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Properties

Label 2872.1
Level 2872
Weight 1
Dimension 23
Nonzero newspaces 1
Newform subspaces 5
Sturm bound 515520
Trace bound 0

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Defining parameters

Level: \( N \) = \( 2872 = 2^{3} \cdot 359 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 5 \)
Sturm bound: \(515520\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2872))\).

Total New Old
Modular forms 2207 737 1470
Cusp forms 59 23 36
Eisenstein series 2148 714 1434

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 23 0 0 0

Trace form

\( 23 q + 4 q^{4} - 15 q^{9} + O(q^{10}) \) \( 23 q + 4 q^{4} - 15 q^{9} + 4 q^{16} - 4 q^{23} - 15 q^{25} - 4 q^{34} + 4 q^{36} - 4 q^{41} + 23 q^{49} + 4 q^{64} - 4 q^{73} + 23 q^{81} - 19 q^{90} + 15 q^{92} - 4 q^{94} - 19 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2872))\)

We only show spaces with odd 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
2872.1.b \(\chi_{2872}(717, \cdot)\) 2872.1.b.a 1 1
2872.1.b.b 1
2872.1.b.c 1
2872.1.b.d 2
2872.1.b.e 18
2872.1.d \(\chi_{2872}(719, \cdot)\) None 0 1
2872.1.f \(\chi_{2872}(2155, \cdot)\) None 0 1
2872.1.h \(\chi_{2872}(2153, \cdot)\) None 0 1
2872.1.j \(\chi_{2872}(57, \cdot)\) None 0 178
2872.1.l \(\chi_{2872}(3, \cdot)\) None 0 178
2872.1.n \(\chi_{2872}(15, \cdot)\) None 0 178
2872.1.p \(\chi_{2872}(13, \cdot)\) None 0 178

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2872))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2872)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(359))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(718))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1436))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2872))\)\(^{\oplus 1}\)