# Properties

 Label 4225.2 Level 4225 Weight 2 Dimension 642287 Nonzero newspaces 48 Sturm bound 2839200

## Defining parameters

 Level: $$N$$ = $$4225 = 5^{2} \cdot 13^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$48$$ Sturm bound: $$2839200$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(4225))$$.

Total New Old
Modular forms 716184 650672 65512
Cusp forms 703417 642287 61130
Eisenstein series 12767 8385 4382

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(4225))$$

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 available newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
4225.2.a $$\chi_{4225}(1, \cdot)$$ 4225.2.a.a 1 1
4225.2.a.b 1
4225.2.a.c 1
4225.2.a.d 1
4225.2.a.e 1
4225.2.a.f 1
4225.2.a.g 1
4225.2.a.h 1
4225.2.a.i 1
4225.2.a.j 1
4225.2.a.k 1
4225.2.a.l 1
4225.2.a.m 1
4225.2.a.n 1
4225.2.a.o 1
4225.2.a.p 1
4225.2.a.q 1
4225.2.a.r 2
4225.2.a.s 2
4225.2.a.t 2
4225.2.a.u 2
4225.2.a.v 2
4225.2.a.w 2
4225.2.a.x 2
4225.2.a.y 2
4225.2.a.z 2
4225.2.a.ba 3
4225.2.a.bb 3
4225.2.a.bc 3
4225.2.a.bd 3
4225.2.a.be 3
4225.2.a.bf 3
4225.2.a.bg 3
4225.2.a.bh 3
4225.2.a.bi 4
4225.2.a.bj 4
4225.2.a.bk 4
4225.2.a.bl 4
4225.2.a.bm 5
4225.2.a.bn 5
4225.2.a.bo 5
4225.2.a.bp 5
4225.2.a.bq 6
4225.2.a.br 6
4225.2.a.bs 9
4225.2.a.bt 9
4225.2.a.bu 10
4225.2.a.bv 10
4225.2.a.bw 12
4225.2.a.bx 12
4225.2.a.by 12
4225.2.a.bz 12
4225.2.a.ca 18
4225.2.a.cb 18
4225.2.b $$\chi_{4225}(2874, \cdot)$$ n/a 222 1
4225.2.c $$\chi_{4225}(1351, \cdot)$$ n/a 230 1
4225.2.d $$\chi_{4225}(4224, \cdot)$$ n/a 220 1
4225.2.e $$\chi_{4225}(2726, \cdot)$$ n/a 456 2
4225.2.f $$\chi_{4225}(1282, \cdot)$$ n/a 442 2
4225.2.k $$\chi_{4225}(268, \cdot)$$ n/a 442 2
4225.2.l $$\chi_{4225}(846, \cdot)$$ n/a 1508 4
4225.2.m $$\chi_{4225}(699, \cdot)$$ n/a 440 2
4225.2.n $$\chi_{4225}(2051, \cdot)$$ n/a 458 2
4225.2.o $$\chi_{4225}(1374, \cdot)$$ n/a 444 2
4225.2.p $$\chi_{4225}(844, \cdot)$$ n/a 1504 4
4225.2.q $$\chi_{4225}(506, \cdot)$$ n/a 1496 4
4225.2.r $$\chi_{4225}(339, \cdot)$$ n/a 1504 4
4225.2.s $$\chi_{4225}(357, \cdot)$$ n/a 884 4
4225.2.x $$\chi_{4225}(418, \cdot)$$ n/a 884 4
4225.2.y $$\chi_{4225}(326, \cdot)$$ n/a 3420 12
4225.2.z $$\chi_{4225}(146, \cdot)$$ n/a 3008 8
4225.2.ba $$\chi_{4225}(577, \cdot)$$ n/a 3000 8
4225.2.bf $$\chi_{4225}(408, \cdot)$$ n/a 3000 8
4225.2.bg $$\chi_{4225}(324, \cdot)$$ n/a 3264 12
4225.2.bh $$\chi_{4225}(51, \cdot)$$ n/a 3408 12
4225.2.bi $$\chi_{4225}(274, \cdot)$$ n/a 3240 12
4225.2.bj $$\chi_{4225}(484, \cdot)$$ n/a 2992 8
4225.2.bk $$\chi_{4225}(316, \cdot)$$ n/a 2992 8
4225.2.bl $$\chi_{4225}(654, \cdot)$$ n/a 3008 8
4225.2.bm $$\chi_{4225}(126, \cdot)$$ n/a 6864 24
4225.2.bn $$\chi_{4225}(57, \cdot)$$ n/a 6504 24
4225.2.bs $$\chi_{4225}(18, \cdot)$$ n/a 6504 24
4225.2.bt $$\chi_{4225}(188, \cdot)$$ n/a 6000 16
4225.2.by $$\chi_{4225}(258, \cdot)$$ n/a 6000 16
4225.2.bz $$\chi_{4225}(66, \cdot)$$ n/a 21696 48
4225.2.ca $$\chi_{4225}(74, \cdot)$$ n/a 6480 24
4225.2.cb $$\chi_{4225}(101, \cdot)$$ n/a 6840 24
4225.2.cc $$\chi_{4225}(49, \cdot)$$ n/a 6528 24
4225.2.cd $$\chi_{4225}(14, \cdot)$$ n/a 21792 48
4225.2.ce $$\chi_{4225}(116, \cdot)$$ n/a 21792 48
4225.2.cf $$\chi_{4225}(64, \cdot)$$ n/a 21696 48
4225.2.cg $$\chi_{4225}(7, \cdot)$$ n/a 13008 48
4225.2.cl $$\chi_{4225}(32, \cdot)$$ n/a 13008 48
4225.2.cm $$\chi_{4225}(16, \cdot)$$ n/a 43392 96
4225.2.cn $$\chi_{4225}(47, \cdot)$$ n/a 43488 96
4225.2.cs $$\chi_{4225}(8, \cdot)$$ n/a 43488 96
4225.2.ct $$\chi_{4225}(4, \cdot)$$ n/a 43392 96
4225.2.cu $$\chi_{4225}(36, \cdot)$$ n/a 43584 96
4225.2.cv $$\chi_{4225}(9, \cdot)$$ n/a 43584 96
4225.2.cw $$\chi_{4225}(2, \cdot)$$ n/a 86976 192
4225.2.db $$\chi_{4225}(28, \cdot)$$ n/a 86976 192

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(4225))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(4225)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(65))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(169))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(325))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(845))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4225))$$$$^{\oplus 1}$$