## Defining parameters

 Level: $$N$$ = $$4598 = 2 \cdot 11^{2} \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$24$$ Sturm bound: $$2613600$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(4598))$$.

Total New Old
Modular forms 659160 213023 446137
Cusp forms 647641 213023 434618
Eisenstein series 11519 0 11519

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(4598))$$

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
4598.2.a $$\chi_{4598}(1, \cdot)$$ 4598.2.a.a 1 1
4598.2.a.b 1
4598.2.a.c 1
4598.2.a.d 1
4598.2.a.e 1
4598.2.a.f 1
4598.2.a.g 1
4598.2.a.h 1
4598.2.a.i 1
4598.2.a.j 1
4598.2.a.k 1
4598.2.a.l 1
4598.2.a.m 1
4598.2.a.n 1
4598.2.a.o 1
4598.2.a.p 1
4598.2.a.q 1
4598.2.a.r 1
4598.2.a.s 1
4598.2.a.t 2
4598.2.a.u 2
4598.2.a.v 2
4598.2.a.w 2
4598.2.a.x 2
4598.2.a.y 2
4598.2.a.z 2
4598.2.a.ba 2
4598.2.a.bb 2
4598.2.a.bc 2
4598.2.a.bd 2
4598.2.a.be 2
4598.2.a.bf 2
4598.2.a.bg 2
4598.2.a.bh 2
4598.2.a.bi 2
4598.2.a.bj 2
4598.2.a.bk 3
4598.2.a.bl 3
4598.2.a.bm 3
4598.2.a.bn 3
4598.2.a.bo 3
4598.2.a.bp 3
4598.2.a.bq 4
4598.2.a.br 4
4598.2.a.bs 4
4598.2.a.bt 4
4598.2.a.bu 4
4598.2.a.bv 4
4598.2.a.bw 8
4598.2.a.bx 8
4598.2.a.by 8
4598.2.a.bz 8
4598.2.a.ca 8
4598.2.a.cb 8
4598.2.a.cc 10
4598.2.a.cd 10
4598.2.b $$\chi_{4598}(4597, \cdot)$$ n/a 180 1
4598.2.e $$\chi_{4598}(3389, \cdot)$$ n/a 366 2
4598.2.f $$\chi_{4598}(1939, \cdot)$$ n/a 648 4
4598.2.h $$\chi_{4598}(483, \cdot)$$ n/a 360 2
4598.2.j $$\chi_{4598}(727, \cdot)$$ n/a 1086 6
4598.2.m $$\chi_{4598}(645, \cdot)$$ n/a 720 4
4598.2.n $$\chi_{4598}(419, \cdot)$$ n/a 1980 10
4598.2.o $$\chi_{4598}(729, \cdot)$$ n/a 1440 8
4598.2.r $$\chi_{4598}(241, \cdot)$$ n/a 1080 6
4598.2.t $$\chi_{4598}(417, \cdot)$$ n/a 2200 10
4598.2.w $$\chi_{4598}(1129, \cdot)$$ n/a 1440 8
4598.2.y $$\chi_{4598}(45, \cdot)$$ n/a 4400 20
4598.2.z $$\chi_{4598}(9, \cdot)$$ n/a 4320 24
4598.2.ba $$\chi_{4598}(115, \cdot)$$ n/a 7920 40
4598.2.bd $$\chi_{4598}(65, \cdot)$$ n/a 4400 20
4598.2.be $$\chi_{4598}(699, \cdot)$$ n/a 4320 24
4598.2.bh $$\chi_{4598}(23, \cdot)$$ n/a 13200 60
4598.2.bj $$\chi_{4598}(151, \cdot)$$ n/a 8800 40
4598.2.bl $$\chi_{4598}(49, \cdot)$$ n/a 17600 80
4598.2.bn $$\chi_{4598}(21, \cdot)$$ n/a 13200 60
4598.2.bp $$\chi_{4598}(107, \cdot)$$ n/a 17600 80
4598.2.bs $$\chi_{4598}(5, \cdot)$$ n/a 52800 240
4598.2.bu $$\chi_{4598}(13, \cdot)$$ n/a 52800 240

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(4598))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(4598)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(121))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(209))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(242))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(418))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2299))$$$$^{\oplus 2}$$