# Properties

 Label 4176.2 Level 4176 Weight 2 Dimension 213854 Nonzero newspaces 56 Sturm bound 1935360

## Defining parameters

 Level: $$N$$ = $$4176 = 2^{4} \cdot 3^{2} \cdot 29$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$56$$ Sturm bound: $$1935360$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(4176))$$.

Total New Old
Modular forms 490112 216040 274072
Cusp forms 477569 213854 263715
Eisenstein series 12543 2186 10357

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(4176))$$

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
4176.2.a $$\chi_{4176}(1, \cdot)$$ 4176.2.a.a 1 1
4176.2.a.b 1
4176.2.a.c 1
4176.2.a.d 1
4176.2.a.e 1
4176.2.a.f 1
4176.2.a.g 1
4176.2.a.h 1
4176.2.a.i 1
4176.2.a.j 1
4176.2.a.k 1
4176.2.a.l 1
4176.2.a.m 1
4176.2.a.n 1
4176.2.a.o 1
4176.2.a.p 1
4176.2.a.q 1
4176.2.a.r 1
4176.2.a.s 1
4176.2.a.t 1
4176.2.a.u 1
4176.2.a.v 1
4176.2.a.w 1
4176.2.a.x 1
4176.2.a.y 1
4176.2.a.z 1
4176.2.a.ba 1
4176.2.a.bb 1
4176.2.a.bc 1
4176.2.a.bd 1
4176.2.a.be 1
4176.2.a.bf 1
4176.2.a.bg 1
4176.2.a.bh 1
4176.2.a.bi 1
4176.2.a.bj 1
4176.2.a.bk 1
4176.2.a.bl 2
4176.2.a.bm 2
4176.2.a.bn 2
4176.2.a.bo 2
4176.2.a.bp 2
4176.2.a.bq 2
4176.2.a.br 2
4176.2.a.bs 2
4176.2.a.bt 2
4176.2.a.bu 3
4176.2.a.bv 3
4176.2.a.bw 3
4176.2.a.bx 3
4176.2.a.by 3
4176.2.c $$\chi_{4176}(4175, \cdot)$$ 4176.2.c.a 4 1
4176.2.c.b 8
4176.2.c.c 8
4176.2.c.d 40
4176.2.e $$\chi_{4176}(3887, \cdot)$$ 4176.2.e.a 4 1
4176.2.e.b 4
4176.2.e.c 4
4176.2.e.d 4
4176.2.e.e 40
4176.2.f $$\chi_{4176}(2089, \cdot)$$ None 0 1
4176.2.h $$\chi_{4176}(2377, \cdot)$$ None 0 1
4176.2.j $$\chi_{4176}(1799, \cdot)$$ None 0 1
4176.2.l $$\chi_{4176}(2087, \cdot)$$ None 0 1
4176.2.o $$\chi_{4176}(289, \cdot)$$ 4176.2.o.a 2 1
4176.2.o.b 2
4176.2.o.c 2
4176.2.o.d 2
4176.2.o.e 2
4176.2.o.f 2
4176.2.o.g 2
4176.2.o.h 2
4176.2.o.i 2
4176.2.o.j 2
4176.2.o.k 2
4176.2.o.l 4
4176.2.o.m 4
4176.2.o.n 4
4176.2.o.o 4
4176.2.o.p 6
4176.2.o.q 6
4176.2.o.r 8
4176.2.o.s 16
4176.2.q $$\chi_{4176}(1393, \cdot)$$ n/a 336 2
4176.2.r $$\chi_{4176}(3439, \cdot)$$ n/a 150 2
4176.2.u $$\chi_{4176}(2105, \cdot)$$ None 0 2
4176.2.v $$\chi_{4176}(1061, \cdot)$$ n/a 480 2
4176.2.x $$\chi_{4176}(1333, \cdot)$$ n/a 596 2
4176.2.z $$\chi_{4176}(1045, \cdot)$$ n/a 560 2
4176.2.bc $$\chi_{4176}(1781, \cdot)$$ n/a 480 2
4176.2.be $$\chi_{4176}(1027, \cdot)$$ n/a 596 2
4176.2.bf $$\chi_{4176}(755, \cdot)$$ n/a 448 2
4176.2.bh $$\chi_{4176}(1043, \cdot)$$ n/a 480 2
4176.2.bj $$\chi_{4176}(307, \cdot)$$ n/a 596 2
4176.2.bm $$\chi_{4176}(1351, \cdot)$$ None 0 2
4176.2.bn $$\chi_{4176}(17, \cdot)$$ n/a 120 2
4176.2.bq $$\chi_{4176}(1681, \cdot)$$ n/a 356 2
4176.2.bt $$\chi_{4176}(695, \cdot)$$ None 0 2
4176.2.bv $$\chi_{4176}(407, \cdot)$$ None 0 2
4176.2.bx $$\chi_{4176}(985, \cdot)$$ None 0 2
4176.2.bz $$\chi_{4176}(697, \cdot)$$ None 0 2
4176.2.ca $$\chi_{4176}(1103, \cdot)$$ n/a 336 2
4176.2.cc $$\chi_{4176}(1391, \cdot)$$ n/a 360 2
4176.2.ce $$\chi_{4176}(721, \cdot)$$ n/a 444 6
4176.2.cg $$\chi_{4176}(1409, \cdot)$$ n/a 712 4
4176.2.ch $$\chi_{4176}(679, \cdot)$$ None 0 4
4176.2.cj $$\chi_{4176}(331, \cdot)$$ n/a 2864 4
4176.2.cm $$\chi_{4176}(59, \cdot)$$ n/a 2688 4
4176.2.co $$\chi_{4176}(347, \cdot)$$ n/a 2864 4
4176.2.cq $$\chi_{4176}(1003, \cdot)$$ n/a 2864 4
