Properties

Label 4026.2
Level 4026
Weight 2
Dimension 109677
Nonzero newspaces 84
Sturm bound 1785600

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Defining parameters

Level: \( N \) = \( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 84 \)
Sturm bound: \(1785600\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4026))\).

Total New Old
Modular forms 451200 109677 341523
Cusp forms 441601 109677 331924
Eisenstein series 9599 0 9599

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4026))\)

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
4026.2.a \(\chi_{4026}(1, \cdot)\) 4026.2.a.a 1 1
4026.2.a.b 1
4026.2.a.c 1
4026.2.a.d 1
4026.2.a.e 1
4026.2.a.f 1
4026.2.a.g 1
4026.2.a.h 1
4026.2.a.i 1
4026.2.a.j 1
4026.2.a.k 2
4026.2.a.l 2
4026.2.a.m 2
4026.2.a.n 3
4026.2.a.o 3
4026.2.a.p 3
4026.2.a.q 4
4026.2.a.r 4
4026.2.a.s 4
4026.2.a.t 4
4026.2.a.u 5
4026.2.a.v 5
4026.2.a.w 6
4026.2.a.x 6
4026.2.a.y 7
4026.2.a.z 7
4026.2.a.ba 7
4026.2.a.bb 8
4026.2.a.bc 9
4026.2.b \(\chi_{4026}(2441, \cdot)\) n/a 240 1
4026.2.d \(\chi_{4026}(4025, \cdot)\) n/a 248 1
4026.2.g \(\chi_{4026}(1585, \cdot)\) n/a 104 1
4026.2.i \(\chi_{4026}(2575, \cdot)\) n/a 208 2
4026.2.j \(\chi_{4026}(1231, \cdot)\) n/a 248 2
4026.2.m \(\chi_{4026}(1475, \cdot)\) n/a 408 2
4026.2.n \(\chi_{4026}(619, \cdot)\) n/a 496 4
4026.2.o \(\chi_{4026}(949, \cdot)\) n/a 496 4
4026.2.p \(\chi_{4026}(367, \cdot)\) n/a 480 4
4026.2.q \(\chi_{4026}(1057, \cdot)\) n/a 432 4
4026.2.r \(\chi_{4026}(1351, \cdot)\) n/a 496 4
4026.2.s \(\chi_{4026}(1681, \cdot)\) n/a 496 4
4026.2.u \(\chi_{4026}(1783, \cdot)\) n/a 200 2
4026.2.x \(\chi_{4026}(197, \cdot)\) n/a 496 2
4026.2.z \(\chi_{4026}(989, \cdot)\) n/a 496 2
4026.2.bb \(\chi_{4026}(41, \cdot)\) n/a 992 4
4026.2.bd \(\chi_{4026}(569, \cdot)\) n/a 992 4
4026.2.be \(\chi_{4026}(895, \cdot)\) n/a 496 4
4026.2.bl \(\chi_{4026}(487, \cdot)\) n/a 496 4
4026.2.bm \(\chi_{4026}(235, \cdot)\) n/a 496 4
4026.2.bn \(\chi_{4026}(163, \cdot)\) n/a 496 4
4026.2.br \(\chi_{4026}(529, \cdot)\) n/a 416 4
4026.2.bu \(\chi_{4026}(497, \cdot)\) n/a 992 4
4026.2.bv \(\chi_{4026}(857, \cdot)\) n/a 992 4
4026.2.bz \(\chi_{4026}(1139, \cdot)\) n/a 992 4
4026.2.ca \(\chi_{4026}(1613, \cdot)\) n/a 992 4
4026.2.cb \(\chi_{4026}(365, \cdot)\) n/a 992 4
4026.2.cd \(\chi_{4026}(131, \cdot)\) n/a 992 4
4026.2.ch \(\chi_{4026}(611, \cdot)\) n/a 960 4
4026.2.ci \(\chi_{4026}(95, \cdot)\) n/a 992 4
4026.2.cj \(\chi_{4026}(1559, \cdot)\) n/a 992 4
4026.2.cm \(\chi_{4026}(149, \cdot)\) n/a 992 4
4026.2.co \(\chi_{4026}(1699, \cdot)\) n/a 496 4
4026.2.cq \(\chi_{4026}(947, \cdot)\) n/a 832 4
4026.2.ct \(\chi_{4026}(703, \cdot)\) n/a 496 4
4026.2.cu \(\chi_{4026}(25, \cdot)\) n/a 992 8
4026.2.cv \(\chi_{4026}(361, \cdot)\) n/a 992 8
