# Properties

 Label 4410.2 Level 4410 Weight 2 Dimension 117929 Nonzero newspaces 60 Sturm bound 2032128

## Defining parameters

 Level: $$N$$ = $$4410 = 2 \cdot 3^{2} \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$60$$ Sturm bound: $$2032128$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(4410))$$.

Total New Old
Modular forms 515712 117929 397783
Cusp forms 500353 117929 382424
Eisenstein series 15359 0 15359

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(4410))$$

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
4410.2.a $$\chi_{4410}(1, \cdot)$$ 4410.2.a.a 1 1
4410.2.a.b 1
4410.2.a.c 1
4410.2.a.d 1
4410.2.a.e 1
4410.2.a.f 1
4410.2.a.g 1
4410.2.a.h 1
4410.2.a.i 1
4410.2.a.j 1
4410.2.a.k 1
4410.2.a.l 1
4410.2.a.m 1
4410.2.a.n 1
4410.2.a.o 1
4410.2.a.p 1
4410.2.a.q 1
4410.2.a.r 1
4410.2.a.s 1
4410.2.a.t 1
4410.2.a.u 1
4410.2.a.v 1
4410.2.a.w 1
4410.2.a.x 1
4410.2.a.y 1
4410.2.a.z 1
4410.2.a.ba 1
4410.2.a.bb 1
4410.2.a.bc 1
4410.2.a.bd 1
4410.2.a.be 1
4410.2.a.bf 1
4410.2.a.bg 1
4410.2.a.bh 1
4410.2.a.bi 1
4410.2.a.bj 1
4410.2.a.bk 1
4410.2.a.bl 1
4410.2.a.bm 1
4410.2.a.bn 2
4410.2.a.bo 2
4410.2.a.bp 2
4410.2.a.bq 2
4410.2.a.br 2
4410.2.a.bs 2
4410.2.a.bt 2
4410.2.a.bu 2
4410.2.a.bv 2
4410.2.a.bw 2
4410.2.a.bx 2
4410.2.a.by 2
4410.2.a.bz 2
4410.2.a.ca 2
4410.2.b $$\chi_{4410}(881, \cdot)$$ 4410.2.b.a 8 1
4410.2.b.b 8
4410.2.b.c 8
4410.2.b.d 8
4410.2.b.e 8
4410.2.b.f 8
4410.2.d $$\chi_{4410}(4409, \cdot)$$ 4410.2.d.a 16 1
4410.2.d.b 16
4410.2.d.c 24
4410.2.d.d 24
4410.2.g $$\chi_{4410}(3529, \cdot)$$ n/a 102 1
4410.2.i $$\chi_{4410}(3301, \cdot)$$ n/a 320 2
4410.2.j $$\chi_{4410}(1471, \cdot)$$ n/a 328 2
4410.2.k $$\chi_{4410}(361, \cdot)$$ n/a 136 2
4410.2.l $$\chi_{4410}(961, \cdot)$$ n/a 320 2
4410.2.m $$\chi_{4410}(197, \cdot)$$ n/a 164 2
4410.2.p $$\chi_{4410}(1567, \cdot)$$ n/a 200 2
4410.2.r $$\chi_{4410}(2579, \cdot)$$ n/a 480 2
4410.2.t $$\chi_{4410}(3461, \cdot)$$ n/a 320 2
4410.2.u $$\chi_{4410}(1549, \cdot)$$ n/a 200 2
4410.2.z $$\chi_{4410}(589, \cdot)$$ n/a 492 2
4410.2.ba $$\chi_{4410}(2419, \cdot)$$ n/a 480 2
4410.2.be $$\chi_{4410}(521, \cdot)$$ n/a 112 2
4410.2.bf $$\chi_{4410}(1469, \cdot)$$ n/a 480 2
4410.2.bi $$\chi_{4410}(509, \cdot)$$ n/a 480 2
4410.2.bk $$\chi_{4410}(1391, \cdot)$$ n/a 320 2
4410.2.bl $$\chi_{4410}(2351, \cdot)$$ n/a 320 2
4410.2.bo $$\chi_{4410}(1979, \cdot)$$ n/a 160 2
4410.2.bq $$\chi_{4410}(79, \cdot)$$ n/a 480 2
4410.2.bs $$\chi_{4410}(631, \cdot)$$ n/a 576 6
4410.2.bu $$\chi_{4410}(1733, \cdot)$$ n/a 960 4
4410.2.bw $$\chi_{4410}(1207, \cdot)$$ n/a 400 4
4410.2.bx $$\chi_{4410}(607, \cdot)$$ n/a 960 4
4410.2.ca $$\chi_{4410}(97, \cdot)$$ n/a 960 4
4410.2.cb $$\chi_{4410}(1373, \cdot)$$ n/a 984 4
4410.2.ce $$\chi_{4410}(263, \cdot)$$ n/a 960 4
