Properties

 Label 4830.2 Level 4830 Weight 2 Dimension 133087 Nonzero newspaces 48 Sturm bound 2433024

Defining parameters

 Level: $$N$$ = $$4830 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 23$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$48$$ Sturm bound: $$2433024$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(4830))$$.

Total New Old
Modular forms 616704 133087 483617
Cusp forms 599809 133087 466722
Eisenstein series 16895 0 16895

Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(4830))$$

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
4830.2.a $$\chi_{4830}(1, \cdot)$$ 4830.2.a.a 1 1
4830.2.a.b 1
4830.2.a.c 1
4830.2.a.d 1
4830.2.a.e 1
4830.2.a.f 1
4830.2.a.g 1
4830.2.a.h 1
4830.2.a.i 1
4830.2.a.j 1
4830.2.a.k 1
4830.2.a.l 1
4830.2.a.m 1
4830.2.a.n 1
4830.2.a.o 1
4830.2.a.p 1
4830.2.a.q 1
4830.2.a.r 1
4830.2.a.s 1
4830.2.a.t 1
4830.2.a.u 1
4830.2.a.v 1
4830.2.a.w 1
4830.2.a.x 1
4830.2.a.y 1
4830.2.a.z 1
4830.2.a.ba 1
4830.2.a.bb 1
4830.2.a.bc 1
4830.2.a.bd 1
4830.2.a.be 1
4830.2.a.bf 1
4830.2.a.bg 1
4830.2.a.bh 1
4830.2.a.bi 1
4830.2.a.bj 1
4830.2.a.bk 1
4830.2.a.bl 1
4830.2.a.bm 2
4830.2.a.bn 2
4830.2.a.bo 2
4830.2.a.bp 2
4830.2.a.bq 2
4830.2.a.br 2
4830.2.a.bs 2
4830.2.a.bt 2
4830.2.a.bu 2
4830.2.a.bv 2
4830.2.a.bw 3
4830.2.a.bx 3
4830.2.a.by 3
4830.2.a.bz 3
4830.2.a.ca 3
4830.2.a.cb 3
4830.2.a.cc 3
4830.2.a.cd 4
4830.2.a.ce 4
4830.2.b $$\chi_{4830}(461, \cdot)$$ n/a 240 1
4830.2.e $$\chi_{4830}(3541, \cdot)$$ n/a 128 1
4830.2.f $$\chi_{4830}(3359, \cdot)$$ n/a 352 1
4830.2.i $$\chi_{4830}(1609, \cdot)$$ n/a 192 1
4830.2.j $$\chi_{4830}(2759, \cdot)$$ n/a 288 1
4830.2.m $$\chi_{4830}(2899, \cdot)$$ n/a 136 1
4830.2.n $$\chi_{4830}(4691, \cdot)$$ n/a 192 1
4830.2.q $$\chi_{4830}(1381, \cdot)$$ n/a 240 2
4830.2.s $$\chi_{4830}(323, \cdot)$$ n/a 528 2
4830.2.t $$\chi_{4830}(2437, \cdot)$$ n/a 288 2
4830.2.w $$\chi_{4830}(2897, \cdot)$$ n/a 768 2
4830.2.x $$\chi_{4830}(3037, \cdot)$$ n/a 352 2
4830.2.ba $$\chi_{4830}(2209, \cdot)$$ n/a 352 2
4830.2.bb $$\chi_{4830}(2069, \cdot)$$ n/a 768 2
4830.2.be $$\chi_{4830}(1241, \cdot)$$ n/a 512 2
4830.2.bh $$\chi_{4830}(2161, \cdot)$$ n/a 256 2
4830.2.bi $$\chi_{4830}(1151, \cdot)$$ n/a 464 2
4830.2.bl $$\chi_{4830}(229, \cdot)$$ n/a 384 2
4830.2.bm $$\chi_{4830}(1979, \cdot)$$ n/a 704 2
4830.2.bo $$\chi_{4830}(211, \cdot)$$ n/a 960 10
4830.2.bp $$\chi_{4830}(1657, \cdot)$$ n/a 704 4
4830.2.bs $$\chi_{4830}(1517, \cdot)$$ n/a 1536 4
4830.2.bt $$\chi_{4830}(1747, \cdot)$$ n/a 768 4
4830.2.bw $$\chi_{4830}(737, \cdot)$$ n/a 1408 4
4830.2.bz $$\chi_{4830}(281, \cdot)$$ n/a 1920 10
4830.2.ca $$\chi_{4830}(169, \cdot)$$ n/a 1440 10
4830.2.cd $$\chi_{4830}(659, \cdot)$$ n/a 2880 10
4830.2.ce $$\chi_{4830}(559, \cdot)$$ n/a 1920 10
4830.2.ch $$\chi_{4830}(209, \cdot)$$ n/a 3840 10
4830.2.ci $$\chi_{4830}(181, \cdot)$$ n/a 1280 10
4830.2.cl $$\chi_{4830}(41, \cdot)$$ n/a 2560 10
4830.2.cm $$\chi_{4830}(121, \cdot)$$ n/a 2560 20
4830.2.co $$\chi_{4830}(13, \cdot)$$ n/a 3840 20
4830.2.cp $$\chi_{4830}(83, \cdot)$$ n/a 7680 20
4830.2.cs $$\chi_{4830}(43, \cdot)$$ n/a 2880 20
4830.2.ct $$\chi_{4830}(197, \cdot)$$ n/a 5760 20
4830.2.cw $$\chi_{4830}(59, \cdot)$$ n/a 7680 20
4830.2.cx $$\chi_{4830}(19, \cdot)$$ n/a 3840 20
4830.2.da $$\chi_{4830}(101, \cdot)$$ n/a 5120 20
4830.2.db $$\chi_{4830}(61, \cdot)$$ n/a 2560 20
4830.2.de $$\chi_{4830}(11, \cdot)$$ n/a 5120 20
4830.2.dh $$\chi_{4830}(149, \cdot)$$ n/a 7680 20
4830.2.di $$\chi_{4830}(289, \cdot)$$ n/a 3840 20
4830.2.dk $$\chi_{4830}(233, \cdot)$$ n/a 15360 40
4830.2.dn $$\chi_{4830}(37, \cdot)$$ n/a 7680 40
4830.2.do $$\chi_{4830}(17, \cdot)$$ n/a 15360 40
4830.2.dr $$\chi_{4830}(73, \cdot)$$ n/a 7680 40

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

Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(4830))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(4830)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(46))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(69))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(70))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(105))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(115))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(138))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(161))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(210))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(230))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(322))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(345))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(483))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(690))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(805))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(966))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1610))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2415))$$$$^{\oplus 2}$$