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Properties

Label 16272.2
Level 16272
Weight 2
Dimension 3269984
Nonzero newspaces 104
Sturm bound 29417472

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Defining parameters

Level: \( N \) = \( 16272 = 2^{4} \cdot 3^{2} \cdot 113 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 104 \)
Sturm bound: \(29417472\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(16272))\).

Total New Old
Modular forms 7379456 3278974 4100482
Cusp forms 7329281 3269984 4059297
Eisenstein series 50175 8990 41185

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(16272))\)

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
16272.2.a \(\chi_{16272}(1, \cdot)\) 16272.2.a.a 1 1
16272.2.a.b 1
16272.2.a.c 1
16272.2.a.d 1
16272.2.a.e 1
16272.2.a.f 1
16272.2.a.g 1
16272.2.a.h 1
16272.2.a.i 1
16272.2.a.j 1
16272.2.a.k 1
16272.2.a.l 1
16272.2.a.m 1
16272.2.a.n 1
16272.2.a.o 1
16272.2.a.p 1
16272.2.a.q 1
16272.2.a.r 1
16272.2.a.s 1
16272.2.a.t 1
16272.2.a.u 1
16272.2.a.v 1
16272.2.a.w 1
16272.2.a.x 1
16272.2.a.y 1
16272.2.a.z 1
16272.2.a.ba 1
16272.2.a.bb 1
16272.2.a.bc 1
16272.2.a.bd 1
16272.2.a.be 1
16272.2.a.bf 1
16272.2.a.bg 1
16272.2.a.bh 1
16272.2.a.bi 1
16272.2.a.bj 1
16272.2.a.bk 1
16272.2.a.bl 1
16272.2.a.bm 1
16272.2.a.bn 1
16272.2.a.bo 2
16272.2.a.bp 2
16272.2.a.bq 2
16272.2.a.br 2
16272.2.a.bs 2
16272.2.a.bt 2
16272.2.a.bu 2
16272.2.a.bv 2
16272.2.a.bw 2
16272.2.a.bx 2
16272.2.a.by 2
16272.2.a.bz 2
16272.2.a.ca 2
16272.2.a.cb 2
16272.2.a.cc 3
16272.2.a.cd 3
16272.2.a.ce 3
16272.2.a.cf 3
16272.2.a.cg 3
16272.2.a.ch 3
16272.2.a.ci 4
16272.2.a.cj 4
16272.2.a.ck 4
16272.2.a.cl 5
16272.2.a.cm 5
16272.2.a.cn 5
16272.2.a.co 5
16272.2.a.cp 5
16272.2.a.cq 5
16272.2.a.cr 5
16272.2.a.cs 6
16272.2.a.ct 6
16272.2.a.cu 6
16272.2.a.cv 7
16272.2.a.cw 7
16272.2.a.cx 7
16272.2.a.cy 7
16272.2.a.cz 9
16272.2.a.da 9
16272.2.a.db 9
16272.2.a.dc 9
16272.2.a.dd 11
16272.2.a.de 11
16272.2.a.df 11
16272.2.a.dg 16
16272.2.a.dh 16
16272.2.e \(\chi_{16272}(1583, \cdot)\) n/a 224 1
16272.2.i \(\chi_{16272}(14689, \cdot)\) n/a 284 1
16272.2.m \(\chi_{16272}(16271, \cdot)\) n/a 228 1
16272.2.q \(\chi_{16272}(5425, \cdot)\) n/a 1344 2
16272.2.s \(\chi_{16272}(15157, \cdot)\) n/a 2276 2
16272.2.u \(\chi_{16272}(467, \cdot)\) n/a 1824 2
16272.2.v \(\chi_{16272}(5183, \cdot)\) n/a 456 2
16272.2.x \(\chi_{16272}(2485, \cdot)\) n/a 2276 2
16272.2.z \(\chi_{16272}(4069, \cdot)\) n/a 2240 2
16272.2.bd \(\chi_{16272}(3601, \cdot)\) n/a 568 2
16272.2.bg \(\chi_{16272}(5651, \cdot)\) n/a 1792 2
16272.2.bi \(\chi_{16272}(4067, \cdot)\) n/a 1824 2
16272.2.bl \(\chi_{16272}(7021, \cdot)\) n/a 2276 2
16272.2.bn \(\chi_{16272}(8603, \cdot)\) n/a 1824 2
16272.2.bs \(\chi_{16272}(5423, \cdot)\) n/a 1368 2
