## Defining parameters

 Level: $$N$$ = $$5390 = 2 \cdot 5 \cdot 7^{2} \cdot 11$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$48$$ Sturm bound: $$3386880$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(5390))$$.

Total New Old
Modular forms 856320 244136 612184
Cusp forms 837121 244136 592985
Eisenstein series 19199 0 19199

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(5390))$$

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
5390.2.a $$\chi_{5390}(1, \cdot)$$ 5390.2.a.a 1 1
5390.2.a.b 1
5390.2.a.c 1
5390.2.a.d 1
5390.2.a.e 1
5390.2.a.f 1
5390.2.a.g 1
5390.2.a.h 1
5390.2.a.i 1
5390.2.a.j 1
5390.2.a.k 1
5390.2.a.l 1
5390.2.a.m 1
5390.2.a.n 1
5390.2.a.o 1
5390.2.a.p 1
5390.2.a.q 1
5390.2.a.r 1
5390.2.a.s 1
5390.2.a.t 1
5390.2.a.u 1
5390.2.a.v 1
5390.2.a.w 1
5390.2.a.x 1
5390.2.a.y 1
5390.2.a.z 1
5390.2.a.ba 1
5390.2.a.bb 1
5390.2.a.bc 1
5390.2.a.bd 1
5390.2.a.be 1
5390.2.a.bf 1
5390.2.a.bg 1
5390.2.a.bh 1
5390.2.a.bi 1
5390.2.a.bj 1
5390.2.a.bk 2
5390.2.a.bl 2
5390.2.a.bm 2
5390.2.a.bn 2
5390.2.a.bo 2
5390.2.a.bp 2
5390.2.a.bq 2
5390.2.a.br 2
5390.2.a.bs 2
5390.2.a.bt 2
5390.2.a.bu 2
5390.2.a.bv 3
5390.2.a.bw 3
5390.2.a.bx 3
5390.2.a.by 3
5390.2.a.bz 3
5390.2.a.ca 3
5390.2.a.cb 4
5390.2.a.cc 4
5390.2.a.cd 4
5390.2.a.ce 4
5390.2.a.cf 4
5390.2.a.cg 4
5390.2.a.ch 5
5390.2.a.ci 5
5390.2.a.cj 6
5390.2.a.ck 6
5390.2.a.cl 6
5390.2.a.cm 6
5390.2.c $$\chi_{5390}(1079, \cdot)$$ n/a 206 1
5390.2.e $$\chi_{5390}(4311, \cdot)$$ n/a 160 1
5390.2.g $$\chi_{5390}(5389, \cdot)$$ n/a 240 1
5390.2.i $$\chi_{5390}(3301, \cdot)$$ n/a 272 2
5390.2.l $$\chi_{5390}(3037, \cdot)$$ n/a 400 2
5390.2.m $$\chi_{5390}(197, \cdot)$$ n/a 492 2
5390.2.n $$\chi_{5390}(1961, \cdot)$$ n/a 656 4
5390.2.o $$\chi_{5390}(1979, \cdot)$$ n/a 480 2
5390.2.r $$\chi_{5390}(4379, \cdot)$$ n/a 400 2
5390.2.t $$\chi_{5390}(901, \cdot)$$ n/a 320 2
5390.2.v $$\chi_{5390}(771, \cdot)$$ n/a 1152 6
5390.2.x $$\chi_{5390}(1469, \cdot)$$ n/a 960 4
5390.2.z $$\chi_{5390}(391, \cdot)$$ n/a 640 4
5390.2.bb $$\chi_{5390}(3039, \cdot)$$ n/a 984 4
5390.2.bd $$\chi_{5390}(1783, \cdot)$$ n/a 800 4
5390.2.be $$\chi_{5390}(263, \cdot)$$ n/a 960 4
5390.2.bj $$\chi_{5390}(769, \cdot)$$ n/a 2016 6
5390.2.bl $$\chi_{5390}(461, \cdot)$$ n/a 1344 6
5390.2.bn $$\chi_{5390}(309, \cdot)$$ n/a 1680 6
5390.2.bo $$\chi_{5390}(361, \cdot)$$ n/a 1280 8
5390.2.bp $$\chi_{5390}(393, \cdot)$$ n/a 1968 8
5390.2.bq $$\chi_{5390}(97, \cdot)$$ n/a 1920 8
5390.2.bt $$\chi_{5390}(221, \cdot)$$ n/a 2208 12
5390.2.bw $$\chi_{5390}(43, \cdot)$$ n/a 4032 12
5390.2.bx $$\chi_{5390}(573, \cdot)$$ n/a 3360 12
5390.2.bz $$\chi_{5390}(2371, \cdot)$$ n/a 1280 8
5390.2.cb $$\chi_{5390}(949, \cdot)$$ n/a 1920 8
5390.2.ce $$\chi_{5390}(19, \cdot)$$ n/a 1920 8
5390.2.cf $$\chi_{5390}(71, \cdot)$$ n/a 5376 24
5390.2.cg $$\chi_{5390}(131, \cdot)$$ n/a 2688 12
5390.2.ci $$\chi_{5390}(529, \cdot)$$ n/a 3360 12
5390.2.cl $$\chi_{5390}(439, \cdot)$$ n/a 4032 12
5390.2.cp $$\chi_{5390}(557, \cdot)$$ n/a 3840 16
5390.2.cq $$\chi_{5390}(313, \cdot)$$ n/a 3840 16
5390.2.cr $$\chi_{5390}(169, \cdot)$$ n/a 8064 24
5390.2.ct $$\chi_{5390}(41, \cdot)$$ n/a 5376 24
5390.2.cv $$\chi_{5390}(139, \cdot)$$ n/a 8064 24
5390.2.cy $$\chi_{5390}(417, \cdot)$$ n/a 8064 24
5390.2.cz $$\chi_{5390}(243, \cdot)$$ n/a 6720 24
5390.2.dc $$\chi_{5390}(81, \cdot)$$ n/a 10752 48
5390.2.dd $$\chi_{5390}(27, \cdot)$$ n/a 16128 48
5390.2.de $$\chi_{5390}(57, \cdot)$$ n/a 16128 48
5390.2.di $$\chi_{5390}(299, \cdot)$$ n/a 16128 48
5390.2.dl $$\chi_{5390}(9, \cdot)$$ n/a 16128 48
5390.2.dn $$\chi_{5390}(61, \cdot)$$ n/a 10752 48
5390.2.dq $$\chi_{5390}(3, \cdot)$$ n/a 32256 96
5390.2.dr $$\chi_{5390}(107, \cdot)$$ n/a 32256 96

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(5390))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(5390)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(55))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(70))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(77))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(98))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(110))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(154))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(245))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(385))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(490))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(539))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(770))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1078))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2695))$$$$^{\oplus 2}$$