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Properties

Label 8967.2
Level 8967
Weight 2
Dimension 2092156
Nonzero newspaces 120
Sturm bound 11665920

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Defining parameters

Level: \( N \) = \( 8967 = 3 \cdot 7^{2} \cdot 61 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 120 \)
Sturm bound: \(11665920\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8967))\).

Total New Old
Modular forms 2930880 2103604 827276
Cusp forms 2902081 2092156 809925
Eisenstein series 28799 11448 17351

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8967))\)

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
8967.2.a \(\chi_{8967}(1, \cdot)\) 8967.2.a.a 1 1
8967.2.a.b 1
8967.2.a.c 1
8967.2.a.d 1
8967.2.a.e 1
8967.2.a.f 1
8967.2.a.g 1
8967.2.a.h 1
8967.2.a.i 1
8967.2.a.j 1
8967.2.a.k 1
8967.2.a.l 1
8967.2.a.m 1
8967.2.a.n 2
8967.2.a.o 2
8967.2.a.p 2
8967.2.a.q 2
8967.2.a.r 2
8967.2.a.s 3
8967.2.a.t 4
8967.2.a.u 5
8967.2.a.v 5
8967.2.a.w 5
8967.2.a.x 6
8967.2.a.y 6
8967.2.a.z 8
8967.2.a.ba 10
8967.2.a.bb 10
8967.2.a.bc 10
8967.2.a.bd 11
8967.2.a.be 15
8967.2.a.bf 15
8967.2.a.bg 16
8967.2.a.bh 16
8967.2.a.bi 19
8967.2.a.bj 19
8967.2.a.bk 21
8967.2.a.bl 21
8967.2.a.bm 21
8967.2.a.bn 21
8967.2.a.bo 22
8967.2.a.bp 22
8967.2.a.bq 38
8967.2.a.br 38
8967.2.d \(\chi_{8967}(6467, \cdot)\) n/a 800 1
8967.2.e \(\chi_{8967}(2500, \cdot)\) n/a 422 1
8967.2.h \(\chi_{8967}(8966, \cdot)\) n/a 820 1
8967.2.i \(\chi_{8967}(1843, \cdot)\) n/a 826 2
8967.2.j \(\chi_{8967}(1831, \cdot)\) n/a 800 2
8967.2.k \(\chi_{8967}(2941, \cdot)\) n/a 850 2
8967.2.l \(\chi_{8967}(4195, \cdot)\) n/a 826 2
8967.2.o \(\chi_{8967}(538, \cdot)\) n/a 824 2
8967.2.p \(\chi_{8967}(50, \cdot)\) n/a 1676 2
8967.2.q \(\chi_{8967}(4999, \cdot)\) n/a 1696 4
8967.2.t \(\chi_{8967}(1390, \cdot)\) n/a 826 2
8967.2.u \(\chi_{8967}(3890, \cdot)\) n/a 1638 2
8967.2.v \(\chi_{8967}(1097, \cdot)\) n/a 1636 2
8967.2.w \(\chi_{8967}(1844, \cdot)\) n/a 1638 2
8967.2.x \(\chi_{8967}(3674, \cdot)\) n/a 1636 2
8967.2.be \(\chi_{8967}(6175, \cdot)\) n/a 846 2
8967.2.bf \(\chi_{8967}(440, \cdot)\) n/a 1636 2
8967.2.bg \(\chi_{8967}(4637, \cdot)\) n/a 1600 2
8967.2.bh \(\chi_{8967}(7429, \cdot)\) n/a 826 2
8967.2.bi \(\chi_{8967}(962, \cdot)\) n/a 1638 2
8967.2.bj \(\chi_{8967}(1402, \cdot)\) n/a 828 2
8967.2.bs \(\chi_{8967}(4196, \cdot)\) n/a 1638 2
8967.2.bt \(\chi_{8967}(1282, \cdot)\) n/a 3360 6
8967.2.bu \(\chi_{8967}(881, \cdot)\) n/a 3280 4
8967.2.bx \(\chi_{8967}(2498, \cdot)\) n/a 3280 4
8967.2.by \(\chi_{8967}(3382, \cdot)\) n/a 1688 4
