Properties

Label 441.1
Level 441
Weight 1
Dimension 14
Nonzero newspaces 4
Newform subspaces 4
Sturm bound 14112
Trace bound 4

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Defining parameters

Level: \( N \) = \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 4 \)
Sturm bound: \(14112\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(441))\).

Total New Old
Modular forms 508 232 276
Cusp forms 28 14 14
Eisenstein series 480 218 262

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 14 0 0 0

Trace form

\( 14q + 2q^{4} + q^{7} + O(q^{10}) \) \( 14q + 2q^{4} + q^{7} - 2q^{16} - 12q^{22} - 2q^{25} - q^{28} - 3q^{37} - 2q^{43} - q^{49} - 7q^{52} - 7q^{61} + 5q^{64} - 4q^{67} - 4q^{79} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(441))\)

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
441.1.b \(\chi_{441}(197, \cdot)\) 441.1.b.a 2 1
441.1.d \(\chi_{441}(244, \cdot)\) None 0 1
441.1.j \(\chi_{441}(263, \cdot)\) None 0 2
441.1.k \(\chi_{441}(31, \cdot)\) None 0 2
441.1.l \(\chi_{441}(97, \cdot)\) None 0 2
441.1.m \(\chi_{441}(19, \cdot)\) 441.1.m.a 2 2
441.1.n \(\chi_{441}(128, \cdot)\) None 0 2
441.1.q \(\chi_{441}(116, \cdot)\) 441.1.q.a 4 2
441.1.r \(\chi_{441}(50, \cdot)\) None 0 2
441.1.t \(\chi_{441}(166, \cdot)\) None 0 2
441.1.v \(\chi_{441}(55, \cdot)\) 441.1.v.a 6 6
441.1.x \(\chi_{441}(8, \cdot)\) None 0 6
441.1.bc \(\chi_{441}(40, \cdot)\) None 0 12
441.1.be \(\chi_{441}(29, \cdot)\) None 0 12
441.1.bf \(\chi_{441}(44, \cdot)\) None 0 12
441.1.bi \(\chi_{441}(2, \cdot)\) None 0 12
441.1.bj \(\chi_{441}(10, \cdot)\) None 0 12
441.1.bk \(\chi_{441}(13, \cdot)\) None 0 12
441.1.bl \(\chi_{441}(61, \cdot)\) None 0 12
441.1.bm \(\chi_{441}(11, \cdot)\) None 0 12

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(441))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(441)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 2}\)