# Properties

 Label 6171.2 Level 6171 Weight 2 Dimension 1.01687e+06 Nonzero newspaces 40 Sturm bound 5.57568e+06

## Defining parameters

 Level: $$N$$ = $$6171 = 3 \cdot 11^{2} \cdot 17$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$40$$ Sturm bound: $$5575680$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(6171))$$.

Total New Old
Modular forms 1404160 1025306 378854
Cusp forms 1383681 1016874 366807
Eisenstein series 20479 8432 12047

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(6171))$$

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
6171.2.a $$\chi_{6171}(1, \cdot)$$ 6171.2.a.a 1 1
6171.2.a.b 1
6171.2.a.c 1
6171.2.a.d 1
6171.2.a.e 1
6171.2.a.f 1
6171.2.a.g 1
6171.2.a.h 1
6171.2.a.i 1
6171.2.a.j 2
6171.2.a.k 2
6171.2.a.l 2
6171.2.a.m 2
6171.2.a.n 2
6171.2.a.o 2
6171.2.a.p 2
6171.2.a.q 3
6171.2.a.r 3
6171.2.a.s 3
6171.2.a.t 4
6171.2.a.u 5
6171.2.a.v 5
6171.2.a.w 6
6171.2.a.x 6
6171.2.a.y 6
6171.2.a.z 6
6171.2.a.ba 6
6171.2.a.bb 6
6171.2.a.bc 6
6171.2.a.bd 7
6171.2.a.be 7
6171.2.a.bf 8
6171.2.a.bg 8
6171.2.a.bh 8
6171.2.a.bi 8
6171.2.a.bj 12
6171.2.a.bk 12
6171.2.a.bl 12
6171.2.a.bm 12
6171.2.a.bn 14
6171.2.a.bo 14
6171.2.a.bp 20
6171.2.a.bq 20
6171.2.a.br 20
6171.2.a.bs 20
6171.2.f $$\chi_{6171}(2177, \cdot)$$ n/a 576 1
6171.2.g $$\chi_{6171}(3994, \cdot)$$ n/a 328 1
6171.2.h $$\chi_{6171}(6170, \cdot)$$ n/a 632 1
6171.2.i $$\chi_{6171}(2903, \cdot)$$ n/a 1264 2
6171.2.j $$\chi_{6171}(727, \cdot)$$ n/a 656 2
6171.2.m $$\chi_{6171}(511, \cdot)$$ n/a 1152 4
6171.2.o $$\chi_{6171}(1090, \cdot)$$ n/a 1304 4
6171.2.q $$\chi_{6171}(3266, \cdot)$$ n/a 2528 4
6171.2.r $$\chi_{6171}(2702, \cdot)$$ n/a 2528 4
6171.2.s $$\chi_{6171}(1291, \cdot)$$ n/a 1296 4
6171.2.t $$\chi_{6171}(239, \cdot)$$ n/a 2304 4
6171.2.y $$\chi_{6171}(562, \cdot)$$ n/a 3520 10
6171.2.z $$\chi_{6171}(241, \cdot)$$ n/a 2592 8
6171.2.ba $$\chi_{6171}(122, \cdot)$$ n/a 5088 8
6171.2.bf $$\chi_{6171}(565, \cdot)$$ n/a 2592 8
6171.2.bg $$\chi_{6171}(965, \cdot)$$ n/a 5056 8
6171.2.bh $$\chi_{6171}(560, \cdot)$$ n/a 7880 10
6171.2.bi $$\chi_{6171}(67, \cdot)$$ n/a 3960 10
6171.2.bj $$\chi_{6171}(494, \cdot)$$ n/a 7040 10
6171.2.bo $$\chi_{6171}(161, \cdot)$$ n/a 10112 16
6171.2.bq $$\chi_{6171}(202, \cdot)$$ n/a 5184 16
6171.2.bu $$\chi_{6171}(166, \cdot)$$ n/a 7920 20
6171.2.bv $$\chi_{6171}(98, \cdot)$$ n/a 15760 20
6171.2.bw $$\chi_{6171}(103, \cdot)$$ n/a 14080 40
6171.2.bz $$\chi_{6171}(245, \cdot)$$ n/a 20224 32
6171.2.ca $$\chi_{6171}(40, \cdot)$$ n/a 10368 32
6171.2.cb $$\chi_{6171}(32, \cdot)$$ n/a 31520 40
6171.2.cd $$\chi_{6171}(100, \cdot)$$ n/a 15840 40
6171.2.cj $$\chi_{6171}(35, \cdot)$$ n/a 28160 40
6171.2.ck $$\chi_{6171}(16, \cdot)$$ n/a 15840 40
6171.2.cl $$\chi_{6171}(50, \cdot)$$ n/a 31520 40
6171.2.co $$\chi_{6171}(23, \cdot)$$ n/a 63040 80
6171.2.cp $$\chi_{6171}(10, \cdot)$$ n/a 31680 80
6171.2.cq $$\chi_{6171}(140, \cdot)$$ n/a 63040 80
6171.2.cr $$\chi_{6171}(4, \cdot)$$ n/a 31680 80
6171.2.cv $$\chi_{6171}(25, \cdot)$$ n/a 63360 160
6171.2.cx $$\chi_{6171}(2, \cdot)$$ n/a 126080 160
6171.2.cy $$\chi_{6171}(7, \cdot)$$ n/a 126720 320
6171.2.cz $$\chi_{6171}(5, \cdot)$$ n/a 252160 320

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(6171))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(6171)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(17))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(51))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(121))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(187))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(363))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(561))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2057))$$$$^{\oplus 2}$$