8967.2.cd \(\chi_{8967}(2774, \cdot)\) n/a 3276 4
8967.2.ce \(\chi_{8967}(2236, \cdot)\) n/a 1652 4
8967.2.cf \(\chi_{8967}(1048, \cdot)\) n/a 1656 4
8967.2.cg \(\chi_{8967}(2480, \cdot)\) n/a 3276 4
8967.2.ch \(\chi_{8967}(3578, \cdot)\) n/a 3348 4
8967.2.ci \(\chi_{8967}(4066, \cdot)\) n/a 1656 4
8967.2.cj \(\chi_{8967}(2530, \cdot)\) n/a 1652 4
8967.2.ck \(\chi_{8967}(1292, \cdot)\) n/a 3272 4
8967.2.cr \(\chi_{8967}(1280, \cdot)\) n/a 6912 6
8967.2.cu \(\chi_{8967}(1219, \cdot)\) n/a 3480 6
8967.2.cv \(\chi_{8967}(62, \cdot)\) n/a 6720 6
8967.2.cy \(\chi_{8967}(361, \cdot)\) n/a 3304 8
8967.2.cz \(\chi_{8967}(1537, \cdot)\) n/a 3304 8
8967.2.da \(\chi_{8967}(508, \cdot)\) n/a 3312 8
8967.2.db \(\chi_{8967}(442, \cdot)\) n/a 3400 8
8967.2.dc \(\chi_{8967}(1126, \cdot)\) n/a 3296 8
8967.2.dd \(\chi_{8967}(638, \cdot)\) n/a 6704 8
8967.2.dg \(\chi_{8967}(352, \cdot)\) n/a 6948 12
8967.2.dh \(\chi_{8967}(169, \cdot)\) n/a 6936 12
8967.2.di \(\chi_{8967}(184, \cdot)\) n/a 6720 12
8967.2.dj \(\chi_{8967}(562, \cdot)\) n/a 6948 12
8967.2.dk \(\chi_{8967}(743, \cdot)\) n/a 13824 12
8967.2.dl \(\chi_{8967}(1231, \cdot)\) n/a 6960 12
8967.2.do \(\chi_{8967}(1391, \cdot)\) n/a 6552 8
8967.2.dx \(\chi_{8967}(736, \cdot)\) n/a 3384 8
8967.2.dy \(\chi_{8967}(1175, \cdot)\) n/a 6544 8
8967.2.dz \(\chi_{8967}(668, \cdot)\) n/a 6544 8
8967.2.ea \(\chi_{8967}(961, \cdot)\) n/a 3304 8
8967.2.eb \(\chi_{8967}(1550, \cdot)\) n/a 6552 8
8967.2.ec \(\chi_{8967}(2284, \cdot)\) n/a 3312 8
8967.2.ej \(\chi_{8967}(1979, \cdot)\) n/a 6544 8
8967.2.ek \(\chi_{8967}(80, \cdot)\) n/a 6552 8
8967.2.el \(\chi_{8967}(293, \cdot)\) n/a 6544 8
8967.2.em \(\chi_{8967}(655, \cdot)\) n/a 3304 8
8967.2.en \(\chi_{8967}(362, \cdot)\) n/a 6552 8
8967.2.eq \(\chi_{8967}(253, \cdot)\) n/a 13920 24
8967.2.er \(\chi_{8967}(353, \cdot)\) n/a 13836 12
8967.2.fa \(\chi_{8967}(121, \cdot)\) n/a 6936 12
8967.2.fb \(\chi_{8967}(257, \cdot)\) n/a 13836 12
8967.2.fc \(\chi_{8967}(319, \cdot)\) n/a 6948 12
8967.2.fd \(\chi_{8967}(794, \cdot)\) n/a 13440 12
8967.2.fe \(\chi_{8967}(230, \cdot)\) n/a 13848 12
8967.2.ff \(\chi_{8967}(841, \cdot)\) n/a 6936 12
8967.2.fm \(\chi_{8967}(902, \cdot)\) n/a 13848 12
8967.2.fn \(\chi_{8967}(563, \cdot)\) n/a 13836 12
8967.2.fo \(\chi_{8967}(731, \cdot)\) n/a 13848 12
8967.2.fp \(\chi_{8967}(47, \cdot)\) n/a 13836 12
8967.2.fq \(\chi_{8967}(109, \cdot)\) n/a 6948 12
8967.2.fz \(\chi_{8967}(313, \cdot)\) n/a 6624 16
8967.2.ga \(\chi_{8967}(932, \cdot)\) n/a 13392 16
8967.2.gb \(\chi_{8967}(128, \cdot)\) n/a 13104 16
8967.2.gc \(\chi_{8967}(31, \cdot)\) n/a 6608 16
