# Properties

 Label 4005.2 Level 4005 Weight 2 Dimension 411366 Nonzero newspaces 56 Sturm bound 2.28096e+06

## Defining parameters

 Level: $$N$$ = $$4005 = 3^{2} \cdot 5 \cdot 89$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$56$$ Sturm bound: $$2280960$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(4005))$$.

Total New Old
Modular forms 575872 416066 159806
Cusp forms 564609 411366 153243
Eisenstein series 11263 4700 6563

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(4005))$$

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
4005.2.a $$\chi_{4005}(1, \cdot)$$ 4005.2.a.a 1 1
4005.2.a.b 1
4005.2.a.c 1
4005.2.a.d 1
4005.2.a.e 2
4005.2.a.f 2
4005.2.a.g 2
4005.2.a.h 2
4005.2.a.i 3
4005.2.a.j 3
4005.2.a.k 4
4005.2.a.l 4
4005.2.a.m 4
4005.2.a.n 6
4005.2.a.o 7
4005.2.a.p 8
4005.2.a.q 9
4005.2.a.r 10
4005.2.a.s 10
4005.2.a.t 10
4005.2.a.u 12
4005.2.a.v 12
4005.2.a.w 17
4005.2.a.x 17
4005.2.c $$\chi_{4005}(2404, \cdot)$$ n/a 220 1
4005.2.e $$\chi_{4005}(2224, \cdot)$$ n/a 224 1
4005.2.g $$\chi_{4005}(3826, \cdot)$$ n/a 150 1
4005.2.i $$\chi_{4005}(1336, \cdot)$$ n/a 704 2
4005.2.k $$\chi_{4005}(1369, \cdot)$$ n/a 444 2
4005.2.l $$\chi_{4005}(233, \cdot)$$ n/a 360 2
4005.2.n $$\chi_{4005}(2402, \cdot)$$ n/a 360 2
4005.2.o $$\chi_{4005}(2582, \cdot)$$ n/a 352 2
4005.2.r $$\chi_{4005}(2348, \cdot)$$ n/a 360 2
4005.2.u $$\chi_{4005}(856, \cdot)$$ n/a 300 2
4005.2.w $$\chi_{4005}(1156, \cdot)$$ n/a 720 2
4005.2.y $$\chi_{4005}(889, \cdot)$$ n/a 1072 2
4005.2.ba $$\chi_{4005}(1069, \cdot)$$ n/a 1056 2
4005.2.bd $$\chi_{4005}(611, \cdot)$$ n/a 480 4
4005.2.be $$\chi_{4005}(838, \cdot)$$ n/a 892 4
4005.2.bf $$\chi_{4005}(37, \cdot)$$ n/a 892 4
4005.2.bj $$\chi_{4005}(764, \cdot)$$ n/a 720 4
4005.2.bk $$\chi_{4005}(91, \cdot)$$ n/a 1500 10
4005.2.bl $$\chi_{4005}(301, \cdot)$$ n/a 1440 4
4005.2.bo $$\chi_{4005}(767, \cdot)$$ n/a 2144 4
4005.2.br $$\chi_{4005}(713, \cdot)$$ n/a 2112 4
4005.2.bs $$\chi_{4005}(533, \cdot)$$ n/a 2144 4
4005.2.bu $$\chi_{4005}(212, \cdot)$$ n/a 2144 4
4005.2.bv $$\chi_{4005}(34, \cdot)$$ n/a 2144 4
4005.2.by $$\chi_{4005}(406, \cdot)$$ n/a 1500 10
4005.2.ca $$\chi_{4005}(289, \cdot)$$ n/a 2240 10
4005.2.cc $$\chi_{4005}(64, \cdot)$$ n/a 2240 10
4005.2.ce $$\chi_{4005}(344, \cdot)$$ n/a 4288 8
4005.2.ci $$\chi_{4005}(457, \cdot)$$ n/a 4288 8
4005.2.cj $$\chi_{4005}(52, \cdot)$$ n/a 4288 8
4005.2.ck $$\chi_{4005}(101, \cdot)$$ n/a 2880 8
4005.2.cm $$\chi_{4005}(16, \cdot)$$ n/a 7200 20
4005.2.cn $$\chi_{4005}(136, \cdot)$$ n/a 3000 20
4005.2.cq $$\chi_{4005}(53, \cdot)$$ n/a 3600 20
4005.2.ct $$\chi_{4005}(8, \cdot)$$ n/a 3600 20
4005.2.cu $$\chi_{4005}(278, \cdot)$$ n/a 3600 20
4005.2.cw $$\chi_{4005}(17, \cdot)$$ n/a 3600 20
4005.2.cx $$\chi_{4005}(109, \cdot)$$ n/a 4440 20
4005.2.da $$\chi_{4005}(4, \cdot)$$ n/a 10720 20
4005.2.dc $$\chi_{4005}(139, \cdot)$$ n/a 10720 20
4005.2.de $$\chi_{4005}(526, \cdot)$$ n/a 7200 20
4005.2.dg $$\chi_{4005}(224, \cdot)$$ n/a 7200 40
4005.2.dk $$\chi_{4005}(28, \cdot)$$ n/a 8920 40
4005.2.dl $$\chi_{4005}(82, \cdot)$$ n/a 8920 40
4005.2.dm $$\chi_{4005}(26, \cdot)$$ n/a 4800 40
4005.2.dp $$\chi_{4005}(49, \cdot)$$ n/a 21440 40
4005.2.dq $$\chi_{4005}(47, \cdot)$$ n/a 21440 40
4005.2.ds $$\chi_{4005}(203, \cdot)$$ n/a 21440 40
4005.2.dt $$\chi_{4005}(2, \cdot)$$ n/a 21440 40
4005.2.dw $$\chi_{4005}(68, \cdot)$$ n/a 21440 40
4005.2.dz $$\chi_{4005}(106, \cdot)$$ n/a 14400 40
4005.2.eb $$\chi_{4005}(41, \cdot)$$ n/a 28800 80
4005.2.ec $$\chi_{4005}(43, \cdot)$$ n/a 42880 80
4005.2.ed $$\chi_{4005}(7, \cdot)$$ n/a 42880 80
4005.2.eh $$\chi_{4005}(14, \cdot)$$ n/a 42880 80

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(4005))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(4005)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(89))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(267))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(445))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(801))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1335))$$$$^{\oplus 2}$$