# Properties

 Label 9025.2 Level 9025 Weight 2 Dimension 2968323 Nonzero newspaces 36 Sturm bound 12996000

## Defining parameters

 Level: $$N$$ = $$9025 = 5^{2} \cdot 19^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$36$$ Sturm bound: $$12996000$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(9025))$$.

Total New Old
Modular forms 3263112 2987532 275580
Cusp forms 3234889 2968323 266566
Eisenstein series 28223 19209 9014

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(9025))$$

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
9025.2.a $$\chi_{9025}(1, \cdot)$$ 9025.2.a.a 1 1
9025.2.a.b 1
9025.2.a.c 1
9025.2.a.d 1
9025.2.a.e 1
9025.2.a.f 1
9025.2.a.g 1
9025.2.a.h 1
9025.2.a.i 1
9025.2.a.j 1
9025.2.a.k 2
9025.2.a.l 2
9025.2.a.m 2
9025.2.a.n 2
9025.2.a.o 2
9025.2.a.p 2
9025.2.a.q 2
9025.2.a.r 2
9025.2.a.s 2
9025.2.a.t 2
9025.2.a.u 2
9025.2.a.v 2
9025.2.a.w 3
9025.2.a.x 3
9025.2.a.y 3
9025.2.a.z 3
9025.2.a.ba 3
9025.2.a.bb 3
9025.2.a.bc 3
9025.2.a.bd 3
9025.2.a.be 3
9025.2.a.bf 4
9025.2.a.bg 4
9025.2.a.bh 4
9025.2.a.bi 4
9025.2.a.bj 4
9025.2.a.bk 4
9025.2.a.bl 4
9025.2.a.bm 4
9025.2.a.bn 4
9025.2.a.bo 4
9025.2.a.bp 4
9025.2.a.bq 6
9025.2.a.br 6
9025.2.a.bs 6
9025.2.a.bt 6
9025.2.a.bu 6
9025.2.a.bv 6
9025.2.a.bw 6
9025.2.a.bx 6
9025.2.a.by 6
9025.2.a.bz 6
9025.2.a.ca 6
9025.2.a.cb 8
9025.2.a.cc 9
9025.2.a.cd 9
9025.2.a.ce 9
9025.2.a.cf 9
9025.2.a.cg 10
9025.2.a.ch 10
9025.2.a.ci 10
9025.2.a.cj 10
9025.2.a.ck 16
9025.2.a.cl 16
9025.2.a.cm 16
9025.2.a.cn 20
9025.2.a.co 20
9025.2.a.cp 21
9025.2.a.cq 21
9025.2.a.cr 21
9025.2.a.cs 21
9025.2.a.ct 24
9025.2.a.cu 24
9025.2.a.cv 40
9025.2.b $$\chi_{9025}(6499, \cdot)$$ n/a 494 1
9025.2.e $$\chi_{9025}(1151, \cdot)$$ n/a 1030 2
9025.2.g $$\chi_{9025}(1082, \cdot)$$ n/a 988 2
9025.2.h $$\chi_{9025}(1806, \cdot)$$ n/a 3340 4
9025.2.j $$\chi_{9025}(4624, \cdot)$$ n/a 988 2
9025.2.l $$\chi_{9025}(776, \cdot)$$ n/a 3084 6
9025.2.n $$\chi_{9025}(1084, \cdot)$$ n/a 3344 4
9025.2.p $$\chi_{9025}(293, \cdot)$$ n/a 1976 4
9025.2.r $$\chi_{9025}(1736, \cdot)$$ n/a 6672 8
9025.2.u $$\chi_{9025}(99, \cdot)$$ n/a 2964 6
9025.2.v $$\chi_{9025}(476, \cdot)$$ n/a 10764 18
9025.2.w $$\chi_{9025}(2887, \cdot)$$ n/a 6672 8
9025.2.y $$\chi_{9025}(429, \cdot)$$ n/a 6672 8
9025.2.bc $$\chi_{9025}(307, \cdot)$$ n/a 5928 12
9025.2.bf $$\chi_{9025}(324, \cdot)$$ n/a 10224 18
9025.2.bg $$\chi_{9025}(606, \cdot)$$ n/a 20016 24
9025.2.bh $$\chi_{9025}(26, \cdot)$$ n/a 21528 36
9025.2.bj $$\chi_{9025}(1152, \cdot)$$ n/a 13344 16
9025.2.bk $$\chi_{9025}(18, \cdot)$$ n/a 20448 36
9025.2.bn $$\chi_{9025}(54, \cdot)$$ n/a 20016 24
9025.2.bp $$\chi_{9025}(96, \cdot)$$ n/a 68256 72
9025.2.br $$\chi_{9025}(49, \cdot)$$ n/a 20448 36
9025.2.bt $$\chi_{9025}(101, \cdot)$$ n/a 64692 108
9025.2.bu $$\chi_{9025}(127, \cdot)$$ n/a 40032 48
9025.2.bx $$\chi_{9025}(39, \cdot)$$ n/a 68256 72
9025.2.ca $$\chi_{9025}(107, \cdot)$$ n/a 40896 72
9025.2.cb $$\chi_{9025}(11, \cdot)$$ n/a 136512 144
9025.2.cc $$\chi_{9025}(24, \cdot)$$ n/a 61344 108
9025.2.cg $$\chi_{9025}(37, \cdot)$$ n/a 136512 144
9025.2.cj $$\chi_{9025}(64, \cdot)$$ n/a 136512 144
9025.2.ck $$\chi_{9025}(32, \cdot)$$ n/a 122688 216
9025.2.cm $$\chi_{9025}(6, \cdot)$$ n/a 409536 432
9025.2.cn $$\chi_{9025}(8, \cdot)$$ n/a 273024 288
9025.2.cq $$\chi_{9025}(4, \cdot)$$ n/a 409536 432
9025.2.ct $$\chi_{9025}(2, \cdot)$$ n/a 819072 864

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(9025))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(9025)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(95))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(361))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(475))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1805))$$$$^{\oplus 2}$$