Properties

Label 276.1
Level 276
Weight 1
Dimension 6
Nonzero newspaces 1
Newforms 4
Sturm bound 4224
Trace bound 0

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Defining parameters

Level: \( N \) = \( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newforms: \( 4 \)
Sturm bound: \(4224\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(276))\).

Total New Old
Modular forms 232 50 182
Cusp forms 12 6 6
Eisenstein series 220 44 176

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

\( 6q - 3q^{6} + O(q^{10}) \) \( 6q - 3q^{6} - 3q^{12} + 3q^{18} - 6q^{25} + 3q^{36} + 3q^{48} - 6q^{49} - 6q^{52} - 6q^{58} + 6q^{64} + 3q^{78} + 6q^{82} + 6q^{93} + 6q^{94} - 3q^{96} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(276))\)

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
276.1.b \(\chi_{276}(229, \cdot)\) None 0 1
276.1.d \(\chi_{276}(185, \cdot)\) None 0 1
276.1.f \(\chi_{276}(139, \cdot)\) None 0 1
276.1.h \(\chi_{276}(275, \cdot)\) 276.1.h.a 1 1
276.1.h.b 1
276.1.h.c 2
276.1.h.d 2
276.1.j \(\chi_{276}(11, \cdot)\) None 0 10
276.1.l \(\chi_{276}(31, \cdot)\) None 0 10
276.1.n \(\chi_{276}(29, \cdot)\) None 0 10
276.1.p \(\chi_{276}(37, \cdot)\) None 0 10

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(276))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(276)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 6}\)