# Properties

 Label 8047.2 Level 8047 Weight 2 Dimension 2.64339e+06 Nonzero newspaces 30 Sturm bound 1.07285e+07

## Defining parameters

 Level: $$N$$ = $$8047 = 13 \cdot 619$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$30$$ Sturm bound: $$10728480$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(8047))$$.

Total New Old
Modular forms 2689536 2656963 32573
Cusp forms 2674705 2643387 31318
Eisenstein series 14831 13576 1255

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(8047))$$

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
8047.2.a $$\chi_{8047}(1, \cdot)$$ 8047.2.a.a 2 1
8047.2.a.b 142
8047.2.a.c 151
8047.2.a.d 156
8047.2.a.e 168
8047.2.c $$\chi_{8047}(1858, \cdot)$$ n/a 720 1
8047.2.e $$\chi_{8047}(3461, \cdot)$$ n/a 1442 2
8047.2.f $$\chi_{8047}(620, \cdot)$$ n/a 1444 2
8047.2.g $$\chi_{8047}(3966, \cdot)$$ n/a 1240 2
8047.2.h $$\chi_{8047}(2109, \cdot)$$ n/a 1442 2
8047.2.i $$\chi_{8047}(2475, \cdot)$$ n/a 1440 2
8047.2.k $$\chi_{8047}(6556, \cdot)$$ n/a 1442 2
8047.2.q $$\chi_{8047}(1239, \cdot)$$ n/a 1440 2
8047.2.r $$\chi_{8047}(985, \cdot)$$ n/a 1442 2
8047.2.u $$\chi_{8047}(5823, \cdot)$$ n/a 1444 2
8047.2.w $$\chi_{8047}(5205, \cdot)$$ n/a 2888 4
8047.2.ba $$\chi_{8047}(253, \cdot)$$ n/a 2884 4
8047.2.bb $$\chi_{8047}(618, \cdot)$$ n/a 2888 4
8047.2.bc $$\chi_{8047}(1605, \cdot)$$ n/a 2884 4
8047.2.be $$\chi_{8047}(79, \cdot)$$ n/a 63240 102
8047.2.bg $$\chi_{8047}(38, \cdot)$$ n/a 73440 102
8047.2.bi $$\chi_{8047}(16, \cdot)$$ n/a 147084 204
8047.2.bj $$\chi_{8047}(53, \cdot)$$ n/a 126480 204
8047.2.bk $$\chi_{8047}(9, \cdot)$$ n/a 147288 204
8047.2.bl $$\chi_{8047}(61, \cdot)$$ n/a 147084 204
8047.2.bn $$\chi_{8047}(8, \cdot)$$ n/a 146880 204
8047.2.bp $$\chi_{8047}(25, \cdot)$$ n/a 147288 204
8047.2.bs $$\chi_{8047}(36, \cdot)$$ n/a 147084 204
8047.2.bt $$\chi_{8047}(127, \cdot)$$ n/a 147288 204
8047.2.bz $$\chi_{8047}(4, \cdot)$$ n/a 147084 204
8047.2.cb $$\chi_{8047}(59, \cdot)$$ n/a 294168 408
8047.2.cc $$\chi_{8047}(50, \cdot)$$ n/a 294576 408
8047.2.cd $$\chi_{8047}(2, \cdot)$$ n/a 294168 408
8047.2.ch $$\chi_{8047}(18, \cdot)$$ n/a 294576 408

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(8047))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(8047)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(619))$$$$^{\oplus 2}$$