Properties

Label 1441.1
Level 1441
Weight 1
Dimension 20
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 171600
Trace bound 0

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Defining parameters

Level: \( N \) = \( 1441 = 11 \cdot 131 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(171600\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1441))\).

Total New Old
Modular forms 1324 1180 144
Cusp forms 24 20 4
Eisenstein series 1300 1160 140

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

\( 20q - 5q^{4} - 5q^{9} + O(q^{10}) \) \( 20q - 5q^{4} - 5q^{9} - 5q^{16} - 5q^{25} + 20q^{33} + 15q^{35} - 5q^{36} - 10q^{39} - 10q^{45} - 5q^{49} - 10q^{53} - 10q^{63} - 5q^{64} - 10q^{75} - 5q^{81} - 10q^{89} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1441))\)

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
1441.1.b \(\chi_{1441}(263, \cdot)\) None 0 1
1441.1.c \(\chi_{1441}(1178, \cdot)\) None 0 1
1441.1.k \(\chi_{1441}(697, \cdot)\) None 0 4
1441.1.l \(\chi_{1441}(61, \cdot)\) None 0 4
1441.1.r \(\chi_{1441}(201, \cdot)\) None 0 4
1441.1.s \(\chi_{1441}(875, \cdot)\) None 0 4
1441.1.t \(\chi_{1441}(446, \cdot)\) None 0 4
1441.1.u \(\chi_{1441}(130, \cdot)\) 1441.1.u.a 20 4
1441.1.v \(\chi_{1441}(78, \cdot)\) None 0 4
1441.1.w \(\chi_{1441}(525, \cdot)\) None 0 4
1441.1.x \(\chi_{1441}(351, \cdot)\) None 0 4
1441.1.y \(\chi_{1441}(42, \cdot)\) None 0 4
1441.1.z \(\chi_{1441}(335, \cdot)\) None 0 4
1441.1.ba \(\chi_{1441}(315, \cdot)\) None 0 4
1441.1.be \(\chi_{1441}(155, \cdot)\) None 0 12
1441.1.bf \(\chi_{1441}(230, \cdot)\) None 0 12
1441.1.bn \(\chi_{1441}(7, \cdot)\) None 0 48
1441.1.bo \(\chi_{1441}(37, \cdot)\) None 0 48
1441.1.bp \(\chi_{1441}(14, \cdot)\) None 0 48
1441.1.bq \(\chi_{1441}(21, \cdot)\) None 0 48
1441.1.br \(\chi_{1441}(39, \cdot)\) None 0 48
1441.1.bs \(\chi_{1441}(23, \cdot)\) None 0 48
1441.1.bt \(\chi_{1441}(47, \cdot)\) None 0 48
1441.1.bu \(\chi_{1441}(46, \cdot)\) None 0 48
1441.1.bv \(\chi_{1441}(105, \cdot)\) None 0 48
1441.1.bw \(\chi_{1441}(115, \cdot)\) None 0 48
1441.1.cc \(\chi_{1441}(28, \cdot)\) None 0 48
1441.1.cd \(\chi_{1441}(26, \cdot)\) None 0 48

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1441))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1441)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(131))\)\(^{\oplus 2}\)