# Properties

 Label 5929.2 Level 5929 Weight 2 Dimension 1336194 Nonzero newspaces 32 Sturm bound 5691840

## Defining parameters

 Level: $$N$$ = $$5929 = 7^{2} \cdot 11^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$32$$ Sturm bound: $$5691840$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(5929))$$.

Total New Old
Modular forms 1432560 1349823 82737
Cusp forms 1413361 1336194 77167
Eisenstein series 19199 13629 5570

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(5929))$$

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
5929.2.a $$\chi_{5929}(1, \cdot)$$ 5929.2.a.a 1 1
5929.2.a.b 1
5929.2.a.c 1
5929.2.a.d 1
5929.2.a.e 1
5929.2.a.f 1
5929.2.a.g 1
5929.2.a.h 1
5929.2.a.i 2
5929.2.a.j 2
5929.2.a.k 2
5929.2.a.l 2
5929.2.a.m 2
5929.2.a.n 2
5929.2.a.o 2
5929.2.a.p 2
5929.2.a.q 2
5929.2.a.r 2
5929.2.a.s 2
5929.2.a.t 3
5929.2.a.u 3
5929.2.a.v 3
5929.2.a.w 3
5929.2.a.x 3
5929.2.a.y 3
5929.2.a.z 4
5929.2.a.ba 4
5929.2.a.bb 4
5929.2.a.bc 4
5929.2.a.bd 4
5929.2.a.be 4
5929.2.a.bf 4
5929.2.a.bg 4
5929.2.a.bh 4
5929.2.a.bi 4
5929.2.a.bj 6
5929.2.a.bk 6
5929.2.a.bl 6
5929.2.a.bm 6
5929.2.a.bn 7
5929.2.a.bo 7
5929.2.a.bp 7
5929.2.a.bq 7
5929.2.a.br 8
5929.2.a.bs 8
5929.2.a.bt 8
5929.2.a.bu 8
5929.2.a.bv 10
5929.2.a.bw 10
5929.2.a.bx 10
5929.2.a.by 10
5929.2.a.bz 10
5929.2.a.ca 12
5929.2.a.cb 12
5929.2.a.cc 12
5929.2.a.cd 14
5929.2.a.ce 14
5929.2.a.cf 16
5929.2.a.cg 24
5929.2.a.ch 24
5929.2.b $$\chi_{5929}(5928, \cdot)$$ n/a 344 1
5929.2.e $$\chi_{5929}(606, \cdot)$$ n/a 690 2
5929.2.f $$\chi_{5929}(148, \cdot)$$ n/a 1396 4
5929.2.i $$\chi_{5929}(362, \cdot)$$ n/a 688 2
5929.2.j $$\chi_{5929}(848, \cdot)$$ n/a 2994 6
5929.2.m $$\chi_{5929}(1322, \cdot)$$ n/a 1376 4
5929.2.n $$\chi_{5929}(540, \cdot)$$ n/a 4460 10
5929.2.q $$\chi_{5929}(846, \cdot)$$ n/a 2976 6
5929.2.r $$\chi_{5929}(753, \cdot)$$ n/a 2752 8
5929.2.s $$\chi_{5929}(485, \cdot)$$ n/a 6000 12
5929.2.u $$\chi_{5929}(538, \cdot)$$ n/a 4360 10
5929.2.w $$\chi_{5929}(215, \cdot)$$ n/a 2752 8
5929.2.z $$\chi_{5929}(67, \cdot)$$ n/a 8720 20
5929.2.ba $$\chi_{5929}(323, \cdot)$$ n/a 11904 24
5929.2.bb $$\chi_{5929}(241, \cdot)$$ n/a 5952 12
5929.2.be $$\chi_{5929}(246, \cdot)$$ n/a 17840 40
5929.2.bg $$\chi_{5929}(472, \cdot)$$ n/a 8720 20
5929.2.bi $$\chi_{5929}(118, \cdot)$$ n/a 11904 24
5929.2.bl $$\chi_{5929}(78, \cdot)$$ n/a 36840 60
5929.2.bm $$\chi_{5929}(9, \cdot)$$ n/a 23808 48
5929.2.bo $$\chi_{5929}(195, \cdot)$$ n/a 17440 40
5929.2.br $$\chi_{5929}(76, \cdot)$$ n/a 36840 60
5929.2.bt $$\chi_{5929}(214, \cdot)$$ n/a 34880 80
5929.2.bw $$\chi_{5929}(40, \cdot)$$ n/a 23808 48
5929.2.bx $$\chi_{5929}(23, \cdot)$$ n/a 73680 120
5929.2.bz $$\chi_{5929}(19, \cdot)$$ n/a 34880 80
5929.2.cb $$\chi_{5929}(15, \cdot)$$ n/a 147360 240
5929.2.cd $$\chi_{5929}(10, \cdot)$$ n/a 73680 120
5929.2.cg $$\chi_{5929}(6, \cdot)$$ n/a 147360 240
5929.2.ci $$\chi_{5929}(4, \cdot)$$ n/a 294720 480
5929.2.ck $$\chi_{5929}(17, \cdot)$$ n/a 294720 480

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(5929))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(5929)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(77))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(121))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(539))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(847))$$$$^{\oplus 2}$$