# Properties

 Label 4592.2 Level 4592 Weight 2 Dimension 345590 Nonzero newspaces 80 Sturm bound 2580480

## Defining parameters

 Level: $$N$$ = $$4592 = 2^{4} \cdot 7 \cdot 41$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$80$$ Sturm bound: $$2580480$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(4592))$$.

Total New Old
Modular forms 651840 349102 302738
Cusp forms 638401 345590 292811
Eisenstein series 13439 3512 9927

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(4592))$$

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
4592.2.a $$\chi_{4592}(1, \cdot)$$ 4592.2.a.a 1 1
4592.2.a.b 1
4592.2.a.c 1
4592.2.a.d 1
4592.2.a.e 1
4592.2.a.f 1
4592.2.a.g 1
4592.2.a.h 1
4592.2.a.i 1
4592.2.a.j 1
4592.2.a.k 1
4592.2.a.l 1
4592.2.a.m 2
4592.2.a.n 2
4592.2.a.o 2
4592.2.a.p 2
4592.2.a.q 2
4592.2.a.r 3
4592.2.a.s 3
4592.2.a.t 3
4592.2.a.u 3
4592.2.a.v 3
4592.2.a.w 3
4592.2.a.x 4
4592.2.a.y 4
4592.2.a.z 4
4592.2.a.ba 4
4592.2.a.bb 5
4592.2.a.bc 5
4592.2.a.bd 5
4592.2.a.be 5
4592.2.a.bf 6
4592.2.a.bg 6
4592.2.a.bh 7
4592.2.a.bi 8
4592.2.a.bj 8
4592.2.a.bk 9
4592.2.b $$\chi_{4592}(2297, \cdot)$$ None 0 1
4592.2.e $$\chi_{4592}(4591, \cdot)$$ n/a 168 1
4592.2.f $$\chi_{4592}(3361, \cdot)$$ n/a 126 1
4592.2.i $$\chi_{4592}(3527, \cdot)$$ None 0 1
4592.2.j $$\chi_{4592}(1231, \cdot)$$ n/a 160 1
4592.2.m $$\chi_{4592}(1065, \cdot)$$ None 0 1
4592.2.n $$\chi_{4592}(2295, \cdot)$$ None 0 1
4592.2.q $$\chi_{4592}(1313, \cdot)$$ n/a 320 2
4592.2.s $$\chi_{4592}(419, \cdot)$$ n/a 1336 2
4592.2.t $$\chi_{4592}(1485, \cdot)$$ n/a 1008 2
4592.2.w $$\chi_{4592}(1959, \cdot)$$ None 0 2
4592.2.y $$\chi_{4592}(337, \cdot)$$ n/a 252 2
4592.2.z $$\chi_{4592}(2213, \cdot)$$ n/a 1008 2
4592.2.ba $$\chi_{4592}(83, \cdot)$$ n/a 1280 2
4592.2.bf $$\chi_{4592}(1149, \cdot)$$ n/a 960 2
4592.2.bg $$\chi_{4592}(1147, \cdot)$$ n/a 1336 2
4592.2.bi $$\chi_{4592}(1567, \cdot)$$ n/a 336 2
4592.2.bk $$\chi_{4592}(729, \cdot)$$ None 0 2
4592.2.bm $$\chi_{4592}(3781, \cdot)$$ n/a 1008 2
4592.2.bn $$\chi_{4592}(2715, \cdot)$$ n/a 1336 2
4592.2.bp $$\chi_{4592}(2353, \cdot)$$ n/a 504 4
4592.2.br $$\chi_{4592}(327, \cdot)$$ None 0 2
4592.2.bu $$\chi_{4592}(2377, \cdot)$$ None 0 2
4592.2.bv $$\chi_{4592}(3855, \cdot)$$ n/a 320 2
4592.2.by $$\chi_{4592}(1559, \cdot)$$ None 0 2
4592.2.bz $$\chi_{4592}(81, \cdot)$$ n/a 332 2
4592.2.cc $$\chi_{4592}(2623, \cdot)$$ n/a 336 2
