## Defining parameters

 Level: $$N$$ = $$4508 = 2^{2} \cdot 7^{2} \cdot 23$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$32$$ Sturm bound: $$2483712$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(4508))$$.

Total New Old
Modular forms 627528 348300 279228
Cusp forms 614329 344224 270105
Eisenstein series 13199 4076 9123

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(4508))$$

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
4508.2.a $$\chi_{4508}(1, \cdot)$$ 4508.2.a.a 1 1
4508.2.a.b 1
4508.2.a.c 1
4508.2.a.d 1
4508.2.a.e 4
4508.2.a.f 5
4508.2.a.g 5
4508.2.a.h 6
4508.2.a.i 6
4508.2.a.j 6
4508.2.a.k 7
4508.2.a.l 7
4508.2.a.m 7
4508.2.a.n 7
4508.2.a.o 10
4508.2.c $$\chi_{4508}(1471, \cdot)$$ n/a 482 1
4508.2.d $$\chi_{4508}(2253, \cdot)$$ 4508.2.d.a 32 1
4508.2.d.b 48
4508.2.f $$\chi_{4508}(783, \cdot)$$ n/a 440 1
4508.2.i $$\chi_{4508}(3313, \cdot)$$ n/a 148 2
4508.2.k $$\chi_{4508}(1795, \cdot)$$ n/a 880 2
4508.2.m $$\chi_{4508}(3265, \cdot)$$ n/a 160 2
4508.2.p $$\chi_{4508}(275, \cdot)$$ n/a 944 2
4508.2.q $$\chi_{4508}(645, \cdot)$$ n/a 624 6
4508.2.r $$\chi_{4508}(197, \cdot)$$ n/a 820 10
4508.2.u $$\chi_{4508}(139, \cdot)$$ n/a 3696 6
4508.2.w $$\chi_{4508}(321, \cdot)$$ n/a 672 6
4508.2.x $$\chi_{4508}(183, \cdot)$$ n/a 4008 6
4508.2.z $$\chi_{4508}(93, \cdot)$$ n/a 1224 12
4508.2.bc $$\chi_{4508}(587, \cdot)$$ n/a 4720 10
4508.2.be $$\chi_{4508}(97, \cdot)$$ n/a 800 10
4508.2.bf $$\chi_{4508}(99, \cdot)$$ n/a 4820 10
4508.2.bh $$\chi_{4508}(165, \cdot)$$ n/a 1600 20
4508.2.bi $$\chi_{4508}(919, \cdot)$$ n/a 8016 12
4508.2.bl $$\chi_{4508}(45, \cdot)$$ n/a 1344 12
4508.2.bn $$\chi_{4508}(47, \cdot)$$ n/a 7392 12
4508.2.bp $$\chi_{4508}(67, \cdot)$$ n/a 9440 20
4508.2.bs $$\chi_{4508}(129, \cdot)$$ n/a 1600 20
4508.2.bu $$\chi_{4508}(31, \cdot)$$ n/a 9440 20
4508.2.bw $$\chi_{4508}(29, \cdot)$$ n/a 6720 60
4508.2.by $$\chi_{4508}(15, \cdot)$$ n/a 40080 60
4508.2.bz $$\chi_{4508}(125, \cdot)$$ n/a 6720 60
4508.2.cb $$\chi_{4508}(27, \cdot)$$ n/a 40080 60
4508.2.ce $$\chi_{4508}(9, \cdot)$$ n/a 13440 120
4508.2.cg $$\chi_{4508}(3, \cdot)$$ n/a 80160 120
4508.2.ci $$\chi_{4508}(5, \cdot)$$ n/a 13440 120
4508.2.cl $$\chi_{4508}(11, \cdot)$$ n/a 80160 120

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(4508))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(4508)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(46))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(92))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(98))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(161))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(196))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(322))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(644))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1127))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2254))$$$$^{\oplus 2}$$