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Properties

Label 4016.2
Level 4016
Weight 2
Dimension 282371
Nonzero newspaces 16
Sturm bound 2016000

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Defining parameters

Level: \( N \) = \( 4016 = 2^{4} \cdot 251 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(2016000\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4016))\).

Total New Old
Modular forms 507500 284611 222889
Cusp forms 500501 282371 218130
Eisenstein series 6999 2240 4759

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4016))\)

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
4016.2.a \(\chi_{4016}(1, \cdot)\) 4016.2.a.a 2 1
4016.2.a.b 2
4016.2.a.c 4
4016.2.a.d 5
4016.2.a.e 5
4016.2.a.f 6
4016.2.a.g 7
4016.2.a.h 9
4016.2.a.i 12
4016.2.a.j 14
4016.2.a.k 17
4016.2.a.l 19
4016.2.a.m 23
4016.2.b \(\chi_{4016}(2009, \cdot)\) None 0 1
4016.2.e \(\chi_{4016}(4015, \cdot)\) n/a 126 1
4016.2.f \(\chi_{4016}(2007, \cdot)\) None 0 1
4016.2.j \(\chi_{4016}(1005, \cdot)\) n/a 1000 2
4016.2.k \(\chi_{4016}(1003, \cdot)\) n/a 1004 2
4016.2.m \(\chi_{4016}(113, \cdot)\) n/a 500 4
4016.2.o \(\chi_{4016}(231, \cdot)\) None 0 4
4016.2.r \(\chi_{4016}(2121, \cdot)\) None 0 4
4016.2.s \(\chi_{4016}(2239, \cdot)\) n/a 504 4
4016.2.v \(\chi_{4016}(283, \cdot)\) n/a 4016 8
4016.2.w \(\chi_{4016}(149, \cdot)\) n/a 4016 8
4016.2.y \(\chi_{4016}(241, \cdot)\) n/a 2500 20
4016.2.z \(\chi_{4016}(47, \cdot)\) n/a 2520 20
4016.2.bc \(\chi_{4016}(151, \cdot)\) None 0 20
4016.2.bd \(\chi_{4016}(25, \cdot)\) None 0 20
4016.2.bg \(\chi_{4016}(5, \cdot)\) n/a 20080 40
4016.2.bh \(\chi_{4016}(171, \cdot)\) n/a 20080 40
4016.2.bk \(\chi_{4016}(17, \cdot)\) n/a 12500 100
4016.2.bm \(\chi_{4016}(95, \cdot)\) n/a 12600 100
4016.2.bo \(\chi_{4016}(55, \cdot)\) None 0 100
4016.2.bq \(\chi_{4016}(9, \cdot)\) None 0 100
4016.2.bu \(\chi_{4016}(13, \cdot)\) n/a 100400 200
4016.2.bv \(\chi_{4016}(11, \cdot)\) n/a 100400 200

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4016))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4016)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(251))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(502))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1004))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2008))\)\(^{\oplus 2}\)