8967.2.gd \(\chi_{8967}(1420, \cdot)\) n/a 6624 16
8967.2.ge \(\chi_{8967}(557, \cdot)\) n/a 13088 16
8967.2.gf \(\chi_{8967}(116, \cdot)\) n/a 13104 16
8967.2.gg \(\chi_{8967}(166, \cdot)\) n/a 6608 16
8967.2.gl \(\chi_{8967}(64, \cdot)\) n/a 13920 24
8967.2.gm \(\chi_{8967}(20, \cdot)\) n/a 27648 24
8967.2.gp \(\chi_{8967}(41, \cdot)\) n/a 27648 24
8967.2.gw \(\chi_{8967}(11, \cdot)\) n/a 27696 24
8967.2.gx \(\chi_{8967}(223, \cdot)\) n/a 13872 24
8967.2.gy \(\chi_{8967}(40, \cdot)\) n/a 13896 24
8967.2.gz \(\chi_{8967}(32, \cdot)\) n/a 27672 24
8967.2.ha \(\chi_{8967}(29, \cdot)\) n/a 27696 24
8967.2.hb \(\chi_{8967}(355, \cdot)\) n/a 13872 24
8967.2.hc \(\chi_{8967}(334, \cdot)\) n/a 13896 24
8967.2.hd \(\chi_{8967}(212, \cdot)\) n/a 27672 24
8967.2.hg \(\chi_{8967}(22, \cdot)\) n/a 27744 48
8967.2.hh \(\chi_{8967}(58, \cdot)\) n/a 27744 48
8967.2.hi \(\chi_{8967}(16, \cdot)\) n/a 27792 48
8967.2.hj \(\chi_{8967}(382, \cdot)\) n/a 27792 48
8967.2.hm \(\chi_{8967}(8, \cdot)\) n/a 55296 48
8967.2.hn \(\chi_{8967}(160, \cdot)\) n/a 27840 48
8967.2.hq \(\chi_{8967}(530, \cdot)\) n/a 55344 48
8967.2.hr \(\chi_{8967}(46, \cdot)\) n/a 27792 48
8967.2.hs \(\chi_{8967}(167, \cdot)\) n/a 55392 48
8967.2.ht \(\chi_{8967}(5, \cdot)\) n/a 55344 48
8967.2.hu \(\chi_{8967}(332, \cdot)\) n/a 55392 48
8967.2.ib \(\chi_{8967}(88, \cdot)\) n/a 27744 48
8967.2.ic \(\chi_{8967}(164, \cdot)\) n/a 55344 48
8967.2.id \(\chi_{8967}(4, \cdot)\) n/a 27792 48
8967.2.ie \(\chi_{8967}(131, \cdot)\) n/a 55392 48
8967.2.if \(\chi_{8967}(83, \cdot)\) n/a 55392 48
8967.2.ig \(\chi_{8967}(106, \cdot)\) n/a 27744 48
8967.2.ip \(\chi_{8967}(110, \cdot)\) n/a 55344 48
8967.2.is \(\chi_{8967}(115, \cdot)\) n/a 55584 96
8967.2.it \(\chi_{8967}(44, \cdot)\) n/a 110688 96
8967.2.iu \(\chi_{8967}(23, \cdot)\) n/a 110784 96
8967.2.iv \(\chi_{8967}(10, \cdot)\) n/a 55584 96
8967.2.iw \(\chi_{8967}(55, \cdot)\) n/a 55488 96
8967.2.ix \(\chi_{8967}(71, \cdot)\) n/a 110784 96
8967.2.iy \(\chi_{8967}(2, \cdot)\) n/a 110688 96
8967.2.iz \(\chi_{8967}(94, \cdot)\) n/a 55488 96

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8967))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8967)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(61))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(183))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(427))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1281))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2989))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8967))\)\(^{\oplus 1}\)