4026.2.cw \(\chi_{4026}(199, \cdot)\) n/a 832 8
4026.2.cx \(\chi_{4026}(301, \cdot)\) n/a 992 8
4026.2.cy \(\chi_{4026}(757, \cdot)\) n/a 992 8
4026.2.cz \(\chi_{4026}(169, \cdot)\) n/a 992 8
4026.2.db \(\chi_{4026}(85, \cdot)\) n/a 992 8
4026.2.dd \(\chi_{4026}(1379, \cdot)\) n/a 1984 8
4026.2.de \(\chi_{4026}(191, \cdot)\) n/a 1984 8
4026.2.df \(\chi_{4026}(389, \cdot)\) n/a 1984 8
4026.2.dg \(\chi_{4026}(377, \cdot)\) n/a 1984 8
4026.2.dl \(\chi_{4026}(23, \cdot)\) n/a 1632 8
4026.2.dm \(\chi_{4026}(175, \cdot)\) n/a 992 8
4026.2.dr \(\chi_{4026}(211, \cdot)\) n/a 992 8
4026.2.ds \(\chi_{4026}(877, \cdot)\) n/a 992 8
4026.2.dt \(\chi_{4026}(721, \cdot)\) n/a 992 8
4026.2.du \(\chi_{4026}(145, \cdot)\) n/a 992 8
4026.2.dw \(\chi_{4026}(53, \cdot)\) n/a 1984 8
4026.2.dz \(\chi_{4026}(229, \cdot)\) n/a 992 8
4026.2.eb \(\chi_{4026}(431, \cdot)\) n/a 1984 8
4026.2.ee \(\chi_{4026}(413, \cdot)\) n/a 1984 8
4026.2.ef \(\chi_{4026}(503, \cdot)\) n/a 1984 8
4026.2.eg \(\chi_{4026}(83, \cdot)\) n/a 1984 8
4026.2.ek \(\chi_{4026}(1781, \cdot)\) n/a 1984 8
4026.2.em \(\chi_{4026}(167, \cdot)\) n/a 1984 8
4026.2.en \(\chi_{4026}(107, \cdot)\) n/a 1984 8
4026.2.eo \(\chi_{4026}(563, \cdot)\) n/a 1984 8
4026.2.es \(\chi_{4026}(65, \cdot)\) n/a 1984 8
4026.2.et \(\chi_{4026}(1601, \cdot)\) n/a 1984 8
4026.2.ew \(\chi_{4026}(463, \cdot)\) n/a 800 8
4026.2.fa \(\chi_{4026}(685, \cdot)\) n/a 992 8
4026.2.fb \(\chi_{4026}(97, \cdot)\) n/a 992 8
4026.2.fc \(\chi_{4026}(1147, \cdot)\) n/a 992 8
4026.2.fj \(\chi_{4026}(49, \cdot)\) n/a 992 8
4026.2.fk \(\chi_{4026}(545, \cdot)\) n/a 1984 8
4026.2.fm \(\chi_{4026}(161, \cdot)\) n/a 1984 8
4026.2.fp \(\chi_{4026}(59, \cdot)\) n/a 3968 16
4026.2.fr \(\chi_{4026}(7, \cdot)\) n/a 1984 16
4026.2.fs \(\chi_{4026}(151, \cdot)\) n/a 1984 16
4026.2.ft \(\chi_{4026}(349, \cdot)\) n/a 1984 16
4026.2.fu \(\chi_{4026}(139, \cdot)\) n/a 1984 16
4026.2.fz \(\chi_{4026}(43, \cdot)\) n/a 1984 16
4026.2.ga \(\chi_{4026}(287, \cdot)\) n/a 3328 16
4026.2.gf \(\chi_{4026}(467, \cdot)\) n/a 3968 16
4026.2.gg \(\chi_{4026}(185, \cdot)\) n/a 3968 16
4026.2.gh \(\chi_{4026}(251, \cdot)\) n/a 3968 16
4026.2.gi \(\chi_{4026}(71, \cdot)\) n/a 3968 16
4026.2.gk \(\chi_{4026}(79, \cdot)\) n/a 1984 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4026))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4026)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(61))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(122))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(183))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(366))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(671))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1342))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2013))\)\(^{\oplus 2}\)