Properties

 Label 8002.2 Level 8002 Weight 2 Dimension 666999 Nonzero newspaces 20 Sturm bound 8.004e+06

Defining parameters

 Level: $$N$$ = $$8002 = 2 \cdot 4001$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$20$$ Sturm bound: $$8004000$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(8002))$$.

Total New Old
Modular forms 2005000 666999 1338001
Cusp forms 1997001 666999 1330002
Eisenstein series 7999 0 7999

Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(8002))$$

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
8002.2.a $$\chi_{8002}(1, \cdot)$$ 8002.2.a.a 1 1
8002.2.a.b 1
8002.2.a.c 1
8002.2.a.d 69
8002.2.a.e 77
8002.2.a.f 89
8002.2.a.g 95
8002.2.b $$\chi_{8002}(8001, \cdot)$$ n/a 334 1
8002.2.c $$\chi_{8002}(899, \cdot)$$ n/a 668 2
8002.2.d $$\chi_{8002}(1401, \cdot)$$ n/a 1336 4
8002.2.e $$\chi_{8002}(2915, \cdot)$$ n/a 1336 4
8002.2.f $$\chi_{8002}(3099, \cdot)$$ n/a 1336 4
8002.2.g $$\chi_{8002}(1115, \cdot)$$ n/a 2664 8
8002.2.h $$\chi_{8002}(1305, \cdot)$$ n/a 2672 8
8002.2.i $$\chi_{8002}(201, \cdot)$$ n/a 6680 20
8002.2.k $$\chi_{8002}(673, \cdot)$$ n/a 5344 16
8002.2.l $$\chi_{8002}(625, \cdot)$$ n/a 6680 20
8002.2.m $$\chi_{8002}(121, \cdot)$$ n/a 10656 32
8002.2.n $$\chi_{8002}(25, \cdot)$$ n/a 13360 40
8002.2.o $$\chi_{8002}(35, \cdot)$$ n/a 33400 100
8002.2.q $$\chi_{8002}(5, \cdot)$$ n/a 26720 80
8002.2.r $$\chi_{8002}(65, \cdot)$$ n/a 33400 100
8002.2.s $$\chi_{8002}(59, \cdot)$$ n/a 53280 160
8002.2.t $$\chi_{8002}(49, \cdot)$$ n/a 66800 200
8002.2.v $$\chi_{8002}(7, \cdot)$$ n/a 133600 400
8002.2.w $$\chi_{8002}(9, \cdot)$$ n/a 266400 800

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

Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(8002))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(8002)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(4001))$$$$^{\oplus 2}$$