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Properties

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

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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

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