Properties

Label 384.1
Level 384
Weight 1
Dimension 2
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 8192
Trace bound 0

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Defining parameters

Level: \( N \) = \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(8192\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(384))\).

Total New Old
Modular forms 328 50 278
Cusp forms 8 2 6
Eisenstein series 320 48 272

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\( 2q + 2q^{9} + O(q^{10}) \) \( 2q + 2q^{9} - 2q^{25} - 4q^{33} - 2q^{49} - 4q^{73} + 2q^{81} + 4q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(384))\)

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
384.1.b \(\chi_{384}(319, \cdot)\) None 0 1
384.1.e \(\chi_{384}(257, \cdot)\) None 0 1
384.1.g \(\chi_{384}(127, \cdot)\) None 0 1
384.1.h \(\chi_{384}(65, \cdot)\) 384.1.h.a 1 1
384.1.h.b 1
384.1.i \(\chi_{384}(161, \cdot)\) None 0 2
384.1.l \(\chi_{384}(31, \cdot)\) None 0 2
384.1.m \(\chi_{384}(79, \cdot)\) None 0 4
384.1.p \(\chi_{384}(17, \cdot)\) None 0 4
384.1.q \(\chi_{384}(41, \cdot)\) None 0 8
384.1.t \(\chi_{384}(7, \cdot)\) None 0 8
384.1.u \(\chi_{384}(19, \cdot)\) None 0 16
384.1.x \(\chi_{384}(5, \cdot)\) None 0 16

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(384))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(384)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 2}\)