4592.2.cd $$\chi_{4592}(3609, \cdot)$$ None 0 2
4592.2.cg $$\chi_{4592}(547, \cdot)$$ n/a 2016 4
4592.2.ci $$\chi_{4592}(629, \cdot)$$ n/a 2672 4
4592.2.cl $$\chi_{4592}(489, \cdot)$$ None 0 4
4592.2.cm $$\chi_{4592}(1777, \cdot)$$ n/a 664 4
4592.2.cp $$\chi_{4592}(407, \cdot)$$ None 0 4
4592.2.cq $$\chi_{4592}(1695, \cdot)$$ n/a 504 4
4592.2.cs $$\chi_{4592}(659, \cdot)$$ n/a 2016 4
4592.2.cu $$\chi_{4592}(741, \cdot)$$ n/a 2672 4
4592.2.cv $$\chi_{4592}(1287, \cdot)$$ None 0 4
4592.2.cy $$\chi_{4592}(113, \cdot)$$ n/a 504 4
4592.2.cz $$\chi_{4592}(783, \cdot)$$ n/a 672 4
4592.2.dc $$\chi_{4592}(57, \cdot)$$ None 0 4
4592.2.df $$\chi_{4592}(3079, \cdot)$$ None 0 4
4592.2.dg $$\chi_{4592}(1849, \cdot)$$ None 0 4
4592.2.dj $$\chi_{4592}(223, \cdot)$$ n/a 672 4
4592.2.dk $$\chi_{4592}(747, \cdot)$$ n/a 2672 4
4592.2.dn $$\chi_{4592}(501, \cdot)$$ n/a 2672 4
4592.2.do $$\chi_{4592}(9, \cdot)$$ None 0 4
4592.2.dq $$\chi_{4592}(255, \cdot)$$ n/a 672 4
4592.2.du $$\chi_{4592}(411, \cdot)$$ n/a 2560 4
4592.2.dv $$\chi_{4592}(1229, \cdot)$$ n/a 2672 4
4592.2.dw $$\chi_{4592}(1475, \cdot)$$ n/a 2672 4
4592.2.dx $$\chi_{4592}(165, \cdot)$$ n/a 2560 4
4592.2.ea $$\chi_{4592}(401, \cdot)$$ n/a 664 4
4592.2.ec $$\chi_{4592}(647, \cdot)$$ None 0 4
4592.2.ee $$\chi_{4592}(2797, \cdot)$$ n/a 2672 4
4592.2.eh $$\chi_{4592}(3043, \cdot)$$ n/a 2672 4
4592.2.ei $$\chi_{4592}(305, \cdot)$$ n/a 1328 8
4592.2.ek $$\chi_{4592}(197, \cdot)$$ n/a 4032 8
4592.2.el $$\chi_{4592}(531, \cdot)$$ n/a 5344 8
4592.2.en $$\chi_{4592}(169, \cdot)$$ None 0 8
4592.2.ep $$\chi_{4592}(1455, \cdot)$$ n/a 1344 8
4592.2.er $$\chi_{4592}(195, \cdot)$$ n/a 5344 8
4592.2.es $$\chi_{4592}(141, \cdot)$$ n/a 4032 8
4592.2.ex $$\chi_{4592}(139, \cdot)$$ n/a 5344 8
4592.2.ey $$\chi_{4592}(701, \cdot)$$ n/a 4032 8
4592.2.ez $$\chi_{4592}(225, \cdot)$$ n/a 1008 8
4592.2.fb $$\chi_{4592}(279, \cdot)$$ None 0 8
4592.2.fe $$\chi_{4592}(251, \cdot)$$ n/a 5344 8
4592.2.ff $$\chi_{4592}(869, \cdot)$$ n/a 4032 8
4592.2.fh $$\chi_{4592}(325, \cdot)$$ n/a 5344 8
4592.2.fj $$\chi_{4592}(219, \cdot)$$ n/a 5344 8
4592.2.fl $$\chi_{4592}(79, \cdot)$$ n/a 1344 8
4592.2.fm $$\chi_{4592}(711, \cdot)$$ None 0 8
4592.2.fp $$\chi_{4592}(465, \cdot)$$ n/a 1328 8
4592.2.fq $$\chi_{4592}(2105, \cdot)$$ None 0 8
4592.2.ft $$\chi_{4592}(437, \cdot)$$ n/a 5344 8
4592.2.fv $$\chi_{4592}(331, \cdot)$$ n/a 5344 8
4592.2.fy $$\chi_{4592}(1615, \cdot)$$ n/a 1344 8
