# Properties

 Label 4028.2 Level 4028 Weight 2 Dimension 291260 Nonzero newspaces 36 Sturm bound 2.02176e+06

## Defining parameters

 Level: $$N$$ = $$4028 = 2^{2} \cdot 19 \cdot 53$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$36$$ Sturm bound: $$2021760$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(4028))$$.

Total New Old
Modular forms 510120 294724 215396
Cusp forms 500761 291260 209501
Eisenstein series 9359 3464 5895

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(4028))$$

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
4028.2.a $$\chi_{4028}(1, \cdot)$$ 4028.2.a.a 1 1
4028.2.a.b 1
4028.2.a.c 19
4028.2.a.d 19
4028.2.a.e 19
4028.2.a.f 19
4028.2.b $$\chi_{4028}(4027, \cdot)$$ n/a 536 1
4028.2.c $$\chi_{4028}(3497, \cdot)$$ 4028.2.c.a 82 1
4028.2.h $$\chi_{4028}(531, \cdot)$$ n/a 520 1
4028.2.i $$\chi_{4028}(425, \cdot)$$ n/a 176 2
4028.2.j $$\chi_{4028}(189, \cdot)$$ n/a 180 2
4028.2.m $$\chi_{4028}(3687, \cdot)$$ n/a 972 2
4028.2.n $$\chi_{4028}(107, \cdot)$$ n/a 1040 2
4028.2.s $$\chi_{4028}(635, \cdot)$$ n/a 1072 2
4028.2.t $$\chi_{4028}(2861, \cdot)$$ n/a 180 2
4028.2.u $$\chi_{4028}(213, \cdot)$$ n/a 516 6
4028.2.w $$\chi_{4028}(825, \cdot)$$ n/a 360 4
4028.2.x $$\chi_{4028}(83, \cdot)$$ n/a 2144 4
4028.2.z $$\chi_{4028}(77, \cdot)$$ n/a 960 12
4028.2.bc $$\chi_{4028}(529, \cdot)$$ n/a 540 6
4028.2.bd $$\chi_{4028}(319, \cdot)$$ n/a 3120 6
4028.2.bf $$\chi_{4028}(211, \cdot)$$ n/a 3216 6
4028.2.bh $$\chi_{4028}(227, \cdot)$$ n/a 6432 12
4028.2.bm $$\chi_{4028}(229, \cdot)$$ n/a 984 12
4028.2.bn $$\chi_{4028}(303, \cdot)$$ n/a 6432 12
4028.2.bo $$\chi_{4028}(23, \cdot)$$ n/a 6432 12
4028.2.br $$\chi_{4028}(129, \cdot)$$ n/a 1080 12
4028.2.bs $$\chi_{4028}(49, \cdot)$$ n/a 2160 24
4028.2.bt $$\chi_{4028}(39, \cdot)$$ n/a 11664 24
4028.2.bw $$\chi_{4028}(569, \cdot)$$ n/a 2160 24
4028.2.bx $$\chi_{4028}(197, \cdot)$$ n/a 2160 24
4028.2.by $$\chi_{4028}(255, \cdot)$$ n/a 12864 24
4028.2.cd $$\chi_{4028}(183, \cdot)$$ n/a 12864 24
4028.2.ce $$\chi_{4028}(81, \cdot)$$ n/a 6480 72
4028.2.cg $$\chi_{4028}(87, \cdot)$$ n/a 25728 48
4028.2.ch $$\chi_{4028}(65, \cdot)$$ n/a 4320 48
4028.2.ck $$\chi_{4028}(59, \cdot)$$ n/a 38592 72
4028.2.cm $$\chi_{4028}(15, \cdot)$$ n/a 38592 72
4028.2.cn $$\chi_{4028}(9, \cdot)$$ n/a 6480 72
4028.2.cq $$\chi_{4028}(21, \cdot)$$ n/a 12960 144
4028.2.ct $$\chi_{4028}(35, \cdot)$$ n/a 77184 144

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(4028))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(4028)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(53))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(106))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(212))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1007))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2014))$$$$^{\oplus 2}$$