# Properties

 Label 5415.2 Level 5415 Weight 2 Dimension 708012 Nonzero newspaces 36 Sturm bound 4158720

## Defining parameters

 Level: $$N$$ = $$5415 = 3 \cdot 5 \cdot 19^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$36$$ Sturm bound: $$4158720$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(5415))$$.

Total New Old
Modular forms 1047744 713636 334108
Cusp forms 1031617 708012 323605
Eisenstein series 16127 5624 10503

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(5415))$$

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
5415.2.a $$\chi_{5415}(1, \cdot)$$ 5415.2.a.a 1 1
5415.2.a.b 1
5415.2.a.c 1
5415.2.a.d 1
5415.2.a.e 1
5415.2.a.f 1
5415.2.a.g 1
5415.2.a.h 1
5415.2.a.i 1
5415.2.a.j 1
5415.2.a.k 1
5415.2.a.l 1
5415.2.a.m 2
5415.2.a.n 2
5415.2.a.o 2
5415.2.a.p 2
5415.2.a.q 2
5415.2.a.r 2
5415.2.a.s 2
5415.2.a.t 2
5415.2.a.u 2
5415.2.a.v 2
5415.2.a.w 3
5415.2.a.x 3
5415.2.a.y 5
5415.2.a.z 5
5415.2.a.ba 6
5415.2.a.bb 6
5415.2.a.bc 6
5415.2.a.bd 6
5415.2.a.be 6
5415.2.a.bf 6
5415.2.a.bg 6
5415.2.a.bh 6
5415.2.a.bi 6
5415.2.a.bj 6
5415.2.a.bk 9
5415.2.a.bl 9
5415.2.a.bm 12
5415.2.a.bn 12
5415.2.a.bo 12
5415.2.a.bp 12
5415.2.a.bq 12
5415.2.a.br 12
5415.2.a.bs 15
5415.2.a.bt 15
5415.2.b $$\chi_{5415}(5414, \cdot)$$ n/a 648 1
5415.2.c $$\chi_{5415}(1084, \cdot)$$ n/a 340 1
5415.2.h $$\chi_{5415}(4331, \cdot)$$ n/a 452 1
5415.2.i $$\chi_{5415}(2956, \cdot)$$ n/a 456 2
5415.2.k $$\chi_{5415}(362, \cdot)$$ n/a 1296 2
5415.2.m $$\chi_{5415}(2887, \cdot)$$ n/a 680 2
5415.2.p $$\chi_{5415}(791, \cdot)$$ n/a 904 2
5415.2.q $$\chi_{5415}(1874, \cdot)$$ n/a 1296 2
5415.2.r $$\chi_{5415}(4039, \cdot)$$ n/a 680 2
5415.2.u $$\chi_{5415}(1111, \cdot)$$ n/a 1356 6
5415.2.v $$\chi_{5415}(68, \cdot)$$ n/a 2592 4
5415.2.x $$\chi_{5415}(1513, \cdot)$$ n/a 1360 4
5415.2.z $$\chi_{5415}(116, \cdot)$$ n/a 2724 6
5415.2.be $$\chi_{5415}(784, \cdot)$$ n/a 2040 6
5415.2.bf $$\chi_{5415}(299, \cdot)$$ n/a 3888 6
5415.2.bg $$\chi_{5415}(286, \cdot)$$ n/a 4536 18
5415.2.bi $$\chi_{5415}(127, \cdot)$$ n/a 4080 12
5415.2.bj $$\chi_{5415}(62, \cdot)$$ n/a 7776 12
5415.2.bl $$\chi_{5415}(56, \cdot)$$ n/a 9144 18
5415.2.bq $$\chi_{5415}(229, \cdot)$$ n/a 6840 18
5415.2.br $$\chi_{5415}(284, \cdot)$$ n/a 13608 18
5415.2.bs $$\chi_{5415}(106, \cdot)$$ n/a 9072 36
5415.2.bt $$\chi_{5415}(37, \cdot)$$ n/a 13680 36
5415.2.bv $$\chi_{5415}(77, \cdot)$$ n/a 27216 36
5415.2.bz $$\chi_{5415}(49, \cdot)$$ n/a 13680 36
5415.2.ca $$\chi_{5415}(164, \cdot)$$ n/a 27216 36
5415.2.cb $$\chi_{5415}(221, \cdot)$$ n/a 18288 36
5415.2.ce $$\chi_{5415}(16, \cdot)$$ n/a 27432 108
5415.2.cg $$\chi_{5415}(88, \cdot)$$ n/a 27360 72
5415.2.ci $$\chi_{5415}(83, \cdot)$$ n/a 54432 72
5415.2.cj $$\chi_{5415}(14, \cdot)$$ n/a 81648 108
5415.2.ck $$\chi_{5415}(4, \cdot)$$ n/a 41040 108
5415.2.cp $$\chi_{5415}(41, \cdot)$$ n/a 54648 108
5415.2.cr $$\chi_{5415}(17, \cdot)$$ n/a 163296 216
5415.2.cs $$\chi_{5415}(13, \cdot)$$ n/a 82080 216

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(5415))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(5415)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(57))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(95))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(285))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(361))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1083))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1805))$$$$^{\oplus 2}$$