Properties

 Label 4704.2 Level 4704 Weight 2 Dimension 242786 Nonzero newspaces 48 Sturm bound 2408448

Defining parameters

 Level: $$N$$ = $$4704 = 2^{5} \cdot 3 \cdot 7^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$48$$ Sturm bound: $$2408448$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(4704))$$.

Total New Old
Modular forms 609792 244726 365066
Cusp forms 594433 242786 351647
Eisenstein series 15359 1940 13419

Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(4704))$$

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
4704.2.a $$\chi_{4704}(1, \cdot)$$ 4704.2.a.a 1 1
4704.2.a.b 1
4704.2.a.c 1
4704.2.a.d 1
4704.2.a.e 1
4704.2.a.f 1
4704.2.a.g 1
4704.2.a.h 1
4704.2.a.i 1
4704.2.a.j 1
4704.2.a.k 1
4704.2.a.l 1
4704.2.a.m 1
4704.2.a.n 1
4704.2.a.o 1
4704.2.a.p 1
4704.2.a.q 1
4704.2.a.r 1
4704.2.a.s 1
4704.2.a.t 1
4704.2.a.u 1
4704.2.a.v 1
4704.2.a.w 1
4704.2.a.x 1
4704.2.a.y 1
4704.2.a.z 1
4704.2.a.ba 1
4704.2.a.bb 1
4704.2.a.bc 1
4704.2.a.bd 1
4704.2.a.be 1
4704.2.a.bf 1
4704.2.a.bg 1
4704.2.a.bh 1
4704.2.a.bi 2
4704.2.a.bj 2
4704.2.a.bk 2
4704.2.a.bl 2
4704.2.a.bm 2
4704.2.a.bn 2
4704.2.a.bo 2
4704.2.a.bp 2
4704.2.a.bq 2
4704.2.a.br 2
4704.2.a.bs 3
4704.2.a.bt 3
4704.2.a.bu 3
4704.2.a.bv 3
4704.2.a.bw 4
4704.2.a.bx 4
4704.2.a.by 4
4704.2.a.bz 4
4704.2.b $$\chi_{4704}(1567, \cdot)$$ 4704.2.b.a 8 1
4704.2.b.b 8
4704.2.b.c 16
4704.2.b.d 16
4704.2.b.e 16
4704.2.b.f 16
4704.2.c $$\chi_{4704}(2353, \cdot)$$ 4704.2.c.a 2 1
4704.2.c.b 4
4704.2.c.c 8
4704.2.c.d 12
4704.2.c.e 16
4704.2.c.f 16
4704.2.c.g 24
4704.2.h $$\chi_{4704}(4607, \cdot)$$ n/a 164 1
4704.2.i $$\chi_{4704}(881, \cdot)$$ n/a 152 1
4704.2.j $$\chi_{4704}(2255, \cdot)$$ n/a 154 1
4704.2.k $$\chi_{4704}(3233, \cdot)$$ n/a 160 1
4704.2.p $$\chi_{4704}(3919, \cdot)$$ 4704.2.p.a 32 1
4704.2.p.b 48
4704.2.q $$\chi_{4704}(961, \cdot)$$ n/a 160 2
4704.2.s $$\chi_{4704}(1079, \cdot)$$ None 0 2
4704.2.u $$\chi_{4704}(391, \cdot)$$ None 0 2
4704.2.w $$\chi_{4704}(1177, \cdot)$$ None 0 2
4704.2.y $$\chi_{4704}(2057, \cdot)$$ None 0 2
4704.2.bb $$\chi_{4704}(2383, \cdot)$$ n/a 160 2
4704.2.bc $$\chi_{4704}(1697, \cdot)$$ n/a 320 2
4704.2.bd $$\chi_{4704}(3215, \cdot)$$ n/a 304 2
4704.2.bi $$\chi_{4704}(4049, \cdot)$$ n/a 304 2
4704.2.bj $$\chi_{4704}(863, \cdot)$$ n/a 320 2
4704.2.bk $$\chi_{4704}(3313, \cdot)$$ n/a 160 2
4704.2.bl $$\chi_{4704}(31, \cdot)$$ n/a 160 2
4704.2.bo $$\chi_{4704}(673, \cdot)$$ n/a 672 6
4704.2.bp $$\chi_{4704}(293, \cdot)$$ n/a 2528 4
4704.2.br $$\chi_{4704}(589, \cdot)$$ n/a 1312 4
4704.2.bt $$\chi_{4704}(491, \cdot)$$ n/a 2584 4
4704.2.bv $$\chi_{4704}(979, \cdot)$$ n/a 1280 4
4704.2.bx $$\chi_{4704}(521, \cdot)$$ None 0 4
4704.2.bz $$\chi_{4704}(361, \cdot)$$ None 0 4
4704.2.cb $$\chi_{4704}(1207, \cdot)$$ None 0 4
4704.2.cd $$\chi_{4704}(263, \cdot)$$ None 0 4
4704.2.cf $$\chi_{4704}(559, \cdot)$$ n/a 672 6
