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Properties

Label 1652.1
Level 1652
Weight 1
Dimension 20
Nonzero newspaces 2
Newform subspaces 6
Sturm bound 167040
Trace bound 1

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Defining parameters

Level: \( N \) = \( 1652 = 2^{2} \cdot 7 \cdot 59 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 6 \)
Sturm bound: \(167040\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1652))\).

Total New Old
Modular forms 1790 592 1198
Cusp forms 50 20 30
Eisenstein series 1740 572 1168

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 20 0 0 0

Trace form

\( 20 q + 8 q^{4} - 2 q^{9} + O(q^{10}) \) \( 20 q + 8 q^{4} - 2 q^{9} + 6 q^{15} + 8 q^{16} - 3 q^{17} - q^{21} - 4 q^{22} + 2 q^{25} - 12 q^{27} - 4 q^{29} + 3 q^{35} + 4 q^{36} - 3 q^{45} - 4 q^{46} + 8 q^{49} - 4 q^{53} - 2 q^{57} - 6 q^{59} - 6 q^{63} + 8 q^{64} + 6 q^{71} + 6 q^{75} - 8 q^{78} - 6 q^{81} - 4 q^{84} - 4 q^{86} - 3 q^{87} - 4 q^{88} + 6 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1652))\)

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
1652.1.c \(\chi_{1652}(237, \cdot)\) None 0 1
1652.1.d \(\chi_{1652}(827, \cdot)\) None 0 1
1652.1.g \(\chi_{1652}(1651, \cdot)\) 1652.1.g.a 2 1
1652.1.g.b 2
1652.1.g.c 2
1652.1.g.d 2
1652.1.h \(\chi_{1652}(589, \cdot)\) None 0 1
1652.1.j \(\chi_{1652}(1061, \cdot)\) 1652.1.j.a 6 2
1652.1.j.b 6
1652.1.k \(\chi_{1652}(943, \cdot)\) None 0 2
1652.1.n \(\chi_{1652}(1299, \cdot)\) None 0 2
1652.1.o \(\chi_{1652}(1181, \cdot)\) None 0 2
1652.1.r \(\chi_{1652}(113, \cdot)\) None 0 28
1652.1.s \(\chi_{1652}(55, \cdot)\) None 0 28
1652.1.v \(\chi_{1652}(15, \cdot)\) None 0 28
1652.1.w \(\chi_{1652}(41, \cdot)\) None 0 28
1652.1.ba \(\chi_{1652}(5, \cdot)\) None 0 56
1652.1.bb \(\chi_{1652}(51, \cdot)\) None 0 56
1652.1.be \(\chi_{1652}(31, \cdot)\) None 0 56
1652.1.bf \(\chi_{1652}(37, \cdot)\) None 0 56

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1652))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1652)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(236))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(413))\)\(^{\oplus 3}\)