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Properties

Label 3652.1
Level 3652
Weight 1
Dimension 28
Nonzero newspaces 2
Newform subspaces 5
Sturm bound 826560
Trace bound 1

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Defining parameters

Level: \( N \) = \( 3652 = 2^{2} \cdot 11 \cdot 83 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 5 \)
Sturm bound: \(826560\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3652))\).

Total New Old
Modular forms 4178 1488 2690
Cusp forms 78 28 50
Eisenstein series 4100 1460 2640

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 28 0 0 0

Trace form

\( 28 q + 4 q^{4} - 2 q^{9} + O(q^{10}) \) \( 28 q + 4 q^{4} - 2 q^{9} + 4 q^{16} + 6 q^{21} + 6 q^{23} - 2 q^{25} - 4 q^{26} - 9 q^{27} + 3 q^{33} + 4 q^{36} - 4 q^{37} - 9 q^{41} - 6 q^{49} + 6 q^{51} - 9 q^{63} + 4 q^{64} - q^{77} - 2 q^{81} - 6 q^{83} - 12 q^{87} - 9 q^{93} - 6 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3652))\)

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
3652.1.c \(\chi_{3652}(3651, \cdot)\) 3652.1.c.a 1 1
3652.1.c.b 1
3652.1.c.c 1
3652.1.c.d 1
3652.1.d \(\chi_{3652}(1827, \cdot)\) None 0 1
3652.1.g \(\chi_{3652}(2157, \cdot)\) None 0 1
3652.1.h \(\chi_{3652}(3321, \cdot)\) None 0 1
3652.1.j \(\chi_{3652}(997, \cdot)\) None 0 4
3652.1.k \(\chi_{3652}(829, \cdot)\) 3652.1.k.a 24 4
3652.1.n \(\chi_{3652}(499, \cdot)\) None 0 4
3652.1.o \(\chi_{3652}(1327, \cdot)\) None 0 4
3652.1.r \(\chi_{3652}(21, \cdot)\) None 0 40
3652.1.s \(\chi_{3652}(45, \cdot)\) None 0 40
3652.1.v \(\chi_{3652}(23, \cdot)\) None 0 40
3652.1.w \(\chi_{3652}(43, \cdot)\) None 0 40
3652.1.ba \(\chi_{3652}(19, \cdot)\) None 0 160
3652.1.bb \(\chi_{3652}(3, \cdot)\) None 0 160
3652.1.be \(\chi_{3652}(5, \cdot)\) None 0 160
3652.1.bf \(\chi_{3652}(17, \cdot)\) None 0 160

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3652))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3652)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(83))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(166))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(332))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(913))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1826))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3652))\)\(^{\oplus 1}\)