# Properties

 Label 7942.2 Level 7942 Weight 2 Dimension 635433 Nonzero newspaces 24 Sturm bound 7797600

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## Defining parameters

 Level: $$N$$ = $$7942 = 2 \cdot 11 \cdot 19^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$24$$ Sturm bound: $$7797600$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(7942))$$.

Total New Old
Modular forms 1959480 635433 1324047
Cusp forms 1939321 635433 1303888
Eisenstein series 20159 0 20159

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(7942))$$

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
7942.2.a $$\chi_{7942}(1, \cdot)$$ 7942.2.a.a 1 1
7942.2.a.b 1
7942.2.a.c 1
7942.2.a.d 1
7942.2.a.e 1
7942.2.a.f 1
7942.2.a.g 1
7942.2.a.h 1
7942.2.a.i 1
7942.2.a.j 1
7942.2.a.k 1
7942.2.a.l 1
7942.2.a.m 1
7942.2.a.n 1
7942.2.a.o 1
7942.2.a.p 1
7942.2.a.q 1
7942.2.a.r 1
7942.2.a.s 1
7942.2.a.t 2
7942.2.a.u 2
7942.2.a.v 2
7942.2.a.w 2
7942.2.a.x 2
7942.2.a.y 2
7942.2.a.z 2
7942.2.a.ba 2
7942.2.a.bb 2
7942.2.a.bc 3
7942.2.a.bd 3
7942.2.a.be 3
7942.2.a.bf 3
7942.2.a.bg 3
7942.2.a.bh 3
7942.2.a.bi 3
7942.2.a.bj 3
7942.2.a.bk 6
7942.2.a.bl 6
7942.2.a.bm 8
7942.2.a.bn 8
7942.2.a.bo 8
7942.2.a.bp 8
7942.2.a.bq 8
7942.2.a.br 8
7942.2.a.bs 12
7942.2.a.bt 12
7942.2.a.bu 12
7942.2.a.bv 12
7942.2.a.bw 12
7942.2.a.bx 12
7942.2.a.by 15
7942.2.a.bz 15
7942.2.a.ca 15
7942.2.a.cb 15
7942.2.a.cc 16
7942.2.a.cd 16
7942.2.b $$\chi_{7942}(7941, \cdot)$$ n/a 340 1
7942.2.e $$\chi_{7942}(6205, \cdot)$$ n/a 572 2
7942.2.f $$\chi_{7942}(1445, \cdot)$$ n/a 1364 4
7942.2.h $$\chi_{7942}(791, \cdot)$$ n/a 680 2
7942.2.j $$\chi_{7942}(595, \cdot)$$ n/a 1692 6
7942.2.m $$\chi_{7942}(721, \cdot)$$ n/a 1360 4
7942.2.n $$\chi_{7942}(653, \cdot)$$ n/a 2720 8
7942.2.q $$\chi_{7942}(307, \cdot)$$ n/a 2040 6
7942.2.r $$\chi_{7942}(419, \cdot)$$ n/a 5652 18
7942.2.t $$\chi_{7942}(293, \cdot)$$ n/a 2720 8
7942.2.x $$\chi_{7942}(417, \cdot)$$ n/a 6840 18
7942.2.y $$\chi_{7942}(245, \cdot)$$ n/a 8160 24
7942.2.z $$\chi_{7942}(45, \cdot)$$ n/a 11304 36
7942.2.ba $$\chi_{7942}(127, \cdot)$$ n/a 8160 24
7942.2.bd $$\chi_{7942}(115, \cdot)$$ n/a 27360 72
7942.2.bf $$\chi_{7942}(65, \cdot)$$ n/a 13680 36
7942.2.bh $$\chi_{7942}(23, \cdot)$$ n/a 34344 108
7942.2.bi $$\chi_{7942}(151, \cdot)$$ n/a 27360 72
7942.2.bl $$\chi_{7942}(49, \cdot)$$ n/a 54720 144
7942.2.bm $$\chi_{7942}(21, \cdot)$$ n/a 41040 108
7942.2.bq $$\chi_{7942}(107, \cdot)$$ n/a 54720 144
7942.2.bs $$\chi_{7942}(5, \cdot)$$ n/a 164160 432
7942.2.bv $$\chi_{7942}(13, \cdot)$$ n/a 164160 432

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(7942))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(7942)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(209))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(361))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(418))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(722))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3971))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(7942))$$$$^{\oplus 1}$$