Properties

 Label 4864.2 Level 4864 Weight 2 Dimension 410648 Nonzero newspaces 36 Sturm bound 2949120

Defining parameters

 Level: $$N$$ = $$4864 = 2^{8} \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$36$$ Sturm bound: $$2949120$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(4864))$$.

Total New Old
Modular forms 743616 414184 329432
Cusp forms 730945 410648 320297
Eisenstein series 12671 3536 9135

Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(4864))$$

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
4864.2.a $$\chi_{4864}(1, \cdot)$$ 4864.2.a.a 1 1
4864.2.a.b 1
4864.2.a.c 1
4864.2.a.d 1
4864.2.a.e 1
4864.2.a.f 1
4864.2.a.g 1
4864.2.a.h 1
4864.2.a.i 1
4864.2.a.j 1
4864.2.a.k 1
4864.2.a.l 1
4864.2.a.m 1
4864.2.a.n 1
4864.2.a.o 1
4864.2.a.p 1
4864.2.a.q 2
4864.2.a.r 2
4864.2.a.s 2
4864.2.a.t 2
4864.2.a.u 2
4864.2.a.v 2
4864.2.a.w 2
4864.2.a.x 2
4864.2.a.y 2
4864.2.a.z 2
4864.2.a.ba 3
4864.2.a.bb 3
4864.2.a.bc 3
4864.2.a.bd 3
4864.2.a.be 3
4864.2.a.bf 3
4864.2.a.bg 3
4864.2.a.bh 3
4864.2.a.bi 4
4864.2.a.bj 4
4864.2.a.bk 4
4864.2.a.bl 4
4864.2.a.bm 8
4864.2.a.bn 8
4864.2.a.bo 8
4864.2.a.bp 8
4864.2.a.bq 8
4864.2.a.br 8
4864.2.a.bs 10
4864.2.a.bt 10
4864.2.b $$\chi_{4864}(2431, \cdot)$$ n/a 156 1
4864.2.c $$\chi_{4864}(2433, \cdot)$$ n/a 144 1
4864.2.h $$\chi_{4864}(4863, \cdot)$$ n/a 156 1
4864.2.i $$\chi_{4864}(1793, \cdot)$$ n/a 312 2
4864.2.k $$\chi_{4864}(1217, \cdot)$$ n/a 288 2
4864.2.m $$\chi_{4864}(1215, \cdot)$$ n/a 320 2
4864.2.n $$\chi_{4864}(255, \cdot)$$ n/a 312 2
4864.2.s $$\chi_{4864}(639, \cdot)$$ n/a 312 2
4864.2.t $$\chi_{4864}(2177, \cdot)$$ n/a 312 2
4864.2.u $$\chi_{4864}(607, \cdot)$$ n/a 624 4
4864.2.v $$\chi_{4864}(609, \cdot)$$ n/a 576 4
4864.2.y $$\chi_{4864}(769, \cdot)$$ n/a 936 6
4864.2.z $$\chi_{4864}(577, \cdot)$$ n/a 640 4
4864.2.bb $$\chi_{4864}(1471, \cdot)$$ n/a 640 4
4864.2.bd $$\chi_{4864}(305, \cdot)$$ n/a 1152 8
4864.2.be $$\chi_{4864}(303, \cdot)$$ n/a 1264 8
4864.2.bj $$\chi_{4864}(385, \cdot)$$ n/a 936 6
4864.2.bl $$\chi_{4864}(127, \cdot)$$ n/a 936 6
4864.2.bm $$\chi_{4864}(1535, \cdot)$$ n/a 936 6
4864.2.bq $$\chi_{4864}(353, \cdot)$$ n/a 1248 8
4864.2.br $$\chi_{4864}(31, \cdot)$$ n/a 1248 8
4864.2.bs $$\chi_{4864}(153, \cdot)$$ None 0 16
4864.2.bv $$\chi_{4864}(151, \cdot)$$ None 0 16
4864.2.bw $$\chi_{4864}(319, \cdot)$$ n/a 1920 12
4864.2.by $$\chi_{4864}(321, \cdot)$$ n/a 1920 12
4864.2.ca $$\chi_{4864}(335, \cdot)$$ n/a 2528 16
4864.2.cb $$\chi_{4864}(49, \cdot)$$ n/a 2528 16
4864.2.ce $$\chi_{4864}(77, \cdot)$$ n/a 18432 32
4864.2.cf $$\chi_{4864}(75, \cdot)$$ n/a 20416 32
4864.2.ci $$\chi_{4864}(161, \cdot)$$ n/a 3744 24
4864.2.cj $$\chi_{4864}(223, \cdot)$$ n/a 3744 24
4864.2.cn $$\chi_{4864}(103, \cdot)$$ None 0 32
4864.2.co $$\chi_{4864}(121, \cdot)$$ None 0 32
4864.2.cs $$\chi_{4864}(17, \cdot)$$ n/a 7584 48
4864.2.ct $$\chi_{4864}(15, \cdot)$$ n/a 7584 48
4864.2.cw $$\chi_{4864}(27, \cdot)$$ n/a 40832 64
4864.2.cx $$\chi_{4864}(45, \cdot)$$ n/a 40832 64
4864.2.cz $$\chi_{4864}(71, \cdot)$$ None 0 96
4864.2.da $$\chi_{4864}(9, \cdot)$$ None 0 96
4864.2.dc $$\chi_{4864}(5, \cdot)$$ n/a 122496 192
4864.2.dd $$\chi_{4864}(3, \cdot)$$ n/a 122496 192

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

Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(4864))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(4864)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 7}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(128))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(152))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(256))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(304))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(608))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1216))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2432))$$$$^{\oplus 2}$$