Properties

Label 420.1
Level 420
Weight 1
Dimension 12
Nonzero newspaces 2
Newform subspaces 4
Sturm bound 9216
Trace bound 1

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Defining parameters

Level: \( N \) = \( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 4 \)
Sturm bound: \(9216\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(420))\).

Total New Old
Modular forms 508 68 440
Cusp forms 28 12 16
Eisenstein series 480 56 424

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 12 0 0 0

Trace form

\( 12 q - 6 q^{9} + O(q^{10}) \) \( 12 q - 6 q^{9} - 6 q^{21} + 6 q^{24} + 6 q^{30} - 6 q^{45} - 12 q^{46} - 12 q^{61} - 12 q^{64} + 6 q^{81} + 6 q^{96} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(420))\)

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
420.1.b \(\chi_{420}(379, \cdot)\) None 0 1
420.1.e \(\chi_{420}(29, \cdot)\) None 0 1
420.1.g \(\chi_{420}(281, \cdot)\) None 0 1
420.1.h \(\chi_{420}(211, \cdot)\) None 0 1
420.1.j \(\chi_{420}(181, \cdot)\) None 0 1
420.1.m \(\chi_{420}(251, \cdot)\) None 0 1
420.1.o \(\chi_{420}(419, \cdot)\) 420.1.o.a 2 1
420.1.o.b 2
420.1.p \(\chi_{420}(349, \cdot)\) None 0 1
420.1.r \(\chi_{420}(223, \cdot)\) None 0 2
420.1.u \(\chi_{420}(293, \cdot)\) None 0 2
420.1.v \(\chi_{420}(253, \cdot)\) None 0 2
420.1.y \(\chi_{420}(323, \cdot)\) None 0 2
420.1.z \(\chi_{420}(131, \cdot)\) None 0 2
420.1.bc \(\chi_{420}(61, \cdot)\) None 0 2
420.1.bd \(\chi_{420}(229, \cdot)\) None 0 2
420.1.be \(\chi_{420}(59, \cdot)\) 420.1.be.a 4 2
420.1.be.b 4
420.1.bg \(\chi_{420}(149, \cdot)\) None 0 2
420.1.bj \(\chi_{420}(79, \cdot)\) None 0 2
420.1.bl \(\chi_{420}(151, \cdot)\) None 0 2
420.1.bm \(\chi_{420}(221, \cdot)\) None 0 2
420.1.bp \(\chi_{420}(23, \cdot)\) None 0 4
420.1.bq \(\chi_{420}(37, \cdot)\) None 0 4
420.1.bt \(\chi_{420}(17, \cdot)\) None 0 4
420.1.bu \(\chi_{420}(103, \cdot)\) None 0 4

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(420))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(420)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 2}\)