Properties

Label 6024.2
Level 6024
Weight 2
Dimension 424240
Nonzero newspaces 24
Sturm bound 4032000

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Defining parameters

Level: \( N \) = \( 6024 = 2^{3} \cdot 3 \cdot 251 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(4032000\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6024))\).

Total New Old
Modular forms 1014000 426232 587768
Cusp forms 1002001 424240 577761
Eisenstein series 11999 1992 10007

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6024))\)

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
6024.2.a \(\chi_{6024}(1, \cdot)\) 6024.2.a.a 1 1
6024.2.a.b 1
6024.2.a.c 1
6024.2.a.d 1
6024.2.a.e 1
6024.2.a.f 1
6024.2.a.g 1
6024.2.a.h 2
6024.2.a.i 2
6024.2.a.j 3
6024.2.a.k 8
6024.2.a.l 11
6024.2.a.m 11
6024.2.a.n 14
6024.2.a.o 14
6024.2.a.p 14
6024.2.a.q 18
6024.2.a.r 20
6024.2.b \(\chi_{6024}(1003, \cdot)\) n/a 504 1
6024.2.e \(\chi_{6024}(503, \cdot)\) None 0 1
6024.2.f \(\chi_{6024}(3013, \cdot)\) n/a 500 1
6024.2.i \(\chi_{6024}(1505, \cdot)\) n/a 252 1
6024.2.j \(\chi_{6024}(3515, \cdot)\) n/a 1000 1
6024.2.m \(\chi_{6024}(4015, \cdot)\) None 0 1
6024.2.n \(\chi_{6024}(4517, \cdot)\) n/a 1004 1
6024.2.q \(\chi_{6024}(721, \cdot)\) n/a 504 4
6024.2.r \(\chi_{6024}(353, \cdot)\) n/a 1008 4
6024.2.u \(\chi_{6024}(1117, \cdot)\) n/a 2016 4
6024.2.v \(\chi_{6024}(1223, \cdot)\) None 0 4
6024.2.y \(\chi_{6024}(283, \cdot)\) n/a 2016 4
6024.2.bb \(\chi_{6024}(389, \cdot)\) n/a 4016 4
6024.2.bc \(\chi_{6024}(2239, \cdot)\) None 0 4
6024.2.bf \(\chi_{6024}(1619, \cdot)\) n/a 4016 4
6024.2.bg \(\chi_{6024}(25, \cdot)\) n/a 2520 20
6024.2.bh \(\chi_{6024}(1067, \cdot)\) n/a 20080 20
6024.2.bi \(\chi_{6024}(653, \cdot)\) n/a 20080 20
6024.2.bj \(\chi_{6024}(151, \cdot)\) None 0 20
6024.2.bo \(\chi_{6024}(377, \cdot)\) n/a 5040 20
6024.2.bp \(\chi_{6024}(187, \cdot)\) n/a 10080 20
6024.2.bq \(\chi_{6024}(455, \cdot)\) None 0 20
6024.2.br \(\chi_{6024}(565, \cdot)\) n/a 10080 20
6024.2.bw \(\chi_{6024}(49, \cdot)\) n/a 12600 100
6024.2.by \(\chi_{6024}(55, \cdot)\) None 0 100
6024.2.cb \(\chi_{6024}(13, \cdot)\) n/a 50400 100
6024.2.cd \(\chi_{6024}(19, \cdot)\) n/a 50400 100
6024.2.ce \(\chi_{6024}(29, \cdot)\) n/a 100400 100
6024.2.cg \(\chi_{6024}(35, \cdot)\) n/a 100400 100
6024.2.cj \(\chi_{6024}(137, \cdot)\) n/a 25200 100
6024.2.cl \(\chi_{6024}(23, \cdot)\) None 0 100

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6024))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6024)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(251))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(502))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(753))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1004))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1506))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2008))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3012))\)\(^{\oplus 2}\)