Properties

 Label 4026.2 Level 4026 Weight 2 Dimension 109677 Nonzero newspaces 84 Sturm bound 1.7856e+06

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

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