4176.2.cs $$\chi_{4176}(365, \cdot)$$ n/a 2864 4
4176.2.cu $$\chi_{4176}(637, \cdot)$$ n/a 2864 4
4176.2.cw $$\chi_{4176}(349, \cdot)$$ n/a 2688 4
4176.2.cx $$\chi_{4176}(1085, \cdot)$$ n/a 2864 4
4176.2.cz $$\chi_{4176}(41, \cdot)$$ None 0 4
4176.2.dc $$\chi_{4176}(655, \cdot)$$ n/a 720 4
4176.2.de $$\chi_{4176}(1153, \cdot)$$ n/a 444 6
4176.2.dh $$\chi_{4176}(71, \cdot)$$ None 0 6
4176.2.dj $$\chi_{4176}(935, \cdot)$$ None 0 6
4176.2.dl $$\chi_{4176}(361, \cdot)$$ None 0 6
4176.2.dn $$\chi_{4176}(1225, \cdot)$$ None 0 6
4176.2.do $$\chi_{4176}(431, \cdot)$$ n/a 360 6
4176.2.dq $$\chi_{4176}(863, \cdot)$$ n/a 360 6
4176.2.ds $$\chi_{4176}(49, \cdot)$$ n/a 2136 12
4176.2.du $$\chi_{4176}(305, \cdot)$$ n/a 720 12
4176.2.dv $$\chi_{4176}(55, \cdot)$$ None 0 12
4176.2.dy $$\chi_{4176}(19, \cdot)$$ n/a 3576 12
4176.2.ea $$\chi_{4176}(107, \cdot)$$ n/a 2880 12
4176.2.ec $$\chi_{4176}(35, \cdot)$$ n/a 2880 12
4176.2.ed $$\chi_{4176}(163, \cdot)$$ n/a 3576 12
4176.2.ef $$\chi_{4176}(917, \cdot)$$ n/a 2880 12
4176.2.ei $$\chi_{4176}(109, \cdot)$$ n/a 3576 12
4176.2.ek $$\chi_{4176}(181, \cdot)$$ n/a 3576 12
4176.2.em $$\chi_{4176}(269, \cdot)$$ n/a 2880 12
4176.2.en $$\chi_{4176}(89, \cdot)$$ None 0 12
4176.2.eq $$\chi_{4176}(127, \cdot)$$ n/a 900 12
4176.2.es $$\chi_{4176}(383, \cdot)$$ n/a 2160 12
4176.2.eu $$\chi_{4176}(239, \cdot)$$ n/a 2160 12
4176.2.ev $$\chi_{4176}(25, \cdot)$$ None 0 12
4176.2.ex $$\chi_{4176}(121, \cdot)$$ None 0 12
4176.2.ez $$\chi_{4176}(23, \cdot)$$ None 0 12
4176.2.fb $$\chi_{4176}(167, \cdot)$$ None 0 12
4176.2.fe $$\chi_{4176}(241, \cdot)$$ n/a 2136 12
4176.2.fg $$\chi_{4176}(31, \cdot)$$ n/a 4320 24
4176.2.fj $$\chi_{4176}(137, \cdot)$$ None 0 24
4176.2.fl $$\chi_{4176}(101, \cdot)$$ n/a 17184 24
4176.2.fm $$\chi_{4176}(13, \cdot)$$ n/a 17184 24
4176.2.fo $$\chi_{4176}(277, \cdot)$$ n/a 17184 24
4176.2.fq $$\chi_{4176}(77, \cdot)$$ n/a 17184 24
4176.2.fs $$\chi_{4176}(43, \cdot)$$ n/a 17184 24
4176.2.fu $$\chi_{4176}(83, \cdot)$$ n/a 17184 24
4176.2.fw $$\chi_{4176}(299, \cdot)$$ n/a 17184 24
4176.2.fz $$\chi_{4176}(619, \cdot)$$ n/a 17184 24
4176.2.gb $$\chi_{4176}(247, \cdot)$$ None 0 24
4176.2.gc $$\chi_{4176}(113, \cdot)$$ n/a 4272 24

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(4176))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(4176)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(29))$$$$^{\oplus 15}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(58))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(87))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(116))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(144))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(174))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(232))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(261))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(348))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(464))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(522))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(696))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1044))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1392))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2088))$$$$^{\oplus 2}$$