Properties

Label 4004.2
Level 4004
Weight 2
Dimension 260824
Nonzero newspaces 120
Sturm bound 1935360

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Defining parameters

Level: \( N \) = \( 4004 = 2^{2} \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 120 \)
Sturm bound: \(1935360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4004))\).

Total New Old
Modular forms 491040 264792 226248
Cusp forms 476641 260824 215817
Eisenstein series 14399 3968 10431

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4004))\)

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
4004.2.a \(\chi_{4004}(1, \cdot)\) 4004.2.a.a 1 1
4004.2.a.b 1
4004.2.a.c 1
4004.2.a.d 4
4004.2.a.e 4
4004.2.a.f 5
4004.2.a.g 6
4004.2.a.h 9
4004.2.a.i 9
4004.2.a.j 10
4004.2.a.k 10
4004.2.b \(\chi_{4004}(3431, \cdot)\) n/a 504 1
4004.2.e \(\chi_{4004}(3849, \cdot)\) 4004.2.e.a 48 1
4004.2.e.b 48
4004.2.f \(\chi_{4004}(1275, \cdot)\) n/a 432 1
4004.2.i \(\chi_{4004}(2001, \cdot)\) n/a 112 1
4004.2.j \(\chi_{4004}(2575, \cdot)\) n/a 480 1
4004.2.m \(\chi_{4004}(2157, \cdot)\) 4004.2.m.a 2 1
4004.2.m.b 30
4004.2.m.c 36
4004.2.n \(\chi_{4004}(727, \cdot)\) n/a 560 1
4004.2.q \(\chi_{4004}(529, \cdot)\) n/a 188 2
4004.2.r \(\chi_{4004}(1145, \cdot)\) n/a 160 2
4004.2.s \(\chi_{4004}(1849, \cdot)\) n/a 144 2
4004.2.t \(\chi_{4004}(1101, \cdot)\) n/a 188 2
4004.2.v \(\chi_{4004}(463, \cdot)\) n/a 840 2
4004.2.w \(\chi_{4004}(265, \cdot)\) n/a 192 2
4004.2.z \(\chi_{4004}(307, \cdot)\) n/a 1328 2
4004.2.ba \(\chi_{4004}(1737, \cdot)\) n/a 168 2
4004.2.bc \(\chi_{4004}(729, \cdot)\) n/a 288 4
4004.2.bd \(\chi_{4004}(901, \cdot)\) n/a 224 2
4004.2.bg \(\chi_{4004}(263, \cdot)\) n/a 1328 2
4004.2.bh \(\chi_{4004}(549, \cdot)\) n/a 224 2
4004.2.bk \(\chi_{4004}(1759, \cdot)\) n/a 1328 2
4004.2.bl \(\chi_{4004}(309, \cdot)\) n/a 136 2
4004.2.bo \(\chi_{4004}(419, \cdot)\) n/a 1120 2
4004.2.bp \(\chi_{4004}(199, \cdot)\) n/a 1120 2
4004.2.bu \(\chi_{4004}(3015, \cdot)\) n/a 1120 2
4004.2.bv \(\chi_{4004}(3301, \cdot)\) n/a 184 2
4004.2.by \(\chi_{4004}(859, \cdot)\) n/a 960 2
4004.2.bz \(\chi_{4004}(815, \cdot)\) n/a 1120 2
4004.2.cc \(\chi_{4004}(2025, \cdot)\) n/a 188 2
4004.2.cf \(\chi_{4004}(1343, \cdot)\) n/a 1120 2
4004.2.cg \(\chi_{4004}(1693, \cdot)\) n/a 224 2
4004.2.cj \(\chi_{4004}(43, \cdot)\) n/a 1008 2
4004.2.ck \(\chi_{4004}(285, \cdot)\) n/a 224 2
4004.2.cn \(\chi_{4004}(2419, \cdot)\) n/a 1152 2
