chi_{6592}(33, \cdot)$$ n/a 6656 32
6592.2.ch $$\chi_{6592}(479, \cdot)$$ n/a 6656 32
6592.2.ci $$\chi_{6592}(39, \cdot)$$ None 0 64
6592.2.ck $$\chi_{6592}(9, \cdot)$$ None 0 64
6592.2.cm $$\chi_{6592}(17, \cdot)$$ n/a 13184 64
6592.2.co $$\chi_{6592}(143, \cdot)$$ n/a 13184 64
6592.2.cs $$\chi_{6592}(13, \cdot)$$ n/a 106240 128
6592.2.ct $$\chi_{6592}(3, \cdot)$$ n/a 106240 128
6592.2.cu $$\chi_{6592}(25, \cdot)$$ None 0 128
6592.2.cw $$\chi_{6592}(71, \cdot)$$ None 0 128
6592.2.da $$\chi_{6592}(11, \cdot)$$ n/a 212480 256
6592.2.db $$\chi_{6592}(29, \cdot)$$ n/a 212480 256

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(6592))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(6592)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 14}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(103))$$$$^{\oplus 7}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(206))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(412))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(824))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1648))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3296))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(6592))$$$$^{\oplus 1}$$