4410.2.cf $$\chi_{4410}(557, \cdot)$$ n/a 320 4
4410.2.ch $$\chi_{4410}(313, \cdot)$$ n/a 960 4
4410.2.cl $$\chi_{4410}(379, \cdot)$$ n/a 840 6
4410.2.cm $$\chi_{4410}(629, \cdot)$$ n/a 672 6
4410.2.co $$\chi_{4410}(251, \cdot)$$ n/a 480 6
4410.2.cq $$\chi_{4410}(331, \cdot)$$ n/a 2688 12
4410.2.cr $$\chi_{4410}(541, \cdot)$$ n/a 1104 12
4410.2.cs $$\chi_{4410}(211, \cdot)$$ n/a 2688 12
4410.2.ct $$\chi_{4410}(121, \cdot)$$ n/a 2688 12
4410.2.cv $$\chi_{4410}(307, \cdot)$$ n/a 1680 12
4410.2.cw $$\chi_{4410}(323, \cdot)$$ n/a 1344 12
4410.2.cy $$\chi_{4410}(319, \cdot)$$ n/a 4032 12
4410.2.dc $$\chi_{4410}(89, \cdot)$$ n/a 1344 12
4410.2.dd $$\chi_{4410}(41, \cdot)$$ n/a 2688 12
4410.2.dg $$\chi_{4410}(101, \cdot)$$ n/a 2688 12
4410.2.di $$\chi_{4410}(479, \cdot)$$ n/a 4032 12
4410.2.dj $$\chi_{4410}(209, \cdot)$$ n/a 4032 12
4410.2.dm $$\chi_{4410}(341, \cdot)$$ n/a 864 12
4410.2.do $$\chi_{4410}(499, \cdot)$$ n/a 4032 12
4410.2.dr $$\chi_{4410}(169, \cdot)$$ n/a 4032 12
4410.2.du $$\chi_{4410}(109, \cdot)$$ n/a 1680 12
4410.2.dx $$\chi_{4410}(311, \cdot)$$ n/a 2688 12
4410.2.dz $$\chi_{4410}(59, \cdot)$$ n/a 4032 12
4410.2.ea $$\chi_{4410}(157, \cdot)$$ n/a 8064 24
4410.2.ec $$\chi_{4410}(113, \cdot)$$ n/a 8064 24
4410.2.ef $$\chi_{4410}(53, \cdot)$$ n/a 2688 24
4410.2.eg $$\chi_{4410}(23, \cdot)$$ n/a 8064 24
4410.2.ej $$\chi_{4410}(103, \cdot)$$ n/a 8064 24
4410.2.ek $$\chi_{4410}(73, \cdot)$$ n/a 3360 24
4410.2.en $$\chi_{4410}(13, \cdot)$$ n/a 8064 24
4410.2.ep $$\chi_{4410}(317, \cdot)$$ n/a 8064 24

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(4410))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(4410)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(63))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(70))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(90))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(98))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(105))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(126))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(147))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(210))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(245))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(294))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(315))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(441))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(490))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(630))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(735))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(882))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1470))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2205))$$$$^{\oplus 2}$$