Properties

 Label 4100.2 Level 4100 Weight 2 Dimension 269048 Nonzero newspaces 98 Sturm bound 2016000

Defining parameters

 Level: $$N$$ = $$4100 = 2^{2} \cdot 5^{2} \cdot 41$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$98$$ Sturm bound: $$2016000$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(4100))$$.

Total New Old
Modular forms 509600 272248 237352
Cusp forms 498401 269048 229353
Eisenstein series 11199 3200 7999

Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(4100))$$

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
4100.2.a $$\chi_{4100}(1, \cdot)$$ 4100.2.a.a 2 1
4100.2.a.b 2
4100.2.a.c 4
4100.2.a.d 4
4100.2.a.e 4
4100.2.a.f 6
4100.2.a.g 7
4100.2.a.h 7
4100.2.a.i 7
4100.2.a.j 7
4100.2.a.k 14
4100.2.b $$\chi_{4100}(901, \cdot)$$ 4100.2.b.a 2 1
4100.2.b.b 2
4100.2.b.c 4
4100.2.b.d 4
4100.2.b.e 4
4100.2.b.f 6
4100.2.b.g 8
4100.2.b.h 10
4100.2.b.i 10
4100.2.b.j 16
4100.2.d $$\chi_{4100}(1149, \cdot)$$ 4100.2.d.a 4 1
4100.2.d.b 4
4100.2.d.c 8
4100.2.d.d 8
4100.2.d.e 8
4100.2.d.f 14
4100.2.d.g 14
4100.2.g $$\chi_{4100}(2049, \cdot)$$ 4100.2.g.a 4 1
4100.2.g.b 4
4100.2.g.c 8
4100.2.g.d 12
4100.2.g.e 16
4100.2.g.f 20
4100.2.j $$\chi_{4100}(2943, \cdot)$$ n/a 748 2
4100.2.k $$\chi_{4100}(2543, \cdot)$$ n/a 720 2
4100.2.n $$\chi_{4100}(1549, \cdot)$$ n/a 124 2
4100.2.p $$\chi_{4100}(401, \cdot)$$ n/a 134 2
4100.2.r $$\chi_{4100}(3443, \cdot)$$ n/a 748 2
4100.2.s $$\chi_{4100}(3043, \cdot)$$ n/a 748 2
4100.2.u $$\chi_{4100}(141, \cdot)$$ n/a 424 4
4100.2.v $$\chi_{4100}(461, \cdot)$$ n/a 424 4
4100.2.w $$\chi_{4100}(221, \cdot)$$ n/a 424 4
4100.2.x $$\chi_{4100}(961, \cdot)$$ n/a 424 4
4100.2.y $$\chi_{4100}(821, \cdot)$$ n/a 400 4
4100.2.z $$\chi_{4100}(201, \cdot)$$ n/a 264 4
4100.2.bb $$\chi_{4100}(899, \cdot)$$ n/a 1496 4
4100.2.bc $$\chi_{4100}(793, \cdot)$$ n/a 252 4
4100.2.bd $$\chi_{4100}(957, \cdot)$$ n/a 252 4
4100.2.bh $$\chi_{4100}(1151, \cdot)$$ n/a 1572 4
4100.2.bj $$\chi_{4100}(549, \cdot)$$ n/a 256 4
4100.2.bl $$\chi_{4100}(701, \cdot)$$ n/a 264 4
4100.2.bm $$\chi_{4100}(769, \cdot)$$ n/a 416 4
4100.2.bs $$\chi_{4100}(189, \cdot)$$ n/a 416 4
4100.2.bt $$\chi_{4100}(209, \cdot)$$ n/a 416 4
4100.2.bw $$\chi_{4100}(269, \cdot)$$ n/a 416 4
4100.2.bz $$\chi_{4100}(409, \cdot)$$ n/a 416 4
4100.2.cc $$\chi_{4100}(329, \cdot)$$ n/a 400 4
4100.2.ce $$\chi_{4100}(81, \cdot)$$ n/a 424 4
4100.2.cg $$\chi_{4100}(761, \cdot)$$ n/a 424 4
4100.2.ch $$\chi_{4100}(469, \cdot)$$ n/a 416 4
4100.2.ck $$\chi_{4100}(789, \cdot)$$ n/a 416 4
4100.2.cl $$\chi_{4100}(2109, \cdot)$$ n/a 416 4
4100.2.cn $$\chi_{4100}(441, \cdot)$$ n/a 424 4
4100.2.cq $$\chi_{4100}(681, \cdot)$$ n/a 424 4
4100.2.cr $$\chi_{4100}(3721, \cdot)$$ n/a 424 4
4100.2.cu $$\chi_{4100}(529, \cdot)$$ n/a 416 4
4100.2.cw $$\chi_{4100}(1849, \cdot)$$ n/a 256 4
4100.2.cy $$\chi_{4100}(43, \cdot)$$ n/a 2992 8
4100.2.db $$\chi_{4100}(583, \cdot)$$ n/a 5008 8
4100.2.dc $$\chi_{4100}(103, \cdot)$$ n/a 5008 8
4100.2.dg $$\chi_{4100}(203, \cdot)$$ n/a 5008 8
4100.2.dh $$\chi_{4100}(923, \cdot)$$ n/a 5008 8
4100.2.di $$\chi_{4100}(1023, \cdot)$$ n/a 5008 8
4100.2.dk $$\chi_{4100}(107, \cdot)$$ n/a 2992 8
4100.2.dm $$\chi_{4100}(1601, \cdot)$$ n/a 536 8
4100.2.do $$\chi_{4100}(49, \cdot)$$ n/a 496 8
4100.2.dr $$\chi_{4100}(543, \cdot)$$ n/a 2992 8
