## Defining parameters

 Level: $$N$$ = $$5054 = 2 \cdot 7 \cdot 19^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$32$$ Sturm bound: $$3119040$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(5054))$$.

Total New Old
Modular forms 785808 247710 538098
Cusp forms 773713 247710 526003
Eisenstein series 12095 0 12095

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(5054))$$

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
5054.2.a $$\chi_{5054}(1, \cdot)$$ 5054.2.a.a 1 1
5054.2.a.b 1
5054.2.a.c 1
5054.2.a.d 2
5054.2.a.e 2
5054.2.a.f 2
5054.2.a.g 2
5054.2.a.h 2
5054.2.a.i 2
5054.2.a.j 2
5054.2.a.k 2
5054.2.a.l 2
5054.2.a.m 2
5054.2.a.n 2
5054.2.a.o 2
5054.2.a.p 2
5054.2.a.q 3
5054.2.a.r 3
5054.2.a.s 3
5054.2.a.t 3
5054.2.a.u 3
5054.2.a.v 4
5054.2.a.w 4
5054.2.a.x 4
5054.2.a.y 4
5054.2.a.z 6
5054.2.a.ba 6
5054.2.a.bb 6
5054.2.a.bc 6
5054.2.a.bd 6
5054.2.a.be 6
5054.2.a.bf 8
5054.2.a.bg 8
5054.2.a.bh 8
5054.2.a.bi 8
5054.2.a.bj 9
5054.2.a.bk 9
5054.2.a.bl 12
5054.2.a.bm 12
5054.2.d $$\chi_{5054}(5053, \cdot)$$ n/a 224 1
5054.2.e $$\chi_{5054}(723, \cdot)$$ n/a 456 2
5054.2.f $$\chi_{5054}(4761, \cdot)$$ n/a 340 2
5054.2.g $$\chi_{5054}(653, \cdot)$$ n/a 456 2
5054.2.h $$\chi_{5054}(429, \cdot)$$ n/a 456 2
5054.2.k $$\chi_{5054}(3181, \cdot)$$ n/a 456 2
5054.2.l $$\chi_{5054}(2887, \cdot)$$ n/a 456 2
5054.2.m $$\chi_{5054}(69, \cdot)$$ n/a 448 2
5054.2.t $$\chi_{5054}(2957, \cdot)$$ n/a 456 2
5054.2.u $$\chi_{5054}(99, \cdot)$$ n/a 1020 6
5054.2.v $$\chi_{5054}(821, \cdot)$$ n/a 1356 6
5054.2.w $$\chi_{5054}(389, \cdot)$$ n/a 1356 6
5054.2.x $$\chi_{5054}(307, \cdot)$$ n/a 1368 6
5054.2.y $$\chi_{5054}(1055, \cdot)$$ n/a 1356 6
5054.2.bd $$\chi_{5054}(299, \cdot)$$ n/a 1356 6
5054.2.bg $$\chi_{5054}(267, \cdot)$$ n/a 3420 18
5054.2.bh $$\chi_{5054}(265, \cdot)$$ n/a 4608 18
5054.2.bk $$\chi_{5054}(163, \cdot)$$ n/a 9072 36
5054.2.bl $$\chi_{5054}(11, \cdot)$$ n/a 9072 36
5054.2.bm $$\chi_{5054}(197, \cdot)$$ n/a 6840 36
5054.2.bn $$\chi_{5054}(39, \cdot)$$ n/a 9072 36
5054.2.bo $$\chi_{5054}(31, \cdot)$$ n/a 9072 36
5054.2.bv $$\chi_{5054}(27, \cdot)$$ n/a 9216 36
5054.2.bw $$\chi_{5054}(75, \cdot)$$ n/a 9072 36
5054.2.bx $$\chi_{5054}(145, \cdot)$$ n/a 9072 36
5054.2.ca $$\chi_{5054}(25, \cdot)$$ n/a 27432 108
5054.2.cb $$\chi_{5054}(9, \cdot)$$ n/a 27432 108
5054.2.cc $$\chi_{5054}(43, \cdot)$$ n/a 20520 108
5054.2.cf $$\chi_{5054}(33, \cdot)$$ n/a 27432 108
5054.2.ck $$\chi_{5054}(3, \cdot)$$ n/a 27432 108
5054.2.cl $$\chi_{5054}(13, \cdot)$$ n/a 27216 108

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(5054))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(5054)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(133))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(266))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(361))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(722))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2527))$$$$^{\oplus 2}$$