Properties

Label 6018.2
Level 6018
Weight 2
Dimension 248673
Nonzero newspaces 20
Sturm bound 4008960

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Defining parameters

Level: \( N \) = \( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 20 \)
Sturm bound: \(4008960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6018))\).

Total New Old
Modular forms 1009664 248673 760991
Cusp forms 994817 248673 746144
Eisenstein series 14847 0 14847

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6018))\)

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
6018.2.a \(\chi_{6018}(1, \cdot)\) 6018.2.a.a 1 1
6018.2.a.b 1
6018.2.a.c 1
6018.2.a.d 1
6018.2.a.e 1
6018.2.a.f 1
6018.2.a.g 1
6018.2.a.h 1
6018.2.a.i 1
6018.2.a.j 1
6018.2.a.k 1
6018.2.a.l 1
6018.2.a.m 3
6018.2.a.n 4
6018.2.a.o 4
6018.2.a.p 5
6018.2.a.q 6
6018.2.a.r 6
6018.2.a.s 8
6018.2.a.t 8
6018.2.a.u 9
6018.2.a.v 9
6018.2.a.w 9
6018.2.a.x 10
6018.2.a.y 10
6018.2.a.z 11
6018.2.a.ba 12
6018.2.a.bb 13
6018.2.a.bc 14
6018.2.b \(\chi_{6018}(4249, \cdot)\) n/a 176 1
6018.2.e \(\chi_{6018}(1769, \cdot)\) n/a 320 1
6018.2.f \(\chi_{6018}(6017, \cdot)\) n/a 360 1
6018.2.i \(\chi_{6018}(353, \cdot)\) n/a 720 2
6018.2.l \(\chi_{6018}(4603, \cdot)\) n/a 352 2
6018.2.n \(\chi_{6018}(355, \cdot)\) n/a 688 4
6018.2.o \(\chi_{6018}(2123, \cdot)\) n/a 1440 4
6018.2.q \(\chi_{6018}(473, \cdot)\) n/a 2784 8
6018.2.t \(\chi_{6018}(235, \cdot)\) n/a 1440 8
6018.2.u \(\chi_{6018}(205, \cdot)\) n/a 4480 28
6018.2.x \(\chi_{6018}(101, \cdot)\) n/a 10080 28
6018.2.y \(\chi_{6018}(443, \cdot)\) n/a 8960 28
6018.2.bb \(\chi_{6018}(169, \cdot)\) n/a 5040 28
6018.2.bc \(\chi_{6018}(361, \cdot)\) n/a 10080 56
6018.2.bf \(\chi_{6018}(47, \cdot)\) n/a 20160 56
6018.2.bh \(\chi_{6018}(77, \cdot)\) n/a 40320 112
6018.2.bi \(\chi_{6018}(19, \cdot)\) n/a 20160 112
6018.2.bk \(\chi_{6018}(31, \cdot)\) n/a 40320 224
6018.2.bn \(\chi_{6018}(5, \cdot)\) n/a 80640 224

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6018))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6018)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(102))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(118))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(177))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(354))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1003))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2006))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3009))\)\(^{\oplus 2}\)