4100.2.dt $$\chi_{4100}(223, \cdot)$$ n/a 5008 8
4100.2.dv $$\chi_{4100}(163, \cdot)$$ n/a 5008 8
4100.2.dw $$\chi_{4100}(127, \cdot)$$ n/a 5008 8
4100.2.dz $$\chi_{4100}(523, \cdot)$$ n/a 5008 8
4100.2.ea $$\chi_{4100}(187, \cdot)$$ n/a 5008 8
4100.2.ec $$\chi_{4100}(61, \cdot)$$ n/a 832 8
4100.2.ee $$\chi_{4100}(169, \cdot)$$ n/a 848 8
4100.2.eh $$\chi_{4100}(689, \cdot)$$ n/a 848 8
4100.2.ei $$\chi_{4100}(1221, \cdot)$$ n/a 832 8
4100.2.ej $$\chi_{4100}(21, \cdot)$$ n/a 832 8
4100.2.ek $$\chi_{4100}(841, \cdot)$$ n/a 832 8
4100.2.eo $$\chi_{4100}(289, \cdot)$$ n/a 848 8
4100.2.ep $$\chi_{4100}(989, \cdot)$$ n/a 848 8
4100.2.eq $$\chi_{4100}(9, \cdot)$$ n/a 848 8
4100.2.ev $$\chi_{4100}(121, \cdot)$$ n/a 832 8
4100.2.ew $$\chi_{4100}(467, \cdot)$$ n/a 5008 8
4100.2.ez $$\chi_{4100}(83, \cdot)$$ n/a 4800 8
4100.2.fa $$\chi_{4100}(303, \cdot)$$ n/a 5008 8
4100.2.fd $$\chi_{4100}(283, \cdot)$$ n/a 5008 8
4100.2.fe $$\chi_{4100}(23, \cdot)$$ n/a 5008 8
4100.2.fh $$\chi_{4100}(863, \cdot)$$ n/a 5008 8
4100.2.fi $$\chi_{4100}(963, \cdot)$$ n/a 5008 8
4100.2.fj $$\chi_{4100}(87, \cdot)$$ n/a 5008 8
4100.2.fn $$\chi_{4100}(323, \cdot)$$ n/a 5008 8
4100.2.fo $$\chi_{4100}(483, \cdot)$$ n/a 5008 8
4100.2.fr $$\chi_{4100}(207, \cdot)$$ n/a 2992 8
4100.2.ft $$\chi_{4100}(19, \cdot)$$ n/a 10016 16
4100.2.fu $$\chi_{4100}(191, \cdot)$$ n/a 10016 16
4100.2.fv $$\chi_{4100}(111, \cdot)$$ n/a 10016 16
4100.2.fw $$\chi_{4100}(151, \cdot)$$ n/a 6288 16
4100.2.fx $$\chi_{4100}(71, \cdot)$$ n/a 10016 16
4100.2.fy $$\chi_{4100}(211, \cdot)$$ n/a 10016 16
4100.2.ge $$\chi_{4100}(313, \cdot)$$ n/a 1680 16
4100.2.gf $$\chi_{4100}(973, \cdot)$$ n/a 1680 16
4100.2.gq $$\chi_{4100}(117, \cdot)$$ n/a 1680 16
4100.2.gr $$\chi_{4100}(13, \cdot)$$ n/a 1680 16
4100.2.gs $$\chi_{4100}(17, \cdot)$$ n/a 1680 16
4100.2.gt $$\chi_{4100}(93, \cdot)$$ n/a 1008 16
4100.2.gu $$\chi_{4100}(137, \cdot)$$ n/a 1680 16
4100.2.gv $$\chi_{4100}(273, \cdot)$$ n/a 1680 16
4100.2.gw $$\chi_{4100}(1137, \cdot)$$ n/a 1680 16
4100.2.gx $$\chi_{4100}(157, \cdot)$$ n/a 1008 16
4100.2.gy $$\chi_{4100}(177, \cdot)$$ n/a 1680 16
4100.2.gz $$\chi_{4100}(217, \cdot)$$ n/a 1680 16
4100.2.hc $$\chi_{4100}(179, \cdot)$$ n/a 10016 16
4100.2.hd $$\chi_{4100}(79, \cdot)$$ n/a 10016 16
4100.2.he $$\chi_{4100}(439, \cdot)$$ n/a 10016 16
4100.2.hf $$\chi_{4100}(99, \cdot)$$ n/a 5984 16
4100.2.hg $$\chi_{4100}(239, \cdot)$$ n/a 10016 16
4100.2.hn $$\chi_{4100}(11, \cdot)$$ n/a 10016 16

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

Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(4100))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(4100)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(41))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(50))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(82))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(100))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(164))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(205))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(410))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(820))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1025))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2050))$$$$^{\oplus 2}$$