4004.2.co \(\chi_{4004}(835, \cdot)\) n/a 1328 2
4004.2.cr \(\chi_{4004}(1473, \cdot)\) n/a 224 2
4004.2.cs \(\chi_{4004}(1187, \cdot)\) n/a 1328 2
4004.2.cv \(\chi_{4004}(2089, \cdot)\) n/a 224 2
4004.2.cw \(\chi_{4004}(2133, \cdot)\) n/a 192 2
4004.2.cz \(\chi_{4004}(571, \cdot)\) n/a 1328 2
4004.2.da \(\chi_{4004}(153, \cdot)\) n/a 224 2
4004.2.dd \(\chi_{4004}(659, \cdot)\) n/a 1008 2
4004.2.dg \(\chi_{4004}(1739, \cdot)\) n/a 1120 2
4004.2.dh \(\chi_{4004}(485, \cdot)\) n/a 188 2
4004.2.dk \(\chi_{4004}(243, \cdot)\) n/a 1120 2
4004.2.dm \(\chi_{4004}(1455, \cdot)\) n/a 2656 4
4004.2.dp \(\chi_{4004}(1065, \cdot)\) n/a 336 4
4004.2.dq \(\chi_{4004}(27, \cdot)\) n/a 2304 4
4004.2.dt \(\chi_{4004}(545, \cdot)\) n/a 448 4
4004.2.du \(\chi_{4004}(183, \cdot)\) n/a 1728 4
4004.2.dx \(\chi_{4004}(937, \cdot)\) n/a 384 4
4004.2.dy \(\chi_{4004}(519, \cdot)\) n/a 2016 4
4004.2.eb \(\chi_{4004}(353, \cdot)\) n/a 376 4
4004.2.ec \(\chi_{4004}(67, \cdot)\) n/a 2240 4
4004.2.ef \(\chi_{4004}(1055, \cdot)\) n/a 2656 4
4004.2.ei \(\chi_{4004}(197, \cdot)\) n/a 336 4
4004.2.ej \(\chi_{4004}(109, \cdot)\) n/a 448 4
4004.2.ek \(\chi_{4004}(2463, \cdot)\) n/a 2656 4
4004.2.el \(\chi_{4004}(395, \cdot)\) n/a 2656 4
4004.2.eo \(\chi_{4004}(1033, \cdot)\) n/a 448 4
4004.2.er \(\chi_{4004}(639, \cdot)\) n/a 2240 4
4004.2.eu \(\chi_{4004}(1189, \cdot)\) n/a 368 4
4004.2.ev \(\chi_{4004}(1321, \cdot)\) n/a 368 4
4004.2.ew \(\chi_{4004}(2619, \cdot)\) n/a 1680 4
4004.2.ex \(\chi_{4004}(1607, \cdot)\) n/a 2240 4
4004.2.fa \(\chi_{4004}(45, \cdot)\) n/a 376 4
4004.2.fd \(\chi_{4004}(1341, \cdot)\) n/a 448 4
4004.2.fe \(\chi_{4004}(747, \cdot)\) n/a 2656 4
4004.2.fg \(\chi_{4004}(9, \cdot)\) n/a 896 8
4004.2.fh \(\chi_{4004}(113, \cdot)\) n/a 672 8
4004.2.fi \(\chi_{4004}(53, \cdot)\) n/a 768 8
4004.2.fj \(\chi_{4004}(289, \cdot)\) n/a 896 8
4004.2.fk \(\chi_{4004}(57, \cdot)\) n/a 672 8
4004.2.fn \(\chi_{4004}(83, \cdot)\) n/a 5312 8
4004.2.fo \(\chi_{4004}(125, \cdot)\) n/a 896 8
4004.2.fr \(\chi_{4004}(603, \cdot)\) n/a 4032 8
4004.2.ft \(\chi_{4004}(3, \cdot)\) n/a 5312 8
4004.2.fu \(\chi_{4004}(361, \cdot)\) n/a 896 8
4004.2.fx \(\chi_{4004}(355, \cdot)\) n/a 5312 8
4004.2.ga \(\chi_{4004}(211, \cdot)\) n/a 4032 8
4004.2.gb \(\chi_{4004}(1161, \cdot)\) n/a 896 8
4004.2.ge \(\chi_{4004}(51, \cdot)\) n/a 5312 8
4004.2.gf \(\chi_{4004}(677, \cdot)\) n/a 768 8