16272.2.bw \(\chi_{16272}(3841, \cdot)\) n/a 1364 2
16272.2.ca \(\chi_{16272}(7007, \cdot)\) n/a 1344 2
16272.2.ce \(\chi_{16272}(3745, \cdot)\) n/a 1704 6
16272.2.cf \(\chi_{16272}(973, \cdot)\) n/a 4552 4
16272.2.ck \(\chi_{16272}(6623, \cdot)\) n/a 912 4
16272.2.cm \(\chi_{16272}(1261, \cdot)\) n/a 4552 4
16272.2.cn \(\chi_{16272}(2843, \cdot)\) n/a 3648 4
16272.2.cq \(\chi_{16272}(5041, \cdot)\) n/a 1136 4
16272.2.cu \(\chi_{16272}(2555, \cdot)\) n/a 3648 4
16272.2.cv \(\chi_{16272}(3179, \cdot)\) n/a 10928 4
16272.2.cx \(\chi_{16272}(1597, \cdot)\) n/a 10928 4
16272.2.db \(\chi_{16272}(227, \cdot)\) n/a 10752 4
16272.2.dd \(\chi_{16272}(1355, \cdot)\) n/a 10928 4
16272.2.dg \(\chi_{16272}(241, \cdot)\) n/a 2728 4
16272.2.dk \(\chi_{16272}(5197, \cdot)\) n/a 10928 4
16272.2.dm \(\chi_{16272}(1357, \cdot)\) n/a 10752 4
16272.2.do \(\chi_{16272}(1823, \cdot)\) n/a 2736 4
16272.2.dq \(\chi_{16272}(5891, \cdot)\) n/a 10928 4
16272.2.ds \(\chi_{16272}(4309, \cdot)\) n/a 10928 4
16272.2.dw \(\chi_{16272}(1439, \cdot)\) n/a 1368 6
16272.2.ea \(\chi_{16272}(1441, \cdot)\) n/a 1704 6
16272.2.ee \(\chi_{16272}(143, \cdot)\) n/a 1368 6
16272.2.ej \(\chi_{16272}(379, \cdot)\) n/a 9104 8
16272.2.em \(\chi_{16272}(161, \cdot)\) n/a 1824 8
16272.2.eo \(\chi_{16272}(523, \cdot)\) n/a 9104 8
16272.2.er \(\chi_{16272}(3581, \cdot)\) n/a 7296 8
16272.2.eu \(\chi_{16272}(1999, \cdot)\) n/a 2280 8
16272.2.ew \(\chi_{16272}(1421, \cdot)\) n/a 7296 8
16272.2.ey \(\chi_{16272}(49, \cdot)\) n/a 8184 12
16272.2.ez \(\chi_{16272}(131, \cdot)\) n/a 21856 8
16272.2.fb \(\chi_{16272}(3937, \cdot)\) n/a 5456 8
16272.2.fg \(\chi_{16272}(1451, \cdot)\) n/a 21856 8
16272.2.fh \(\chi_{16272}(2869, \cdot)\) n/a 21856 8
16272.2.fl \(\chi_{16272}(95, \cdot)\) n/a 5472 8
16272.2.fo \(\chi_{16272}(157, \cdot)\) n/a 21856 8
16272.2.fq \(\chi_{16272}(1907, \cdot)\) n/a 10944 12
16272.2.fs \(\chi_{16272}(325, \cdot)\) n/a 13656 12
16272.2.fv \(\chi_{16272}(323, \cdot)\) n/a 10944 12
16272.2.fx \(\chi_{16272}(1259, \cdot)\) n/a 10944 12
16272.2.ga \(\chi_{16272}(145, \cdot)\) n/a 3408 12
16272.2.ge \(\chi_{16272}(109, \cdot)\) n/a 13656 12
16272.2.gg \(\chi_{16272}(685, \cdot)\) n/a 13656 12
16272.2.gi \(\chi_{16272}(1727, \cdot)\) n/a 2736 12
16272.2.gj \(\chi_{16272}(395, \cdot)\) n/a 10944 12
16272.2.gl \(\chi_{16272}(1477, \cdot)\) n/a 13656 12
16272.2.gq \(\chi_{16272}(335, \cdot)\) n/a 8208 12
16272.2.gu \(\chi_{16272}(97, \cdot)\) n/a 8184 12
16272.2.gy \(\chi_{16272}(911, \cdot)\) n/a 8208 12
16272.2.hc \(\chi_{16272}(605, \cdot)\) n/a 43712 16
16272.2.hf \(\chi_{16272}(607, \cdot)\) n/a 10944 16
16272.2.hj \(\chi_{16272}(749, \cdot)\) n/a 43712 16
16272.2.hk \(\chi_{16272}(3235, \cdot)\) n/a 43712 16
16272.2.hn \(\chi_{16272}(65, \cdot)\) n/a 10912 16
16272.2.hr \(\chi_{16272}(643, \cdot)\) n/a 43712 16
