# Properties

 Label 4002.2 Level 4002 Weight 2 Dimension 110193 Nonzero newspaces 24 Sturm bound 1.77408e+06

## Defining parameters

 Level: $$N$$ = $$4002 = 2 \cdot 3 \cdot 23 \cdot 29$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$24$$ Sturm bound: $$1774080$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(4002))$$.

Total New Old
Modular forms 448448 110193 338255
Cusp forms 438593 110193 328400
Eisenstein series 9855 0 9855

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(4002))$$

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
4002.2.a $$\chi_{4002}(1, \cdot)$$ 4002.2.a.a 1 1
4002.2.a.b 1
4002.2.a.c 1
4002.2.a.d 1
4002.2.a.e 1
4002.2.a.f 1
4002.2.a.g 1
4002.2.a.h 1
4002.2.a.i 1
4002.2.a.j 1
4002.2.a.k 1
4002.2.a.l 1
4002.2.a.m 1
4002.2.a.n 1
4002.2.a.o 1
4002.2.a.p 1
4002.2.a.q 1
4002.2.a.r 1
4002.2.a.s 2
4002.2.a.t 2
4002.2.a.u 2
4002.2.a.v 2
4002.2.a.w 2
4002.2.a.x 2
4002.2.a.y 3
4002.2.a.z 3
4002.2.a.ba 4
4002.2.a.bb 4
4002.2.a.bc 4
4002.2.a.bd 4
4002.2.a.be 5
4002.2.a.bf 6
4002.2.a.bg 7
4002.2.a.bh 7
4002.2.a.bi 8
4002.2.a.bj 8
4002.2.a.bk 8
4002.2.f $$\chi_{4002}(4001, \cdot)$$ n/a 240 1
4002.2.g $$\chi_{4002}(1103, \cdot)$$ n/a 224 1
4002.2.h $$\chi_{4002}(2899, \cdot)$$ n/a 108 1
4002.2.k $$\chi_{4002}(505, \cdot)$$ n/a 240 2
4002.2.l $$\chi_{4002}(737, \cdot)$$ n/a 440 2
4002.2.m $$\chi_{4002}(139, \cdot)$$ n/a 672 6
4002.2.n $$\chi_{4002}(349, \cdot)$$ n/a 1120 10
4002.2.o $$\chi_{4002}(415, \cdot)$$ n/a 648 6
4002.2.p $$\chi_{4002}(413, \cdot)$$ n/a 1440 6
4002.2.q $$\chi_{4002}(689, \cdot)$$ n/a 1440 6
4002.2.v $$\chi_{4002}(289, \cdot)$$ n/a 1200 10
4002.2.w $$\chi_{4002}(755, \cdot)$$ n/a 2240 10
4002.2.x $$\chi_{4002}(521, \cdot)$$ n/a 2400 10
4002.2.bc $$\chi_{4002}(47, \cdot)$$ n/a 2640 12
4002.2.bd $$\chi_{4002}(229, \cdot)$$ n/a 1440 12
4002.2.bg $$\chi_{4002}(41, \cdot)$$ n/a 4800 20
4002.2.bh $$\chi_{4002}(157, \cdot)$$ n/a 2400 20
4002.2.bk $$\chi_{4002}(25, \cdot)$$ n/a 7200 60
4002.2.bp $$\chi_{4002}(5, \cdot)$$ n/a 14400 60
4002.2.bq $$\chi_{4002}(53, \cdot)$$ n/a 14400 60
4002.2.br $$\chi_{4002}(13, \cdot)$$ n/a 7200 60
4002.2.bu $$\chi_{4002}(19, \cdot)$$ n/a 14400 120
4002.2.bv $$\chi_{4002}(77, \cdot)$$ n/a 28800 120

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(4002))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(4002)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(29))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(46))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(58))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(69))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(87))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(138))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(174))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(667))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1334))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2001))$$$$^{\oplus 2}$$