4704.2.ck $$\chi_{4704}(545, \cdot)$$ n/a 1344 6
4704.2.cl $$\chi_{4704}(239, \cdot)$$ n/a 1320 6
4704.2.cm $$\chi_{4704}(209, \cdot)$$ n/a 1320 6
4704.2.cn $$\chi_{4704}(575, \cdot)$$ n/a 1344 6
4704.2.cs $$\chi_{4704}(337, \cdot)$$ n/a 672 6
4704.2.ct $$\chi_{4704}(223, \cdot)$$ n/a 672 6
4704.2.cu $$\chi_{4704}(193, \cdot)$$ n/a 1344 12
4704.2.cw $$\chi_{4704}(19, \cdot)$$ n/a 2560 8
4704.2.cy $$\chi_{4704}(275, \cdot)$$ n/a 5056 8
4704.2.da $$\chi_{4704}(373, \cdot)$$ n/a 2560 8
4704.2.dc $$\chi_{4704}(509, \cdot)$$ n/a 5056 8
4704.2.dd $$\chi_{4704}(41, \cdot)$$ None 0 12
4704.2.df $$\chi_{4704}(169, \cdot)$$ None 0 12
4704.2.dh $$\chi_{4704}(55, \cdot)$$ None 0 12
4704.2.dj $$\chi_{4704}(71, \cdot)$$ None 0 12
4704.2.dn $$\chi_{4704}(703, \cdot)$$ n/a 1344 12
4704.2.do $$\chi_{4704}(529, \cdot)$$ n/a 1344 12
4704.2.dp $$\chi_{4704}(95, \cdot)$$ n/a 2688 12
4704.2.dq $$\chi_{4704}(17, \cdot)$$ n/a 2640 12
4704.2.dv $$\chi_{4704}(431, \cdot)$$ n/a 2640 12
4704.2.dw $$\chi_{4704}(257, \cdot)$$ n/a 2688 12
4704.2.dx $$\chi_{4704}(271, \cdot)$$ n/a 1344 12
4704.2.eb $$\chi_{4704}(155, \cdot)$$ n/a 21408 24
4704.2.ed $$\chi_{4704}(139, \cdot)$$ n/a 10752 24
4704.2.ef $$\chi_{4704}(125, \cdot)$$ n/a 21408 24
4704.2.eh $$\chi_{4704}(85, \cdot)$$ n/a 10752 24
4704.2.ej $$\chi_{4704}(23, \cdot)$$ None 0 24
4704.2.el $$\chi_{4704}(103, \cdot)$$ None 0 24
4704.2.en $$\chi_{4704}(25, \cdot)$$ None 0 24
4704.2.ep $$\chi_{4704}(89, \cdot)$$ None 0 24
4704.2.eq $$\chi_{4704}(37, \cdot)$$ n/a 21504 48
4704.2.es $$\chi_{4704}(5, \cdot)$$ n/a 42816 48
4704.2.eu $$\chi_{4704}(115, \cdot)$$ n/a 21504 48
4704.2.ew $$\chi_{4704}(11, \cdot)$$ n/a 42816 48

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

Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(4704))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(4704)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(84))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(96))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(98))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(112))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(147))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(168))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(196))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(224))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(294))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(336))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(392))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(588))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(672))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(784))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1176))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1568))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2352))$$$$^{\oplus 2}$$