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Properties

Label 4840.2
Level 4840
Weight 2
Dimension 351769
Nonzero newspaces 36
Sturm bound 2787840

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Defining parameters

Level: \( N \) = \( 4840 = 2^{3} \cdot 5 \cdot 11^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 36 \)
Sturm bound: \(2787840\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4840))\).

Total New Old
Modular forms 704640 355141 349499
Cusp forms 689281 351769 337512
Eisenstein series 15359 3372 11987

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4840))\)

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
4840.2.a \(\chi_{4840}(1, \cdot)\) 4840.2.a.a 1 1
4840.2.a.b 1
4840.2.a.c 1
4840.2.a.d 1
4840.2.a.e 1
4840.2.a.f 1
4840.2.a.g 1
4840.2.a.h 1
4840.2.a.i 1
4840.2.a.j 2
4840.2.a.k 2
4840.2.a.l 2
4840.2.a.m 2
4840.2.a.n 2
4840.2.a.o 2
4840.2.a.p 2
4840.2.a.q 3
4840.2.a.r 3
4840.2.a.s 3
4840.2.a.t 3
4840.2.a.u 3
4840.2.a.v 3
4840.2.a.w 4
4840.2.a.x 4
4840.2.a.y 4
4840.2.a.z 4
4840.2.a.ba 6
4840.2.a.bb 6
4840.2.a.bc 6
4840.2.a.bd 6
4840.2.a.be 6
4840.2.a.bf 6
4840.2.a.bg 8
4840.2.a.bh 8
4840.2.b \(\chi_{4840}(969, \cdot)\) n/a 164 1
4840.2.c \(\chi_{4840}(2419, \cdot)\) n/a 632 1
4840.2.f \(\chi_{4840}(3871, \cdot)\) None 0 1
4840.2.g \(\chi_{4840}(2421, \cdot)\) n/a 436 1
4840.2.l \(\chi_{4840}(3389, \cdot)\) n/a 636 1
4840.2.m \(\chi_{4840}(4839, \cdot)\) None 0 1
4840.2.p \(\chi_{4840}(1451, \cdot)\) n/a 432 1
4840.2.r \(\chi_{4840}(243, \cdot)\) n/a 1272 2
4840.2.t \(\chi_{4840}(1693, \cdot)\) n/a 1264 2
4840.2.v \(\chi_{4840}(2177, \cdot)\) n/a 324 2
4840.2.x \(\chi_{4840}(727, \cdot)\) None 0 2
4840.2.y \(\chi_{4840}(81, \cdot)\) n/a 432 4
4840.2.z \(\chi_{4840}(1371, \cdot)\) n/a 1728 4
4840.2.bc \(\chi_{4840}(239, \cdot)\) None 0 4
4840.2.bd \(\chi_{4840}(269, \cdot)\) n/a 2528 4
4840.2.bi \(\chi_{4840}(1461, \cdot)\) n/a 1728 4
4840.2.bj \(\chi_{4840}(2151, \cdot)\) None 0 4
4840.2.bm \(\chi_{4840}(699, \cdot)\) n/a 2528 4
4840.2.bn \(\chi_{4840}(9, \cdot)\) n/a 648 4
4840.2.bo \(\chi_{4840}(441, \cdot)\) n/a 1320 10
4840.2.bp \(\chi_{4840}(233, \cdot)\) n/a 1296 8
4840.2.br \(\chi_{4840}(487, \cdot)\) None 0 8
4840.2.bt \(\chi_{4840}(3, \cdot)\) n/a 5056 8
4840.2.bv \(\chi_{4840}(717, \cdot)\) n/a 5056 8
4840.2.bz \(\chi_{4840}(221, \cdot)\) n/a 5280 10
4840.2.ca \(\chi_{4840}(351, \cdot)\) None 0 10
4840.2.cd \(\chi_{4840}(219, \cdot)\) n/a 7880 10
4840.2.ce \(\chi_{4840}(89, \cdot)\) n/a 1980 10
4840.2.cf \(\chi_{4840}(131, \cdot)\) n/a 5280 10
4840.2.ci \(\chi_{4840}(439, \cdot)\) None 0 10
4840.2.cj \(\chi_{4840}(309, \cdot)\) n/a 7880 10
4840.2.cm \(\chi_{4840}(23, \cdot)\) None 0 20
4840.2.co \(\chi_{4840}(153, \cdot)\) n/a 3960 20
4840.2.cq \(\chi_{4840}(197, \cdot)\) n/a 15760 20
4840.2.cs \(\chi_{4840}(67, \cdot)\) n/a 15760 20
4840.2.cu \(\chi_{4840}(201, \cdot)\) n/a 5280 40
4840.2.cx \(\chi_{4840}(69, \cdot)\) n/a 31520 40
4840.2.cy \(\chi_{4840}(39, \cdot)\) None 0 40
4840.2.db \(\chi_{4840}(51, \cdot)\) n/a 21120 40
4840.2.dc \(\chi_{4840}(49, \cdot)\) n/a 7920 40
4840.2.dd \(\chi_{4840}(19, \cdot)\) n/a 31520 40
4840.2.dg \(\chi_{4840}(151, \cdot)\) None 0 40
4840.2.dh \(\chi_{4840}(141, \cdot)\) n/a 21120 40
4840.2.dl \(\chi_{4840}(13, \cdot)\) n/a 63040 80
4840.2.dn \(\chi_{4840}(147, \cdot)\) n/a 63040 80
4840.2.dp \(\chi_{4840}(47, \cdot)\) None 0 80
4840.2.dr \(\chi_{4840}(17, \cdot)\) n/a 15840 80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4840))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4840)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(220))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(242))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(440))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(484))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(605))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(968))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1210))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2420))\)\(^{\oplus 2}\)