Properties

Label 8034.2
Level 8034
Weight 2
Dimension 440145
Nonzero newspaces 60
Sturm bound 7128576

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Defining parameters

Level: \( N \) = \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 60 \)
Sturm bound: \(7128576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8034))\).

Total New Old
Modular forms 1791936 440145 1351791
Cusp forms 1772353 440145 1332208
Eisenstein series 19583 0 19583

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8034))\)

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
8034.2.a \(\chi_{8034}(1, \cdot)\) 8034.2.a.a 1 1
8034.2.a.b 1
8034.2.a.c 1
8034.2.a.d 1
8034.2.a.e 1
8034.2.a.f 1
8034.2.a.g 1
8034.2.a.h 1
8034.2.a.i 1
8034.2.a.j 1
8034.2.a.k 1
8034.2.a.l 2
8034.2.a.m 2
8034.2.a.n 4
8034.2.a.o 7
8034.2.a.p 8
8034.2.a.q 8
8034.2.a.r 9
8034.2.a.s 10
8034.2.a.t 11
8034.2.a.u 11
8034.2.a.v 11
8034.2.a.w 12
8034.2.a.x 13
8034.2.a.y 13
8034.2.a.z 14
8034.2.a.ba 14
8034.2.a.bb 14
8034.2.a.bc 15
8034.2.a.bd 16
8034.2.b \(\chi_{8034}(8033, \cdot)\) n/a 488 1
8034.2.c \(\chi_{8034}(5563, \cdot)\) n/a 236 1
8034.2.h \(\chi_{8034}(2471, \cdot)\) n/a 416 1
8034.2.i \(\chi_{8034}(3043, \cdot)\) n/a 416 2
8034.2.j \(\chi_{8034}(4897, \cdot)\) n/a 484 2
8034.2.k \(\chi_{8034}(5515, \cdot)\) n/a 484 2
8034.2.l \(\chi_{8034}(1855, \cdot)\) n/a 480 2
8034.2.m \(\chi_{8034}(2059, \cdot)\) n/a 480 2
8034.2.o \(\chi_{8034}(2267, \cdot)\) n/a 952 2
8034.2.s \(\chi_{8034}(3091, \cdot)\) n/a 472 2
8034.2.t \(\chi_{8034}(5561, \cdot)\) n/a 968 2
8034.2.w \(\chi_{8034}(5825, \cdot)\) n/a 832 2
8034.2.x \(\chi_{8034}(263, \cdot)\) n/a 972 2
8034.2.bc \(\chi_{8034}(1901, \cdot)\) n/a 972 2
8034.2.bd \(\chi_{8034}(1499, \cdot)\) n/a 972 2
8034.2.be \(\chi_{8034}(355, \cdot)\) n/a 484 2
8034.2.bj \(\chi_{8034}(6751, \cdot)\) n/a 484 2
8034.2.bk \(\chi_{8034}(881, \cdot)\) n/a 972 2
8034.2.bl \(\chi_{8034}(571, \cdot)\) n/a 488 2
8034.2.bm \(\chi_{8034}(3353, \cdot)\) n/a 968 2
8034.2.bp \(\chi_{8034}(4325, \cdot)\) n/a 968 2
8034.2.bt \(\chi_{8034}(3343, \cdot)\) n/a 968 4
8034.2.bv \(\chi_{8034}(1649, \cdot)\) n/a 1904 4
8034.2.bw \(\chi_{8034}(3239, \cdot)\) n/a 1944 4
8034.2.bz \(\chi_{8034}(983, \cdot)\) n/a 1936 4
8034.2.cb \(\chi_{8034}(1087, \cdot)\) n/a 976 4
8034.2.cd \(\chi_{8034}(1441, \cdot)\) n/a 976 4
8034.2.ce \(\chi_{8034}(253, \cdot)\) n/a 968 4
8034.2.ch \(\chi_{8034}(149, \cdot)\) n/a 1944 4
8034.2.ci \(\chi_{8034}(79, \cdot)\) n/a 3328 16
8034.2.cj \(\chi_{8034}(209, \cdot)\) n/a 6656 16
8034.2.co \(\chi_{8034}(493, \cdot)\) n/a 3840 16
8034.2.cp \(\chi_{8034}(233, \cdot)\) n/a 7808 16
8034.2.cq \(\chi_{8034}(61, \cdot)\) n/a 7808 32
8034.2.cr \(\chi_{8034}(367, \cdot)\) n/a 7744 32
8034.2.cs \(\chi_{8034}(55, \cdot)\) n/a 7744 32
8034.2.ct \(\chi_{8034}(235, \cdot)\) n/a 6656 32
8034.2.cv \(\chi_{8034}(203, \cdot)\) n/a 15616 32
8034.2.cx \(\chi_{8034}(31, \cdot)\) n/a 7680 32
8034.2.da \(\chi_{8034}(113, \cdot)\) n/a 15488 32
8034.2.dd \(\chi_{8034}(77, \cdot)\) n/a 15488 32
8034.2.de \(\chi_{8034}(25, \cdot)\) n/a 7808 32
8034.2.df \(\chi_{8034}(101, \cdot)\) n/a 15552 32
8034.2.dg \(\chi_{8034}(49, \cdot)\) n/a 7744 32
8034.2.dl \(\chi_{8034}(121, \cdot)\) n/a 7744 32
8034.2.dm \(\chi_{8034}(257, \cdot)\) n/a 15552 32
8034.2.dn \(\chi_{8034}(35, \cdot)\) n/a 15552 32
8034.2.ds \(\chi_{8034}(191, \cdot)\) n/a 15552 32
8034.2.dt \(\chi_{8034}(53, \cdot)\) n/a 13312 32
8034.2.dw \(\chi_{8034}(95, \cdot)\) n/a 15488 32
8034.2.dx \(\chi_{8034}(751, \cdot)\) n/a 7808 32
8034.2.ea \(\chi_{8034}(59, \cdot)\) n/a 31104 64
8034.2.ed \(\chi_{8034}(397, \cdot)\) n/a 15488 64
8034.2.ee \(\chi_{8034}(37, \cdot)\) n/a 15616 64
8034.2.eg \(\chi_{8034}(109, \cdot)\) n/a 15616 64
8034.2.ei \(\chi_{8034}(83, \cdot)\) n/a 30976 64
8034.2.el \(\chi_{8034}(41, \cdot)\) n/a 31104 64
8034.2.em \(\chi_{8034}(137, \cdot)\) n/a 30976 64
8034.2.eo \(\chi_{8034}(67, \cdot)\) n/a 15488 64

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8034))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8034)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(103))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(206))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(309))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(618))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1339))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2678))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4017))\)\(^{\oplus 2}\)