Properties

Label 4008.2
Level 4008
Weight 2
Dimension 187570
Nonzero newspaces 12
Sturm bound 1784832

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Defining parameters

Level: \( N \) = \( 4008 = 2^{3} \cdot 3 \cdot 167 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(1784832\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4008))\).

Total New Old
Modular forms 450192 188890 261302
Cusp forms 442225 187570 254655
Eisenstein series 7967 1320 6647

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4008))\)

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
4008.2.a \(\chi_{4008}(1, \cdot)\) 4008.2.a.a 1 1
4008.2.a.b 1
4008.2.a.c 1
4008.2.a.d 1
4008.2.a.e 3
4008.2.a.f 5
4008.2.a.g 7
4008.2.a.h 8
4008.2.a.i 9
4008.2.a.j 10
4008.2.a.k 11
4008.2.a.l 12
4008.2.a.m 13
4008.2.b \(\chi_{4008}(2671, \cdot)\) None 0 1
4008.2.e \(\chi_{4008}(335, \cdot)\) None 0 1
4008.2.f \(\chi_{4008}(2005, \cdot)\) n/a 332 1
4008.2.i \(\chi_{4008}(3005, \cdot)\) n/a 668 1
4008.2.j \(\chi_{4008}(2339, \cdot)\) n/a 664 1
4008.2.m \(\chi_{4008}(667, \cdot)\) n/a 336 1
4008.2.n \(\chi_{4008}(1001, \cdot)\) n/a 168 1
4008.2.q \(\chi_{4008}(25, \cdot)\) n/a 6888 82
4008.2.t \(\chi_{4008}(17, \cdot)\) n/a 13776 82
4008.2.u \(\chi_{4008}(43, \cdot)\) n/a 27552 82
4008.2.x \(\chi_{4008}(11, \cdot)\) n/a 54776 82
4008.2.y \(\chi_{4008}(5, \cdot)\) n/a 54776 82
4008.2.bb \(\chi_{4008}(61, \cdot)\) n/a 27552 82
4008.2.bc \(\chi_{4008}(47, \cdot)\) None 0 82
4008.2.bf \(\chi_{4008}(55, \cdot)\) None 0 82

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4008))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4008)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(167))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(334))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(501))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(668))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1002))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1336))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2004))\)\(^{\oplus 2}\)