16272.2.hs \(\chi_{16272}(539, \cdot)\) n/a 21888 24
16272.2.hw \(\chi_{16272}(289, \cdot)\) n/a 6816 24
16272.2.hz \(\chi_{16272}(251, \cdot)\) n/a 21888 24
16272.2.ia \(\chi_{16272}(1117, \cdot)\) n/a 27312 24
16272.2.ic \(\chi_{16272}(287, \cdot)\) n/a 5472 24
16272.2.ih \(\chi_{16272}(2269, \cdot)\) n/a 27312 24
16272.2.ii \(\chi_{16272}(805, \cdot)\) n/a 65568 24
16272.2.ik \(\chi_{16272}(563, \cdot)\) n/a 65568 24
16272.2.im \(\chi_{16272}(1919, \cdot)\) n/a 16416 24
16272.2.io \(\chi_{16272}(445, \cdot)\) n/a 65568 24
16272.2.iq \(\chi_{16272}(85, \cdot)\) n/a 65568 24
16272.2.iu \(\chi_{16272}(337, \cdot)\) n/a 16368 24
16272.2.ix \(\chi_{16272}(83, \cdot)\) n/a 65568 24
16272.2.iz \(\chi_{16272}(275, \cdot)\) n/a 65568 24
16272.2.jd \(\chi_{16272}(1525, \cdot)\) n/a 65568 24
16272.2.jf \(\chi_{16272}(347, \cdot)\) n/a 65568 24
16272.2.jh \(\chi_{16272}(125, \cdot)\) n/a 43776 48
16272.2.jj \(\chi_{16272}(271, \cdot)\) n/a 13680 48
16272.2.jm \(\chi_{16272}(197, \cdot)\) n/a 43776 48
16272.2.jp \(\chi_{16272}(19, \cdot)\) n/a 54624 48
16272.2.jr \(\chi_{16272}(17, \cdot)\) n/a 10944 48
16272.2.ju \(\chi_{16272}(811, \cdot)\) n/a 54624 48
16272.2.jw \(\chi_{16272}(277, \cdot)\) n/a 131136 48
16272.2.jz \(\chi_{16272}(239, \cdot)\) n/a 32832 48
16272.2.kd \(\chi_{16272}(13, \cdot)\) n/a 131136 48
16272.2.ke \(\chi_{16272}(515, \cdot)\) n/a 131136 48
16272.2.kj \(\chi_{16272}(529, \cdot)\) n/a 32736 48
16272.2.kl \(\chi_{16272}(11, \cdot)\) n/a 131136 48
16272.2.km \(\chi_{16272}(259, \cdot)\) n/a 262272 96
16272.2.kq \(\chi_{16272}(209, \cdot)\) n/a 65472 96
16272.2.kt \(\chi_{16272}(43, \cdot)\) n/a 262272 96
16272.2.ku \(\chi_{16272}(5, \cdot)\) n/a 262272 96
16272.2.ky \(\chi_{16272}(79, \cdot)\) n/a 65664 96
16272.2.lb \(\chi_{16272}(101, \cdot)\) n/a 262272 96

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(16272))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(16272)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(113))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(226))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(339))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(452))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(678))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(904))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1017))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1356))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1808))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2034))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2712))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4068))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5424))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8136))\)\(^{\oplus 2}\)