# Properties

 Label 4140.2 Level 4140 Weight 2 Dimension 191254 Nonzero newspaces 48 Sturm bound 1824768

## Defining parameters

 Level: $$N$$ = $$4140 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 23$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$48$$ Sturm bound: $$1824768$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(4140))$$.

Total New Old
Modular forms 463232 193518 269714
Cusp forms 449153 191254 257899
Eisenstein series 14079 2264 11815

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(4140))$$

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 available newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
4140.2.a $$\chi_{4140}(1, \cdot)$$ 4140.2.a.a 1 1
4140.2.a.b 1
4140.2.a.c 1
4140.2.a.d 1
4140.2.a.e 1
4140.2.a.f 1
4140.2.a.g 1
4140.2.a.h 1
4140.2.a.i 1
4140.2.a.j 1
4140.2.a.k 1
4140.2.a.l 2
4140.2.a.m 2
4140.2.a.n 2
4140.2.a.o 2
4140.2.a.p 2
4140.2.a.q 2
4140.2.a.r 2
4140.2.a.s 3
4140.2.a.t 5
4140.2.a.u 5
4140.2.f $$\chi_{4140}(829, \cdot)$$ 4140.2.f.a 6 1
4140.2.f.b 12
4140.2.f.c 14
4140.2.f.d 24
4140.2.g $$\chi_{4140}(919, \cdot)$$ n/a 356 1
4140.2.h $$\chi_{4140}(1151, \cdot)$$ n/a 176 1
4140.2.i $$\chi_{4140}(1241, \cdot)$$ 4140.2.i.a 16 1
4140.2.i.b 16
4140.2.n $$\chi_{4140}(2069, \cdot)$$ 4140.2.n.a 16 1
4140.2.n.b 32
4140.2.o $$\chi_{4140}(1979, \cdot)$$ n/a 264 1
4140.2.p $$\chi_{4140}(91, \cdot)$$ n/a 240 1
4140.2.q $$\chi_{4140}(1381, \cdot)$$ n/a 176 2
4140.2.r $$\chi_{4140}(827, \cdot)$$ n/a 576 2
4140.2.s $$\chi_{4140}(737, \cdot)$$ 4140.2.s.a 44 2
4140.2.s.b 44
4140.2.t $$\chi_{4140}(1243, \cdot)$$ n/a 660 2
4140.2.u $$\chi_{4140}(1333, \cdot)$$ n/a 120 2
4140.2.z $$\chi_{4140}(1471, \cdot)$$ n/a 1152 2
4140.2.ba $$\chi_{4140}(689, \cdot)$$ n/a 288 2
4140.2.bb $$\chi_{4140}(599, \cdot)$$ n/a 1584 2
4140.2.bg $$\chi_{4140}(2531, \cdot)$$ n/a 1056 2
4140.2.bh $$\chi_{4140}(2621, \cdot)$$ n/a 192 2
4140.2.bi $$\chi_{4140}(2209, \cdot)$$ n/a 264 2
4140.2.bj $$\chi_{4140}(2299, \cdot)$$ n/a 1712 2
4140.2.bo $$\chi_{4140}(361, \cdot)$$ n/a 400 10
4140.2.bt $$\chi_{4140}(1013, \cdot)$$ n/a 528 4
4140.2.bu $$\chi_{4140}(1103, \cdot)$$ n/a 3424 4
4140.2.bv $$\chi_{4140}(1057, \cdot)$$ n/a 576 4
4140.2.bw $$\chi_{4140}(967, \cdot)$$ n/a 3168 4
4140.2.bx $$\chi_{4140}(451, \cdot)$$ n/a 2400 10
4140.2.by $$\chi_{4140}(179, \cdot)$$ n/a 2880 10
4140.2.bz $$\chi_{4140}(89, \cdot)$$ n/a 480 10
4140.2.ce $$\chi_{4140}(341, \cdot)$$ n/a 320 10
4140.2.cf $$\chi_{4140}(71, \cdot)$$ n/a 1920 10
4140.2.cg $$\chi_{4140}(19, \cdot)$$ n/a 3560 10
4140.2.ch $$\chi_{4140}(289, \cdot)$$ n/a 600 10
4140.2.cm $$\chi_{4140}(121, \cdot)$$ n/a 1920 20
4140.2.cr $$\chi_{4140}(37, \cdot)$$ n/a 1200 20
4140.2.cs $$\chi_{4140}(127, \cdot)$$ n/a 7120 20
4140.2.ct $$\chi_{4140}(197, \cdot)$$ n/a 960 20
4140.2.cu $$\chi_{4140}(107, \cdot)$$ n/a 5760 20
4140.2.cz $$\chi_{4140}(79, \cdot)$$ n/a 17120 20
4140.2.da $$\chi_{4140}(49, \cdot)$$ n/a 2880 20
4140.2.db $$\chi_{4140}(221, \cdot)$$ n/a 1920 20
4140.2.dc $$\chi_{4140}(131, \cdot)$$ n/a 11520 20
4140.2.dh $$\chi_{4140}(59, \cdot)$$ n/a 17120 20
4140.2.di $$\chi_{4140}(149, \cdot)$$ n/a 2880 20
4140.2.dj $$\chi_{4140}(511, \cdot)$$ n/a 11520 20
4140.2.dk $$\chi_{4140}(187, \cdot)$$ n/a 34240 40
4140.2.dl $$\chi_{4140}(97, \cdot)$$ n/a 5760 40
4140.2.dm $$\chi_{4140}(83, \cdot)$$ n/a 34240 40
4140.2.dn $$\chi_{4140}(77, \cdot)$$ n/a 5760 40

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(4140))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(4140)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 36}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(46))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(60))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(69))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(90))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(92))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(115))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(138))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(180))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(207))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(230))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(276))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(345))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(414))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(460))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(690))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(828))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1035))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1380))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2070))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4140))$$$$^{\oplus 1}$$