# Properties

 Label 7938.2 Level 7938 Weight 2 Dimension 433344 Nonzero newspaces 44 Sturm bound 6858432

## Defining parameters

 Level: $$N$$ = $$7938 = 2 \cdot 3^{4} \cdot 7^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$44$$ Sturm bound: $$6858432$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(7938))$$.

Total New Old
Modular forms 1727568 433344 1294224
Cusp forms 1701649 433344 1268305
Eisenstein series 25919 0 25919

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(7938))$$

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
7938.2.a $$\chi_{7938}(1, \cdot)$$ 7938.2.a.a 1 1
7938.2.a.b 1
7938.2.a.c 1
7938.2.a.d 1
7938.2.a.e 1
7938.2.a.f 1
7938.2.a.g 1
7938.2.a.h 1
7938.2.a.i 1
7938.2.a.j 1
7938.2.a.k 1
7938.2.a.l 1
7938.2.a.m 1
7938.2.a.n 1
7938.2.a.o 1
7938.2.a.p 1
7938.2.a.q 1
7938.2.a.r 1
7938.2.a.s 1
7938.2.a.t 1
7938.2.a.u 1
7938.2.a.v 1
7938.2.a.w 1
7938.2.a.x 1
7938.2.a.y 1
7938.2.a.z 1
7938.2.a.ba 1
7938.2.a.bb 1
7938.2.a.bc 1
7938.2.a.bd 1
7938.2.a.be 1
7938.2.a.bf 1
7938.2.a.bg 2
7938.2.a.bh 2
7938.2.a.bi 2
7938.2.a.bj 2
7938.2.a.bk 2
7938.2.a.bl 2
7938.2.a.bm 2
7938.2.a.bn 2
7938.2.a.bo 2
7938.2.a.bp 2
7938.2.a.bq 2
7938.2.a.br 2
7938.2.a.bs 2
7938.2.a.bt 2
7938.2.a.bu 3
7938.2.a.bv 3
7938.2.a.bw 3
7938.2.a.bx 3
7938.2.a.by 3
7938.2.a.bz 3
7938.2.a.ca 3
7938.2.a.cb 3
7938.2.a.cc 4
7938.2.a.cd 4
7938.2.a.ce 4
7938.2.a.cf 4
7938.2.a.cg 4
7938.2.a.ch 4
7938.2.a.ci 4
7938.2.a.cj 4
7938.2.a.ck 4
7938.2.a.cl 4
7938.2.a.cm 4
7938.2.a.cn 4
7938.2.a.co 4
7938.2.a.cp 4
7938.2.a.cq 4
7938.2.a.cr 4
7938.2.a.cs 4
7938.2.a.ct 4
7938.2.a.cu 4
7938.2.a.cv 4
7938.2.d $$\chi_{7938}(7937, \cdot)$$ n/a 160 1
7938.2.e $$\chi_{7938}(6535, \cdot)$$ n/a 320 2
7938.2.f $$\chi_{7938}(2647, \cdot)$$ n/a 328 2
7938.2.g $$\chi_{7938}(2431, \cdot)$$ n/a 320 2
7938.2.h $$\chi_{7938}(1243, \cdot)$$ n/a 320 2
7938.2.k $$\chi_{7938}(4049, \cdot)$$ n/a 320 2
7938.2.l $$\chi_{7938}(215, \cdot)$$ n/a 320 2
7938.2.m $$\chi_{7938}(2645, \cdot)$$ n/a 320 2
7938.2.t $$\chi_{7938}(2861, \cdot)$$ n/a 320 2
7938.2.u $$\chi_{7938}(1135, \cdot)$$ n/a 1344 6
7938.2.v $$\chi_{7938}(883, \cdot)$$ n/a 738 6
7938.2.w $$\chi_{7938}(361, \cdot)$$ n/a 720 6
7938.2.x $$\chi_{7938}(1549, \cdot)$$ n/a 720 6
7938.2.y $$\chi_{7938}(1133, \cdot)$$ n/a 1344 6
7938.2.bd $$\chi_{7938}(881, \cdot)$$ n/a 720 6
7938.2.be $$\chi_{7938}(1979, \cdot)$$ n/a 720 6
7938.2.bj $$\chi_{7938}(521, \cdot)$$ n/a 720 6
7938.2.bk $$\chi_{7938}(109, \cdot)$$ n/a 2688 12
7938.2.bl $$\chi_{7938}(163, \cdot)$$ n/a 2688 12
7938.2.bm $$\chi_{7938}(379, \cdot)$$ n/a 2688 12
7938.2.bn $$\chi_{7938}(865, \cdot)$$ n/a 2688 12
7938.2.bo $$\chi_{7938}(67, \cdot)$$ n/a 6480 18
7938.2.bp $$\chi_{7938}(295, \cdot)$$ n/a 6642 18
7938.2.bq $$\chi_{7938}(373, \cdot)$$ n/a 6480 18
7938.2.br $$\chi_{7938}(593, \cdot)$$ n/a 2688 12
7938.2.by $$\chi_{7938}(377, \cdot)$$ n/a 2688 12
7938.2.bz $$\chi_{7938}(269, \cdot)$$ n/a 2688 12
7938.2.ca $$\chi_{7938}(647, \cdot)$$ n/a 2688 12
7938.2.ce $$\chi_{7938}(227, \cdot)$$ n/a 6480 18
7938.2.cj $$\chi_{7938}(803, \cdot)$$ n/a 6480 18
7938.2.ck $$\chi_{7938}(293, \cdot)$$ n/a 6480 18
7938.2.cm $$\chi_{7938}(37, \cdot)$$ n/a 6048 36
7938.2.cn $$\chi_{7938}(289, \cdot)$$ n/a 6048 36
7938.2.co $$\chi_{7938}(127, \cdot)$$ n/a 6048 36
7938.2.cp $$\chi_{7938}(143, \cdot)$$ n/a 6048 36
7938.2.cu $$\chi_{7938}(17, \cdot)$$ n/a 6048 36
7938.2.cv $$\chi_{7938}(125, \cdot)$$ n/a 6048 36
7938.2.cy $$\chi_{7938}(25, \cdot)$$ n/a 54432 108
7938.2.cz $$\chi_{7938}(43, \cdot)$$ n/a 54432 108
7938.2.da $$\chi_{7938}(193, \cdot)$$ n/a 54432 108
7938.2.dc $$\chi_{7938}(41, \cdot)$$ n/a 54432 108
7938.2.dd $$\chi_{7938}(47, \cdot)$$ n/a 54432 108
7938.2.di $$\chi_{7938}(5, \cdot)$$ n/a 54432 108

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(7938))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(7938)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(27))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(54))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(63))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(81))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(98))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(126))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(147))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(162))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(189))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(294))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(378))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(441))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(567))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(882))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1134))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1323))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2646))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3969))$$$$^{\oplus 2}$$