Defining parameters

 Level: $$N$$ = $$4056 = 2^{3} \cdot 3 \cdot 13^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$36$$ Sturm bound: $$1817088$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(4056))$$.

Total New Old
Modular forms 459744 190203 269541
Cusp forms 448801 188567 260234
Eisenstein series 10943 1636 9307

Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(4056))$$

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
4056.2.a $$\chi_{4056}(1, \cdot)$$ 4056.2.a.a 1 1
4056.2.a.b 1
4056.2.a.c 1
4056.2.a.d 1
4056.2.a.e 1
4056.2.a.f 1
4056.2.a.g 1
4056.2.a.h 1
4056.2.a.i 1
4056.2.a.j 1
4056.2.a.k 1
4056.2.a.l 1
4056.2.a.m 1
4056.2.a.n 1
4056.2.a.o 1
4056.2.a.p 1
4056.2.a.q 1
4056.2.a.r 1
4056.2.a.s 1
4056.2.a.t 2
4056.2.a.u 2
4056.2.a.v 2
4056.2.a.w 2
4056.2.a.x 3
4056.2.a.y 3
4056.2.a.z 3
4056.2.a.ba 3
4056.2.a.bb 3
4056.2.a.bc 3
4056.2.a.bd 4
4056.2.a.be 4
4056.2.a.bf 6
4056.2.a.bg 6
4056.2.a.bh 6
4056.2.a.bi 6
4056.2.c $$\chi_{4056}(337, \cdot)$$ 4056.2.c.a 2 1
4056.2.c.b 2
4056.2.c.c 2
4056.2.c.d 2
4056.2.c.e 2
4056.2.c.f 2
4056.2.c.g 2
4056.2.c.h 2
4056.2.c.i 2
4056.2.c.j 2
4056.2.c.k 4
4056.2.c.l 4
4056.2.c.m 6
4056.2.c.n 6
4056.2.c.o 6
4056.2.c.p 8
4056.2.c.q 12
4056.2.c.r 12
4056.2.d $$\chi_{4056}(3719, \cdot)$$ None 0 1
4056.2.g $$\chi_{4056}(2029, \cdot)$$ n/a 310 1
4056.2.h $$\chi_{4056}(2027, \cdot)$$ n/a 596 1
4056.2.j $$\chi_{4056}(1691, \cdot)$$ n/a 598 1
4056.2.m $$\chi_{4056}(2365, \cdot)$$ n/a 308 1
4056.2.n $$\chi_{4056}(4055, \cdot)$$ None 0 1
4056.2.q $$\chi_{4056}(529, \cdot)$$ n/a 152 2
4056.2.t $$\chi_{4056}(2803, \cdot)$$ n/a 616 2
4056.2.u $$\chi_{4056}(775, \cdot)$$ None 0 2
4056.2.x $$\chi_{4056}(2465, \cdot)$$ n/a 308 2
4056.2.y $$\chi_{4056}(437, \cdot)$$ n/a 1192 2
4056.2.ba $$\chi_{4056}(1499, \cdot)$$ n/a 1192 2
4056.2.bb $$\chi_{4056}(2005, \cdot)$$ n/a 616 2
4056.2.be $$\chi_{4056}(191, \cdot)$$ None 0 2
4056.2.bf $$\chi_{4056}(361, \cdot)$$ n/a 156 2
4056.2.bj $$\chi_{4056}(23, \cdot)$$ None 0 2
4056.2.bk $$\chi_{4056}(1837, \cdot)$$ n/a 616 2
4056.2.bn $$\chi_{4056}(1667, \cdot)$$ n/a 1192 2
4056.2.bo $$\chi_{4056}(1709, \cdot)$$ n/a 2384 4
4056.2.bp $$\chi_{4056}(89, \cdot)$$ n/a 616 4
4056.2.bs $$\chi_{4056}(319, \cdot)$$ None 0 4
4056.2.bt $$\chi_{4056}(19, \cdot)$$ n/a 1232 4
4056.2.bw $$\chi_{4056}(313, \cdot)$$ n/a 1104 12
4056.2.bz $$\chi_{4056}(311, \cdot)$$ None 0 12
4056.2.ca $$\chi_{4056}(181, \cdot)$$ n/a 4368 12
4056.2.cd $$\chi_{4056}(131, \cdot)$$ n/a 8688 12
4056.2.cf $$\chi_{4056}(155, \cdot)$$ n/a 8688 12
4056.2.cg $$\chi_{4056}(157, \cdot)$$ n/a 4368 12
4056.2.cj $$\chi_{4056}(287, \cdot)$$ None 0 12
4056.2.ck $$\chi_{4056}(25, \cdot)$$ n/a 1080 12
4056.2.cm $$\chi_{4056}(217, \cdot)$$ n/a 2208 24
4056.2.cp $$\chi_{4056}(5, \cdot)$$ n/a 17376 24
4056.2.cq $$\chi_{4056}(161, \cdot)$$ n/a 4368 24
4056.2.ct $$\chi_{4056}(31, \cdot)$$ None 0 24
4056.2.cu $$\chi_{4056}(187, \cdot)$$ n/a 8736 24
4056.2.cv $$\chi_{4056}(35, \cdot)$$ n/a 17376 24
4056.2.cy $$\chi_{4056}(205, \cdot)$$ n/a 8736 24
4056.2.cz $$\chi_{4056}(95, \cdot)$$ None 0 24
4056.2.dd $$\chi_{4056}(49, \cdot)$$ n/a 2160 24
4056.2.de $$\chi_{4056}(263, \cdot)$$ None 0 24
4056.2.dh $$\chi_{4056}(61, \cdot)$$ n/a 8736 24
4056.2.di $$\chi_{4056}(179, \cdot)$$ n/a 17376 24
4056.2.dk $$\chi_{4056}(67, \cdot)$$ n/a 17472 48
4056.2.dl $$\chi_{4056}(7, \cdot)$$ None 0 48
4056.2.do $$\chi_{4056}(41, \cdot)$$ n/a 8736 48
4056.2.dp $$\chi_{4056}(149, \cdot)$$ n/a 34752 48

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

Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(4056))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(4056)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(26))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(52))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(78))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(104))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(156))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(169))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(312))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(338))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(507))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(676))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1014))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1352))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2028))$$$$^{\oplus 2}$$