# Properties

 Label 7803.2 Level 7803 Weight 2 Dimension 1757453 Nonzero newspaces 30 Sturm bound 8989056

## Defining parameters

 Level: $$N$$ = $$7803 = 3^{3} \cdot 17^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$30$$ Sturm bound: $$8989056$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(7803))$$.

Total New Old
Modular forms 2259264 1769245 490019
Cusp forms 2235265 1757453 477812
Eisenstein series 23999 11792 12207

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(7803))$$

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
7803.2.a $$\chi_{7803}(1, \cdot)$$ 7803.2.a.a 1 1
7803.2.a.b 1
7803.2.a.c 1
7803.2.a.d 1
7803.2.a.e 1
7803.2.a.f 1
7803.2.a.g 1
7803.2.a.h 1
7803.2.a.i 1
7803.2.a.j 1
7803.2.a.k 1
7803.2.a.l 1
7803.2.a.m 1
7803.2.a.n 1
7803.2.a.o 1
7803.2.a.p 1
7803.2.a.q 1
7803.2.a.r 1
7803.2.a.s 1
7803.2.a.t 1
7803.2.a.u 1
7803.2.a.v 2
7803.2.a.w 2
7803.2.a.x 2
7803.2.a.y 2
7803.2.a.z 2
7803.2.a.ba 2
7803.2.a.bb 2
7803.2.a.bc 2
7803.2.a.bd 3
7803.2.a.be 3
7803.2.a.bf 3
7803.2.a.bg 3
7803.2.a.bh 4
7803.2.a.bi 4
7803.2.a.bj 5
7803.2.a.bk 5
7803.2.a.bl 5
7803.2.a.bm 5
7803.2.a.bn 6
7803.2.a.bo 6
7803.2.a.bp 6
7803.2.a.bq 6
7803.2.a.br 10
7803.2.a.bs 10
7803.2.a.bt 12
7803.2.a.bu 12
7803.2.a.bv 12
7803.2.a.bw 12
7803.2.a.bx 15
7803.2.a.by 15
7803.2.a.bz 15
7803.2.a.ca 15
7803.2.a.cb 18
7803.2.a.cc 18
7803.2.a.cd 24
7803.2.a.ce 24
7803.2.a.cf 24
7803.2.a.cg 24
7803.2.d $$\chi_{7803}(5779, \cdot)$$ n/a 360 1
7803.2.e $$\chi_{7803}(2602, \cdot)$$ n/a 512 2
7803.2.f $$\chi_{7803}(2350, \cdot)$$ n/a 720 2
7803.2.h $$\chi_{7803}(577, \cdot)$$ n/a 512 2
7803.2.l $$\chi_{7803}(757, \cdot)$$ n/a 1440 4
7803.2.m $$\chi_{7803}(868, \cdot)$$ n/a 4788 6
7803.2.o $$\chi_{7803}(829, \cdot)$$ n/a 1024 4
7803.2.p $$\chi_{7803}(998, \cdot)$$ n/a 2880 8
7803.2.r $$\chi_{7803}(460, \cdot)$$ n/a 6528 16
7803.2.s $$\chi_{7803}(1444, \cdot)$$ n/a 4776 6
7803.2.w $$\chi_{7803}(712, \cdot)$$ n/a 2048 8
7803.2.x $$\chi_{7803}(271, \cdot)$$ n/a 6528 16
7803.2.bb $$\chi_{7803}(616, \cdot)$$ n/a 9552 12
7803.2.bc $$\chi_{7803}(224, \cdot)$$ n/a 4096 16
7803.2.be $$\chi_{7803}(154, \cdot)$$ n/a 9728 32
7803.2.bg $$\chi_{7803}(55, \cdot)$$ n/a 13056 32
7803.2.bh $$\chi_{7803}(688, \cdot)$$ n/a 19104 24
7803.2.bl $$\chi_{7803}(118, \cdot)$$ n/a 9728 32
7803.2.bm $$\chi_{7803}(298, \cdot)$$ n/a 26112 64
7803.2.bp $$\chi_{7803}(65, \cdot)$$ n/a 38208 48
7803.2.bq $$\chi_{7803}(52, \cdot)$$ n/a 87936 96
7803.2.br $$\chi_{7803}(64, \cdot)$$ n/a 19456 64
7803.2.bu $$\chi_{7803}(80, \cdot)$$ n/a 52224 128
7803.2.bx $$\chi_{7803}(16, \cdot)$$ n/a 87936 96
7803.2.by $$\chi_{7803}(19, \cdot)$$ n/a 38912 128
7803.2.ca $$\chi_{7803}(4, \cdot)$$ n/a 175872 192
7803.2.cd $$\chi_{7803}(44, \cdot)$$ n/a 77824 256
7803.2.cf $$\chi_{7803}(25, \cdot)$$ n/a 351744 384
7803.2.cg $$\chi_{7803}(5, \cdot)$$ n/a 703488 768

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(7803))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(7803)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(17))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(27))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(51))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(153))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(289))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(459))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(867))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2601))$$$$^{\oplus 2}$$