# Properties

 Label 8046.2 Level 8046 Weight 2 Dimension 473556 Nonzero newspaces 18 Sturm bound 7.1928e+06

## Defining parameters

 Level: $$N$$ = $$8046 = 2 \cdot 3^{3} \cdot 149$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$18$$ Sturm bound: $$7192800$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(8046))$$.

Total New Old
Modular forms 1807080 473556 1333524
Cusp forms 1789321 473556 1315765
Eisenstein series 17759 0 17759

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(8046))$$

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
8046.2.a $$\chi_{8046}(1, \cdot)$$ 8046.2.a.a 1 1
8046.2.a.b 1
8046.2.a.c 2
8046.2.a.d 2
8046.2.a.e 8
8046.2.a.f 8
8046.2.a.g 9
8046.2.a.h 9
8046.2.a.i 12
8046.2.a.j 12
8046.2.a.k 12
8046.2.a.l 12
8046.2.a.m 12
8046.2.a.n 12
8046.2.a.o 12
8046.2.a.p 12
8046.2.a.q 14
8046.2.a.r 14
8046.2.a.s 16
8046.2.a.t 16
8046.2.d $$\chi_{8046}(595, \cdot)$$ n/a 200 1
8046.2.e $$\chi_{8046}(2683, \cdot)$$ n/a 296 2
8046.2.f $$\chi_{8046}(701, \cdot)$$ n/a 400 2
8046.2.h $$\chi_{8046}(3277, \cdot)$$ n/a 300 2
8046.2.k $$\chi_{8046}(895, \cdot)$$ n/a 2664 6
8046.2.m $$\chi_{8046}(1385, \cdot)$$ n/a 600 4
8046.2.n $$\chi_{8046}(1489, \cdot)$$ n/a 2700 6
8046.2.r $$\chi_{8046}(491, \cdot)$$ n/a 5400 12
8046.2.s $$\chi_{8046}(379, \cdot)$$ n/a 7200 36
8046.2.t $$\chi_{8046}(217, \cdot)$$ n/a 7200 36
8046.2.w $$\chi_{8046}(19, \cdot)$$ n/a 10800 72
8046.2.y $$\chi_{8046}(161, \cdot)$$ n/a 14400 72
8046.2.bb $$\chi_{8046}(235, \cdot)$$ n/a 10800 72
8046.2.bc $$\chi_{8046}(25, \cdot)$$ n/a 97200 216
8046.2.bd $$\chi_{8046}(71, \cdot)$$ n/a 21600 144
8046.2.bh $$\chi_{8046}(7, \cdot)$$ n/a 97200 216
8046.2.bi $$\chi_{8046}(11, \cdot)$$ n/a 194400 432

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(8046))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(8046)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(27))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(54))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(149))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(298))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(447))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(894))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1341))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2682))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4023))$$$$^{\oplus 2}$$