# Properties

 Label 4014.2 Level 4014 Weight 2 Dimension 118100 Nonzero newspaces 20 Sturm bound 1.79021e+06

## Defining parameters

 Level: $$N$$ = $$4014 = 2 \cdot 3^{2} \cdot 223$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$20$$ Sturm bound: $$1790208$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(4014))$$.

Total New Old
Modular forms 451104 118100 333004
Cusp forms 444001 118100 325901
Eisenstein series 7103 0 7103

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(4014))$$

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
4014.2.a $$\chi_{4014}(1, \cdot)$$ 4014.2.a.a 1 1
4014.2.a.b 1
4014.2.a.c 1
4014.2.a.d 1
4014.2.a.e 1
4014.2.a.f 1
4014.2.a.g 1
4014.2.a.h 1
4014.2.a.i 1
4014.2.a.j 2
4014.2.a.k 2
4014.2.a.l 2
4014.2.a.m 3
4014.2.a.n 3
4014.2.a.o 3
4014.2.a.p 3
4014.2.a.q 4
4014.2.a.r 5
4014.2.a.s 6
4014.2.a.t 6
4014.2.a.u 6
4014.2.a.v 7
4014.2.a.w 7
4014.2.a.x 8
4014.2.a.y 8
4014.2.a.z 8
4014.2.d $$\chi_{4014}(4013, \cdot)$$ 4014.2.d.a 72 1
4014.2.e $$\chi_{4014}(1339, \cdot)$$ n/a 444 2
4014.2.f $$\chi_{4014}(1075, \cdot)$$ n/a 448 2
4014.2.g $$\chi_{4014}(2269, \cdot)$$ n/a 188 2
4014.2.h $$\chi_{4014}(931, \cdot)$$ n/a 448 2
4014.2.k $$\chi_{4014}(1337, \cdot)$$ n/a 448 2
4014.2.l $$\chi_{4014}(407, \cdot)$$ n/a 448 2
4014.2.m $$\chi_{4014}(1601, \cdot)$$ n/a 152 2
4014.2.t $$\chi_{4014}(263, \cdot)$$ n/a 448 2
4014.2.u $$\chi_{4014}(253, \cdot)$$ n/a 3312 36
4014.2.v $$\chi_{4014}(125, \cdot)$$ n/a 2592 36
4014.2.y $$\chi_{4014}(31, \cdot)$$ n/a 16128 72
4014.2.z $$\chi_{4014}(19, \cdot)$$ n/a 6768 72
4014.2.ba $$\chi_{4014}(25, \cdot)$$ n/a 16128 72
4014.2.bb $$\chi_{4014}(7, \cdot)$$ n/a 16128 72
4014.2.bc $$\chi_{4014}(11, \cdot)$$ n/a 16128 72
4014.2.bj $$\chi_{4014}(35, \cdot)$$ n/a 5472 72
4014.2.bk $$\chi_{4014}(5, \cdot)$$ n/a 16128 72
4014.2.bl $$\chi_{4014}(59, \cdot)$$ n/a 16128 72

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(4014))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(4014)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(223))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(446))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(669))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1338))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2007))$$$$^{\oplus 2}$$