4592.2.fz $$\chi_{4592}(25, \cdot)$$ None 0 8
4592.2.gc $$\chi_{4592}(1111, \cdot)$$ None 0 8
4592.2.gf $$\chi_{4592}(1369, \cdot)$$ None 0 8
4592.2.gg $$\chi_{4592}(31, \cdot)$$ n/a 1344 8
4592.2.gj $$\chi_{4592}(865, \cdot)$$ n/a 1328 8
4592.2.gk $$\chi_{4592}(215, \cdot)$$ None 0 8
4592.2.gm $$\chi_{4592}(69, \cdot)$$ n/a 10688 16
4592.2.go $$\chi_{4592}(995, \cdot)$$ n/a 8064 16
4592.2.gq $$\chi_{4592}(15, \cdot)$$ n/a 2016 16
4592.2.gr $$\chi_{4592}(71, \cdot)$$ None 0 16
4592.2.gu $$\chi_{4592}(97, \cdot)$$ n/a 2656 16
4592.2.gv $$\chi_{4592}(153, \cdot)$$ None 0 16
4592.2.gy $$\chi_{4592}(13, \cdot)$$ n/a 10688 16
4592.2.ha $$\chi_{4592}(99, \cdot)$$ n/a 8064 16
4592.2.hc $$\chi_{4592}(613, \cdot)$$ n/a 10688 16
4592.2.hf $$\chi_{4592}(115, \cdot)$$ n/a 10688 16
4592.2.hh $$\chi_{4592}(87, \cdot)$$ None 0 16
4592.2.hj $$\chi_{4592}(289, \cdot)$$ n/a 2656 16
4592.2.hm $$\chi_{4592}(37, \cdot)$$ n/a 10688 16
4592.2.hn $$\chi_{4592}(187, \cdot)$$ n/a 10688 16
4592.2.ho $$\chi_{4592}(277, \cdot)$$ n/a 10688 16
4592.2.hp $$\chi_{4592}(59, \cdot)$$ n/a 10688 16
4592.2.ht $$\chi_{4592}(143, \cdot)$$ n/a 2688 16
4592.2.hv $$\chi_{4592}(121, \cdot)$$ None 0 16
4592.2.hw $$\chi_{4592}(131, \cdot)$$ n/a 10688 16
4592.2.hz $$\chi_{4592}(333, \cdot)$$ n/a 10688 16
4592.2.ib $$\chi_{4592}(11, \cdot)$$ n/a 21376 32
4592.2.id $$\chi_{4592}(101, \cdot)$$ n/a 21376 32
4592.2.ig $$\chi_{4592}(89, \cdot)$$ None 0 32
4592.2.ih $$\chi_{4592}(17, \cdot)$$ n/a 5312 32
4592.2.ik $$\chi_{4592}(135, \cdot)$$ None 0 32
4592.2.il $$\chi_{4592}(95, \cdot)$$ n/a 5376 32
4592.2.in $$\chi_{4592}(275, \cdot)$$ n/a 21376 32
4592.2.ip $$\chi_{4592}(341, \cdot)$$ n/a 21376 32

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(4592))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(4592)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(41))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(82))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(112))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(164))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(287))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(328))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(574))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(656))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1148))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2296))$$$$^{\oplus 2}$$