# Properties

 Label 4025.2 Level 4025 Weight 2 Dimension 553208 Nonzero newspaces 48 Sturm bound 2.5344e+06

## Defining parameters

 Level: $$N$$ = $$4025 = 5^{2} \cdot 7 \cdot 23$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$48$$ Sturm bound: $$2534400$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(4025))$$.

Total New Old
Modular forms 640992 561820 79172
Cusp forms 626209 553208 73001
Eisenstein series 14783 8612 6171

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(4025))$$

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
4025.2.a $$\chi_{4025}(1, \cdot)$$ 4025.2.a.a 1 1
4025.2.a.b 1
4025.2.a.c 1
4025.2.a.d 1
4025.2.a.e 1
4025.2.a.f 1
4025.2.a.g 1
4025.2.a.h 2
4025.2.a.i 2
4025.2.a.j 3
4025.2.a.k 3
4025.2.a.l 4
4025.2.a.m 4
4025.2.a.n 4
4025.2.a.o 4
4025.2.a.p 5
4025.2.a.q 5
4025.2.a.r 5
4025.2.a.s 8
4025.2.a.t 8
4025.2.a.u 8
4025.2.a.v 8
4025.2.a.w 8
4025.2.a.x 12
4025.2.a.y 12
4025.2.a.z 14
4025.2.a.ba 14
4025.2.a.bb 14
4025.2.a.bc 14
4025.2.a.bd 21
4025.2.a.be 21
4025.2.c $$\chi_{4025}(2899, \cdot)$$ n/a 196 1
4025.2.d $$\chi_{4025}(4024, \cdot)$$ n/a 284 1
4025.2.f $$\chi_{4025}(1126, \cdot)$$ n/a 298 1
4025.2.i $$\chi_{4025}(576, \cdot)$$ n/a 556 2
4025.2.k $$\chi_{4025}(2232, \cdot)$$ n/a 528 2
4025.2.l $$\chi_{4025}(1632, \cdot)$$ n/a 432 2
4025.2.n $$\chi_{4025}(806, \cdot)$$ n/a 1312 4
4025.2.q $$\chi_{4025}(551, \cdot)$$ n/a 596 2
4025.2.s $$\chi_{4025}(2299, \cdot)$$ n/a 568 2
4025.2.t $$\chi_{4025}(599, \cdot)$$ n/a 528 2
4025.2.x $$\chi_{4025}(321, \cdot)$$ n/a 1904 4
4025.2.z $$\chi_{4025}(804, \cdot)$$ n/a 1904 4
4025.2.ba $$\chi_{4025}(484, \cdot)$$ n/a 1328 4
4025.2.bc $$\chi_{4025}(351, \cdot)$$ n/a 2280 10
4025.2.bd $$\chi_{4025}(507, \cdot)$$ n/a 1056 4
4025.2.bg $$\chi_{4025}(2207, \cdot)$$ n/a 1136 4
4025.2.bh $$\chi_{4025}(116, \cdot)$$ n/a 3520 8
4025.2.bj $$\chi_{4025}(22, \cdot)$$ n/a 2880 8
4025.2.bk $$\chi_{4025}(622, \cdot)$$ n/a 3520 8
4025.2.bo $$\chi_{4025}(76, \cdot)$$ n/a 2980 10
4025.2.bq $$\chi_{4025}(1049, \cdot)$$ n/a 2840 10
4025.2.br $$\chi_{4025}(449, \cdot)$$ n/a 2160 10
4025.2.bu $$\chi_{4025}(254, \cdot)$$ n/a 3520 8
4025.2.bv $$\chi_{4025}(229, \cdot)$$ n/a 3808 8
4025.2.bx $$\chi_{4025}(206, \cdot)$$ n/a 3808 8
4025.2.ca $$\chi_{4025}(151, \cdot)$$ n/a 5960 20
4025.2.cc $$\chi_{4025}(43, \cdot)$$ n/a 4320 20
4025.2.cd $$\chi_{4025}(118, \cdot)$$ n/a 5680 20
4025.2.cf $$\chi_{4025}(36, \cdot)$$ n/a 14400 40
4025.2.cg $$\chi_{4025}(137, \cdot)$$ n/a 7616 16
4025.2.cj $$\chi_{4025}(47, \cdot)$$ n/a 7040 16
4025.2.cl $$\chi_{4025}(324, \cdot)$$ n/a 5680 20
4025.2.cm $$\chi_{4025}(199, \cdot)$$ n/a 5680 20
4025.2.co $$\chi_{4025}(201, \cdot)$$ n/a 5960 20
4025.2.cs $$\chi_{4025}(29, \cdot)$$ n/a 14400 40
4025.2.ct $$\chi_{4025}(34, \cdot)$$ n/a 19040 40
4025.2.cv $$\chi_{4025}(111, \cdot)$$ n/a 19040 40
4025.2.cy $$\chi_{4025}(107, \cdot)$$ n/a 11360 40
4025.2.db $$\chi_{4025}(82, \cdot)$$ n/a 11360 40
4025.2.dc $$\chi_{4025}(16, \cdot)$$ n/a 38080 80
4025.2.de $$\chi_{4025}(13, \cdot)$$ n/a 38080 80
4025.2.df $$\chi_{4025}(113, \cdot)$$ n/a 28800 80
4025.2.dj $$\chi_{4025}(61, \cdot)$$ n/a 38080 80
4025.2.dl $$\chi_{4025}(19, \cdot)$$ n/a 38080 80
4025.2.dm $$\chi_{4025}(4, \cdot)$$ n/a 38080 80
4025.2.do $$\chi_{4025}(3, \cdot)$$ n/a 76160 160
4025.2.dr $$\chi_{4025}(37, \cdot)$$ n/a 76160 160

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(4025))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(4025)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(115))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(161))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(175))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(575))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(805))$$$$^{\oplus 2}$$