# Properties

 Label 4001.2 Level 4001 Weight 2 Dimension 665001 Nonzero newspaces 20 Sturm bound 2.668e+06

## Defining parameters

 Level: $$N$$ = $$4001$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$20$$ Sturm bound: $$2668000$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(4001))$$.

Total New Old
Modular forms 669000 669000 0
Cusp forms 665001 665001 0
Eisenstein series 3999 3999 0

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(4001))$$

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
4001.2.a $$\chi_{4001}(1, \cdot)$$ 4001.2.a.a 149 1
4001.2.a.b 184
4001.2.b $$\chi_{4001}(4000, \cdot)$$ n/a 332 1
4001.2.c $$\chi_{4001}(899, \cdot)$$ n/a 664 2
4001.2.d $$\chi_{4001}(902, \cdot)$$ n/a 1328 4
4001.2.e $$\chi_{4001}(70, \cdot)$$ n/a 1328 4
4001.2.f $$\chi_{4001}(614, \cdot)$$ n/a 1328 4
4001.2.g $$\chi_{4001}(1115, \cdot)$$ n/a 2664 8
4001.2.h $$\chi_{4001}(152, \cdot)$$ n/a 2656 8
4001.2.i $$\chi_{4001}(196, \cdot)$$ n/a 6640 20
4001.2.k $$\chi_{4001}(673, \cdot)$$ n/a 5312 16
4001.2.l $$\chi_{4001}(14, \cdot)$$ n/a 6640 20
4001.2.m $$\chi_{4001}(121, \cdot)$$ n/a 10656 32
4001.2.n $$\chi_{4001}(25, \cdot)$$ n/a 13280 40
4001.2.o $$\chi_{4001}(26, \cdot)$$ n/a 33200 100
4001.2.q $$\chi_{4001}(5, \cdot)$$ n/a 26560 80
4001.2.r $$\chi_{4001}(16, \cdot)$$ n/a 33200 100
4001.2.s $$\chi_{4001}(58, \cdot)$$ n/a 53280 160
4001.2.t $$\chi_{4001}(4, \cdot)$$ n/a 66400 200
4001.2.v $$\chi_{4001}(2, \cdot)$$ n/a 132800 400
4001.2.w $$\chi_{4001}(9, \cdot)$$ n/a 266400 800

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