# Properties

 Label 9072.2 Level 9072 Weight 2 Dimension 951336 Nonzero newspaces 88 Sturm bound 8957952

## Defining parameters

 Level: $$N$$ = $$9072 = 2^{4} \cdot 3^{4} \cdot 7$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$88$$ Sturm bound: $$8957952$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(9072))$$.

Total New Old
Modular forms 2257632 956376 1301256
Cusp forms 2221345 951336 1270009
Eisenstein series 36287 5040 31247

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(9072))$$

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 available newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
9072.2.a $$\chi_{9072}(1, \cdot)$$ 9072.2.a.a 1 1
9072.2.a.b 1
9072.2.a.c 1
9072.2.a.d 1
9072.2.a.e 1
9072.2.a.f 1
9072.2.a.g 1
9072.2.a.h 1
9072.2.a.i 1
9072.2.a.j 1
9072.2.a.k 1
9072.2.a.l 1
9072.2.a.m 1
9072.2.a.n 1
9072.2.a.o 1
9072.2.a.p 1
9072.2.a.q 1
9072.2.a.r 1
9072.2.a.s 1
9072.2.a.t 1
9072.2.a.u 1
9072.2.a.v 1
9072.2.a.w 1
9072.2.a.x 1
9072.2.a.y 2
9072.2.a.z 2
9072.2.a.ba 2
9072.2.a.bb 2
9072.2.a.bc 2
9072.2.a.bd 2
9072.2.a.be 2
9072.2.a.bf 2
9072.2.a.bg 2
9072.2.a.bh 2
9072.2.a.bi 2
9072.2.a.bj 2
9072.2.a.bk 2
9072.2.a.bl 2
9072.2.a.bm 2
9072.2.a.bn 2
9072.2.a.bo 2
9072.2.a.bp 2
9072.2.a.bq 3
9072.2.a.br 3
9072.2.a.bs 3
9072.2.a.bt 3
9072.2.a.bu 3
9072.2.a.bv 3
9072.2.a.bw 3
9072.2.a.bx 3
9072.2.a.by 3
9072.2.a.bz 3
9072.2.a.ca 3
9072.2.a.cb 3
9072.2.a.cc 3
9072.2.a.cd 3
9072.2.a.ce 4
9072.2.a.cf 4
9072.2.a.cg 4
9072.2.a.ch 4
9072.2.a.ci 4
9072.2.a.cj 4
9072.2.a.ck 4
9072.2.a.cl 4
9072.2.a.cm 5
9072.2.a.cn 5
9072.2.b $$\chi_{9072}(7615, \cdot)$$ n/a 192 1
9072.2.c $$\chi_{9072}(4537, \cdot)$$ None 0 1
9072.2.h $$\chi_{9072}(2591, \cdot)$$ n/a 144 1
9072.2.i $$\chi_{9072}(3401, \cdot)$$ None 0 1
9072.2.j $$\chi_{9072}(7127, \cdot)$$ None 0 1
9072.2.k $$\chi_{9072}(7937, \cdot)$$ n/a 188 1
9072.2.p $$\chi_{9072}(3079, \cdot)$$ None 0 1
9072.2.q $$\chi_{9072}(865, \cdot)$$ n/a 380 2
9072.2.r $$\chi_{9072}(3025, \cdot)$$ n/a 288 2
9072.2.s $$\chi_{9072}(1297, \cdot)$$ n/a 376 2
9072.2.t $$\chi_{9072}(6913, \cdot)$$ n/a 380 2
9072.2.v $$\chi_{9072}(323, \cdot)$$ n/a 1152 2
9072.2.x $$\chi_{9072}(811, \cdot)$$ n/a 1520 2
9072.2.z $$\chi_{9072}(2269, \cdot)$$ n/a 1152 2
9072.2.bb $$\chi_{9072}(1133, \cdot)$$ n/a 1520 2
9072.2.be $$\chi_{9072}(2377, \cdot)$$ None 0 2
9072.2.bf $$\chi_{9072}(3295, \cdot)$$ n/a 384 2
9072.2.bg $$\chi_{9072}(5129, \cdot)$$ None 0 2
9072.2.bh $$\chi_{9072}(3455, \cdot)$$ n/a 384 2
9072.2.bm $$\chi_{9072}(55, \cdot)$$ None 0 2
9072.2.bn $$\chi_{9072}(4807, \cdot)$$ None 0 2
9072.2.bs $$\chi_{9072}(1783, \cdot)$$ None 0 2
9072.2.bt $$\chi_{9072}(4049, \cdot)$$ n/a 376 2
9072.2.bu $$\chi_{9072}(1943, \cdot)$$ None 0 2
9072.2.bz $$\chi_{9072}(1079, \cdot)$$ None 0 2
9072.2.ca $$\chi_{9072}(3617, \cdot)$$ n/a 380 2
9072.2.cb $$\chi_{9072}(4967, \cdot)$$ None 0 2
9072.2.cc $$\chi_{9072}(1889, \cdot)$$ n/a 380 2
9072.2.ch $$\chi_{9072}(5615, \cdot)$$ n/a 288 2
9072.2.ci $$\chi_{9072}(2537, \cdot)$$ None 0 2
9072.2.cj $$\chi_{9072}(431, \cdot)$$ n/a 384 2
9072.2.ck $$\chi_{9072}(377, \cdot)$$ None 0 2
9072.2.cp $$\chi_{9072}(2105, \cdot)$$ None 0 2
9072.2.cq $$\chi_{9072}(3887, \cdot)$$ n/a 384 2
9072.2.cr $$\chi_{9072}(5833, \cdot)$$ None 0 2
9072.2.cs $$\chi_{9072}(3727, \cdot)$$ n/a 384 2
9072.2.cx $$\chi_{9072}(1567, \cdot)$$ n/a 384 2
9072.2.cy $$\chi_{9072}(5401, \cdot)$$ None 0 2
9072.2.cz $$\chi_{9072}(271, \cdot)$$ n/a 384 2
