Properties

Label 972.1
Level 972
Weight 1
Dimension 6
Nonzero newspaces 2
Newform subspaces 4
Sturm bound 52488
Trace bound 1

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Defining parameters

Level: \( N \) = \( 972 = 2^{2} \cdot 3^{5} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 4 \)
Sturm bound: \(52488\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(972))\).

Total New Old
Modular forms 979 198 781
Cusp forms 34 6 28
Eisenstein series 945 192 753

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 6 0 0 0

Trace form

\( 6 q + O(q^{10}) \) \( 6 q + 3 q^{19} + 3 q^{37} - 6 q^{73} - 12 q^{91} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(972))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
972.1.c \(\chi_{972}(485, \cdot)\) 972.1.c.a 1 1
972.1.c.b 1
972.1.d \(\chi_{972}(487, \cdot)\) None 0 1
972.1.f \(\chi_{972}(163, \cdot)\) None 0 2
972.1.g \(\chi_{972}(161, \cdot)\) 972.1.g.a 2 2
972.1.g.b 2
972.1.j \(\chi_{972}(55, \cdot)\) None 0 6
972.1.k \(\chi_{972}(53, \cdot)\) None 0 6
972.1.n \(\chi_{972}(19, \cdot)\) None 0 18
972.1.o \(\chi_{972}(17, \cdot)\) None 0 18
972.1.r \(\chi_{972}(7, \cdot)\) None 0 54
972.1.s \(\chi_{972}(5, \cdot)\) None 0 54

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(972))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(972)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(243))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(324))\)\(^{\oplus 2}\)