4004.2.gi \(\chi_{4004}(633, \cdot)\) n/a 896 8
4004.2.gj \(\chi_{4004}(95, \cdot)\) n/a 5312 8
4004.2.gm \(\chi_{4004}(17, \cdot)\) n/a 896 8
4004.2.gn \(\chi_{4004}(107, \cdot)\) n/a 5312 8
4004.2.gq \(\chi_{4004}(79, \cdot)\) n/a 4608 8
4004.2.gr \(\chi_{4004}(129, \cdot)\) n/a 896 8
4004.2.gu \(\chi_{4004}(127, \cdot)\) n/a 4032 8
4004.2.gv \(\chi_{4004}(237, \cdot)\) n/a 896 8
4004.2.gy \(\chi_{4004}(251, \cdot)\) n/a 5312 8
4004.2.hb \(\chi_{4004}(641, \cdot)\) n/a 896 8
4004.2.hc \(\chi_{4004}(159, \cdot)\) n/a 5312 8
4004.2.hf \(\chi_{4004}(339, \cdot)\) n/a 4608 8
4004.2.hg \(\chi_{4004}(25, \cdot)\) n/a 896 8
4004.2.hj \(\chi_{4004}(103, \cdot)\) n/a 5312 8
4004.2.hm \(\chi_{4004}(75, \cdot)\) n/a 5312 8
4004.2.hp \(\chi_{4004}(867, \cdot)\) n/a 5312 8
4004.2.hq \(\chi_{4004}(225, \cdot)\) n/a 672 8
4004.2.ht \(\chi_{4004}(303, \cdot)\) n/a 5312 8
4004.2.hu \(\chi_{4004}(61, \cdot)\) n/a 896 8
4004.2.hx \(\chi_{4004}(919, \cdot)\) n/a 5312 8
4004.2.hy \(\chi_{4004}(101, \cdot)\) n/a 896 8
4004.2.ia \(\chi_{4004}(19, \cdot)\) n/a 10624 16
4004.2.id \(\chi_{4004}(149, \cdot)\) n/a 1792 16
4004.2.ie \(\chi_{4004}(509, \cdot)\) n/a 1792 16
4004.2.ig \(\chi_{4004}(135, \cdot)\) n/a 10624 16
4004.2.ih \(\chi_{4004}(15, \cdot)\) n/a 8064 16
4004.2.im \(\chi_{4004}(5, \cdot)\) n/a 1792 16
4004.2.in \(\chi_{4004}(97, \cdot)\) n/a 1792 16
4004.2.ip \(\chi_{4004}(487, \cdot)\) n/a 10624 16
4004.2.iq \(\chi_{4004}(305, \cdot)\) n/a 1792 16
4004.2.is \(\chi_{4004}(255, \cdot)\) n/a 10624 16
4004.2.it \(\chi_{4004}(167, \cdot)\) n/a 10624 16
4004.2.iy \(\chi_{4004}(541, \cdot)\) n/a 1792 16
4004.2.iz \(\chi_{4004}(85, \cdot)\) n/a 1344 16
4004.2.jb \(\chi_{4004}(227, \cdot)\) n/a 10624 16
4004.2.jc \(\chi_{4004}(163, \cdot)\) n/a 10624 16
4004.2.jf \(\chi_{4004}(201, \cdot)\) n/a 1792 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4004))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4004)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(143))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(182))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(286))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(308))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(364))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(572))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1001))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2002))\)\(^{\oplus 2}\)