9072.2.da $$\chi_{9072}(1513, \cdot)$$ None 0 2
9072.2.df $$\chi_{9072}(593, \cdot)$$ n/a 380 2
9072.2.dg $$\chi_{9072}(2375, \cdot)$$ None 0 2
9072.2.dh $$\chi_{9072}(2215, \cdot)$$ None 0 2
9072.2.dk $$\chi_{9072}(1009, \cdot)$$ n/a 648 6
9072.2.dl $$\chi_{9072}(289, \cdot)$$ n/a 852 6
9072.2.dm $$\chi_{9072}(2305, \cdot)$$ n/a 852 6
9072.2.dn $$\chi_{9072}(2323, \cdot)$$ n/a 3056 4
9072.2.dp $$\chi_{9072}(1835, \cdot)$$ n/a 2304 4
9072.2.dr $$\chi_{9072}(109, \cdot)$$ n/a 3056 4
9072.2.du $$\chi_{9072}(269, \cdot)$$ n/a 3056 4
9072.2.dv $$\chi_{9072}(1781, \cdot)$$ n/a 3040 4
9072.2.dx $$\chi_{9072}(1621, \cdot)$$ n/a 3040 4
9072.2.ea $$\chi_{9072}(2053, \cdot)$$ n/a 3056 4
9072.2.eb $$\chi_{9072}(2861, \cdot)$$ n/a 3056 4
9072.2.ed $$\chi_{9072}(107, \cdot)$$ n/a 3056 4
9072.2.ef $$\chi_{9072}(1459, \cdot)$$ n/a 3040 4
9072.2.ei $$\chi_{9072}(2539, \cdot)$$ n/a 3056 4
9072.2.ek $$\chi_{9072}(2699, \cdot)$$ n/a 3056 4
9072.2.el $$\chi_{9072}(1619, \cdot)$$ n/a 3040 4
9072.2.en $$\chi_{9072}(1027, \cdot)$$ n/a 3056 4
9072.2.ep $$\chi_{9072}(2645, \cdot)$$ n/a 3056 4
9072.2.er $$\chi_{9072}(757, \cdot)$$ n/a 2304 4
9072.2.eu $$\chi_{9072}(1439, \cdot)$$ n/a 864 6
9072.2.ew $$\chi_{9072}(1207, \cdot)$$ None 0 6
9072.2.ex $$\chi_{9072}(1279, \cdot)$$ n/a 864 6
9072.2.ez $$\chi_{9072}(1367, \cdot)$$ None 0 6
9072.2.fb $$\chi_{9072}(89, \cdot)$$ None 0 6
9072.2.ff $$\chi_{9072}(1385, \cdot)$$ None 0 6
9072.2.fi $$\chi_{9072}(361, \cdot)$$ None 0 6
9072.2.fj $$\chi_{9072}(881, \cdot)$$ n/a 852 6
9072.2.fl $$\chi_{9072}(505, \cdot)$$ None 0 6
9072.2.fo $$\chi_{9072}(17, \cdot)$$ n/a 852 6
9072.2.fp $$\chi_{9072}(359, \cdot)$$ None 0 6
9072.2.fs $$\chi_{9072}(559, \cdot)$$ n/a 864 6
9072.2.fu $$\chi_{9072}(71, \cdot)$$ None 0 6
9072.2.fv $$\chi_{9072}(1711, \cdot)$$ n/a 864 6
9072.2.fy $$\chi_{9072}(199, \cdot)$$ None 0 6
9072.2.fz $$\chi_{9072}(575, \cdot)$$ n/a 648 6
9072.2.gb $$\chi_{9072}(1063, \cdot)$$ None 0 6
9072.2.ge $$\chi_{9072}(1871, \cdot)$$ n/a 864 6
9072.2.gg $$\chi_{9072}(2033, \cdot)$$ n/a 852 6
9072.2.gi $$\chi_{9072}(793, \cdot)$$ None 0 6
9072.2.gk $$\chi_{9072}(521, \cdot)$$ None 0 6
9072.2.gm $$\chi_{9072}(193, \cdot)$$ n/a 7740 18
9072.2.gn $$\chi_{9072}(337, \cdot)$$ n/a 5832 18
9072.2.go $$\chi_{9072}(529, \cdot)$$ n/a 7740 18
9072.2.gp $$\chi_{9072}(451, \cdot)$$ n/a 6864 12
9072.2.gs $$\chi_{9072}(611, \cdot)$$ n/a 6864 12
9072.2.gt $$\chi_{9072}(1045, \cdot)$$ n/a 6864 12
9072.2.gv $$\chi_{9072}(253, \cdot)$$ n/a 5184 12
9072.2.gy $$\chi_{9072}(125, \cdot)$$ n/a 6864 12
9072.2.ha $$\chi_{9072}(773, \cdot)$$ n/a 6864 12
9072.2.hc $$\chi_{9072}(307, \cdot)$$ n/a 6864 12
9072.2.he $$\chi_{9072}(19, \cdot)$$ n/a 6864 12
9072.2.hf $$\chi_{9072}(179, \cdot)$$ n/a 6864 12
9072.2.hh $$\chi_{9072}(827, \cdot)$$ n/a 5184 12
9072.2.hk $$\chi_{9072}(37, \cdot)$$ n/a 6864 12
9072.2.hl $$\chi_{9072}(341, \cdot)$$ n/a 6864 12
9072.2.hn $$\chi_{9072}(25, \cdot)$$ None 0 18
9072.2.hp $$\chi_{9072}(103, \cdot)$$ None 0 18
9072.2.hs $$\chi_{9072}(257, \cdot)$$ n/a 7740 18
9072.2.hu $$\chi_{9072}(527, \cdot)$$ n/a 7776 18
9072.2.hx $$\chi_{9072}(223, \cdot)$$ n/a 7776 18
9072.2.hy $$\chi_{9072}(31, \cdot)$$ n/a 7776 18
9072.2.id $$\chi_{9072}(41, \cdot)$$ None 0 18
9072.2.ie $$\chi_{9072}(185, \cdot)$$ None 0 18
9072.2.ih $$\chi_{9072}(599, \cdot)$$ None 0 18
9072.2.ii $$\chi_{9072}(407, \cdot)$$ None 0 18
9072.2.il $$\chi_{9072}(439, \cdot)$$ None 0 18
9072.2.im $$\chi_{9072}(391, \cdot)$$ None 0 18
