Properties

 Label 5312.2 Level 5312 Weight 2 Dimension 494010 Nonzero newspaces 16 Sturm bound 3526656

Defining parameters

 Level: $$N$$ = $$5312 = 2^{6} \cdot 83$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$16$$ Sturm bound: $$3526656$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(5312))$$.

Total New Old
Modular forms 887568 497574 389994
Cusp forms 875761 494010 381751
Eisenstein series 11807 3564 8243

Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(5312))$$

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
5312.2.a $$\chi_{5312}(1, \cdot)$$ 5312.2.a.a 1 1
5312.2.a.b 1
5312.2.a.c 1
5312.2.a.d 1
5312.2.a.e 1
5312.2.a.f 1
5312.2.a.g 1
5312.2.a.h 1
5312.2.a.i 1
5312.2.a.j 1
5312.2.a.k 1
5312.2.a.l 1
5312.2.a.m 1
5312.2.a.n 1
5312.2.a.o 1
5312.2.a.p 1
5312.2.a.q 2
5312.2.a.r 2
5312.2.a.s 2
5312.2.a.t 2
5312.2.a.u 2
5312.2.a.v 2
5312.2.a.w 2
5312.2.a.x 2
5312.2.a.y 3
5312.2.a.z 3
5312.2.a.ba 3
5312.2.a.bb 3
5312.2.a.bc 3
5312.2.a.bd 3
5312.2.a.be 4
5312.2.a.bf 4
5312.2.a.bg 4
5312.2.a.bh 4
5312.2.a.bi 5
5312.2.a.bj 5
5312.2.a.bk 5
5312.2.a.bl 5
5312.2.a.bm 6
5312.2.a.bn 6
5312.2.a.bo 6
5312.2.a.bp 6
5312.2.a.bq 8
5312.2.a.br 8
5312.2.a.bs 8
5312.2.a.bt 8
5312.2.a.bu 11
5312.2.a.bv 11
5312.2.b $$\chi_{5312}(5311, \cdot)$$ n/a 166 1
5312.2.c $$\chi_{5312}(2657, \cdot)$$ n/a 164 1
5312.2.h $$\chi_{5312}(2655, \cdot)$$ n/a 168 1
5312.2.j $$\chi_{5312}(1329, \cdot)$$ n/a 328 2
5312.2.l $$\chi_{5312}(1327, \cdot)$$ n/a 332 2
5312.2.m $$\chi_{5312}(663, \cdot)$$ None 0 4
5312.2.n $$\chi_{5312}(665, \cdot)$$ None 0 4
5312.2.q $$\chi_{5312}(333, \cdot)$$ n/a 5248 8
5312.2.t $$\chi_{5312}(331, \cdot)$$ n/a 5360 8
5312.2.u $$\chi_{5312}(65, \cdot)$$ n/a 6640 40
5312.2.v $$\chi_{5312}(159, \cdot)$$ n/a 6720 40
5312.2.ba $$\chi_{5312}(33, \cdot)$$ n/a 6720 40
5312.2.bb $$\chi_{5312}(255, \cdot)$$ n/a 6640 40
5312.2.bc $$\chi_{5312}(15, \cdot)$$ n/a 13280 80
5312.2.be $$\chi_{5312}(17, \cdot)$$ n/a 13280 80
5312.2.bi $$\chi_{5312}(9, \cdot)$$ None 0 160
5312.2.bj $$\chi_{5312}(39, \cdot)$$ None 0 160
5312.2.bk $$\chi_{5312}(19, \cdot)$$ n/a 214400 320
5312.2.bn $$\chi_{5312}(21, \cdot)$$ n/a 214400 320

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

Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(5312))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(5312)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(83))$$$$^{\oplus 7}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(166))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(332))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(664))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1328))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2656))$$$$^{\oplus 2}$$