# Properties

 Label 4332.2 Level 4332 Weight 2 Dimension 225234 Nonzero newspaces 24 Sturm bound 2079360

## Defining parameters

 Level: $$N$$ = $$4332 = 2^{2} \cdot 3 \cdot 19^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$24$$ Sturm bound: $$2079360$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(4332))$$.

Total New Old
Modular forms 524880 227110 297770
Cusp forms 514801 225234 289567
Eisenstein series 10079 1876 8203

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(4332))$$

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
4332.2.a $$\chi_{4332}(1, \cdot)$$ 4332.2.a.a 1 1
4332.2.a.b 1
4332.2.a.c 1
4332.2.a.d 1
4332.2.a.e 2
4332.2.a.f 2
4332.2.a.g 2
4332.2.a.h 2
4332.2.a.i 2
4332.2.a.j 2
4332.2.a.k 2
4332.2.a.l 2
4332.2.a.m 2
4332.2.a.n 3
4332.2.a.o 3
4332.2.a.p 4
4332.2.a.q 4
4332.2.a.r 4
4332.2.a.s 4
4332.2.a.t 6
4332.2.a.u 6
4332.2.c $$\chi_{4332}(3611, \cdot)$$ n/a 648 1
4332.2.d $$\chi_{4332}(2165, \cdot)$$ n/a 114 1
4332.2.f $$\chi_{4332}(2887, \cdot)$$ n/a 340 1
4332.2.i $$\chi_{4332}(1873, \cdot)$$ n/a 112 2
4332.2.k $$\chi_{4332}(1015, \cdot)$$ n/a 680 2
4332.2.m $$\chi_{4332}(1151, \cdot)$$ n/a 1296 2
4332.2.p $$\chi_{4332}(293, \cdot)$$ n/a 228 2
4332.2.q $$\chi_{4332}(2581, \cdot)$$ n/a 342 6
4332.2.t $$\chi_{4332}(2465, \cdot)$$ n/a 678 6
4332.2.v $$\chi_{4332}(1859, \cdot)$$ n/a 3888 6
4332.2.w $$\chi_{4332}(127, \cdot)$$ n/a 2040 6
4332.2.y $$\chi_{4332}(229, \cdot)$$ n/a 1152 18
4332.2.bb $$\chi_{4332}(151, \cdot)$$ n/a 6840 18
4332.2.bd $$\chi_{4332}(113, \cdot)$$ n/a 2268 18
4332.2.be $$\chi_{4332}(191, \cdot)$$ n/a 13608 18
4332.2.bg $$\chi_{4332}(49, \cdot)$$ n/a 2304 36
4332.2.bh $$\chi_{4332}(65, \cdot)$$ n/a 4536 36
4332.2.bk $$\chi_{4332}(11, \cdot)$$ n/a 27216 36
4332.2.bm $$\chi_{4332}(31, \cdot)$$ n/a 13680 36
4332.2.bo $$\chi_{4332}(25, \cdot)$$ n/a 6804 108
4332.2.bq $$\chi_{4332}(67, \cdot)$$ n/a 41040 108
4332.2.br $$\chi_{4332}(23, \cdot)$$ n/a 81648 108
4332.2.bt $$\chi_{4332}(29, \cdot)$$ n/a 13716 108

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(4332))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(4332)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(57))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(114))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(228))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(361))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(722))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1083))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1444))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2166))$$$$^{\oplus 2}$$