9072.2.ip $$\chi_{9072}(169, \cdot)$$ None 0 18
9072.2.iq $$\chi_{9072}(457, \cdot)$$ None 0 18
9072.2.ir $$\chi_{9072}(239, \cdot)$$ n/a 5832 18
9072.2.is $$\chi_{9072}(95, \cdot)$$ n/a 7776 18
9072.2.iv $$\chi_{9072}(689, \cdot)$$ n/a 7740 18
9072.2.iw $$\chi_{9072}(209, \cdot)$$ n/a 7740 18
9072.2.ja $$\chi_{9072}(367, \cdot)$$ n/a 7776 18
9072.2.jc $$\chi_{9072}(23, \cdot)$$ None 0 18
9072.2.je $$\chi_{9072}(761, \cdot)$$ None 0 18
9072.2.jg $$\chi_{9072}(347, \cdot)$$ n/a 62064 36
9072.2.jh $$\chi_{9072}(173, \cdot)$$ n/a 62064 36
9072.2.jm $$\chi_{9072}(11, \cdot)$$ n/a 62064 36
9072.2.jn $$\chi_{9072}(155, \cdot)$$ n/a 46656 36
9072.2.jo $$\chi_{9072}(293, \cdot)$$ n/a 62064 36
9072.2.jp $$\chi_{9072}(5, \cdot)$$ n/a 62064 36
9072.2.js $$\chi_{9072}(187, \cdot)$$ n/a 62064 36
9072.2.jt $$\chi_{9072}(205, \cdot)$$ n/a 62064 36
9072.2.jy $$\chi_{9072}(115, \cdot)$$ n/a 62064 36
9072.2.jz $$\chi_{9072}(139, \cdot)$$ n/a 62064 36
9072.2.ka $$\chi_{9072}(85, \cdot)$$ n/a 46656 36
9072.2.kb $$\chi_{9072}(277, \cdot)$$ n/a 62064 36

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(9072))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(9072)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 50}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 40}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 40}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 30}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 32}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 25}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 30}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(27))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 15}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(54))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(63))$$$$^{\oplus 15}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(81))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(84))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(108))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(112))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(126))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(144))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(162))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(168))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(189))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(216))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(252))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(324))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(336))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(378))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(432))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(504))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(567))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(648))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(756))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1008))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1134))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1296))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1512))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2268))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3024))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4536))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(9072))$$$$^{\oplus 1}$$