## Defining parameters

 Level: $$N$$ = $$7220 = 2^{2} \cdot 5 \cdot 19^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$36$$ Sturm bound: $$6238080$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(7220))$$.

Total New Old
Modular forms 1569600 832109 737491
Cusp forms 1549441 826485 722956
Eisenstein series 20159 5624 14535

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(7220))$$

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
7220.2.a $$\chi_{7220}(1, \cdot)$$ 7220.2.a.a 1 1
7220.2.a.b 1
7220.2.a.c 1
7220.2.a.d 1
7220.2.a.e 1
7220.2.a.f 1
7220.2.a.g 1
7220.2.a.h 2
7220.2.a.i 2
7220.2.a.j 2
7220.2.a.k 2
7220.2.a.l 2
7220.2.a.m 2
7220.2.a.n 3
7220.2.a.o 3
7220.2.a.p 4
7220.2.a.q 4
7220.2.a.r 4
7220.2.a.s 8
7220.2.a.t 8
7220.2.a.u 8
7220.2.a.v 9
7220.2.a.w 9
7220.2.a.x 9
7220.2.a.y 9
7220.2.a.z 16
7220.2.c $$\chi_{7220}(2889, \cdot)$$ n/a 170 1
7220.2.d $$\chi_{7220}(7219, \cdot)$$ n/a 988 1
7220.2.f $$\chi_{7220}(4331, \cdot)$$ n/a 680 1
7220.2.i $$\chi_{7220}(3541, \cdot)$$ n/a 224 2
7220.2.k $$\chi_{7220}(723, \cdot)$$ n/a 1978 2
7220.2.l $$\chi_{7220}(5053, \cdot)$$ n/a 340 2
7220.2.n $$\chi_{7220}(791, \cdot)$$ n/a 1360 2
7220.2.r $$\chi_{7220}(429, \cdot)$$ n/a 340 2
7220.2.s $$\chi_{7220}(2459, \cdot)$$ n/a 1976 2
7220.2.u $$\chi_{7220}(821, \cdot)$$ n/a 684 6
7220.2.v $$\chi_{7220}(4263, \cdot)$$ n/a 3952 4
7220.2.y $$\chi_{7220}(293, \cdot)$$ n/a 680 4
7220.2.bb $$\chi_{7220}(299, \cdot)$$ n/a 5928 6
7220.2.bd $$\chi_{7220}(389, \cdot)$$ n/a 1020 6
7220.2.be $$\chi_{7220}(1571, \cdot)$$ n/a 4080 6
7220.2.bg $$\chi_{7220}(381, \cdot)$$ n/a 2304 18
7220.2.bi $$\chi_{7220}(333, \cdot)$$ n/a 2040 12
7220.2.bk $$\chi_{7220}(423, \cdot)$$ n/a 11856 12
7220.2.bn $$\chi_{7220}(151, \cdot)$$ n/a 13680 18
7220.2.bp $$\chi_{7220}(379, \cdot)$$ n/a 20448 18
7220.2.bq $$\chi_{7220}(229, \cdot)$$ n/a 3420 18
7220.2.bs $$\chi_{7220}(121, \cdot)$$ n/a 4608 36
7220.2.bu $$\chi_{7220}(37, \cdot)$$ n/a 6840 36
7220.2.bv $$\chi_{7220}(267, \cdot)$$ n/a 40896 36
7220.2.by $$\chi_{7220}(179, \cdot)$$ n/a 40896 36
7220.2.bz $$\chi_{7220}(49, \cdot)$$ n/a 6840 36
7220.2.cd $$\chi_{7220}(31, \cdot)$$ n/a 27360 36
7220.2.ce $$\chi_{7220}(61, \cdot)$$ n/a 13608 108
7220.2.cf $$\chi_{7220}(217, \cdot)$$ n/a 13680 72
7220.2.ci $$\chi_{7220}(7, \cdot)$$ n/a 81792 72
7220.2.ck $$\chi_{7220}(51, \cdot)$$ n/a 82080 108
7220.2.cl $$\chi_{7220}(9, \cdot)$$ n/a 20520 108
7220.2.cn $$\chi_{7220}(59, \cdot)$$ n/a 122688 108
7220.2.cq $$\chi_{7220}(23, \cdot)$$ n/a 245376 216
7220.2.cs $$\chi_{7220}(13, \cdot)$$ n/a 41040 216

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(7220))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(7220)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(95))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(190))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(361))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(380))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(722))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1444))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1805))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3610))$$$$^{\oplus 2}$$