Properties

Label 672.1
Level 672
Weight 1
Dimension 4
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 24576
Trace bound 0

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Defining parameters

Level: \( N \) = \( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(24576\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(672))\).

Total New Old
Modular forms 840 104 736
Cusp forms 72 4 68
Eisenstein series 768 100 668

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 0

Trace form

\( 4 q + 2 q^{7} - 2 q^{9} + O(q^{10}) \) \( 4 q + 2 q^{7} - 2 q^{9} + 4 q^{15} - 2 q^{31} + 2 q^{33} - 2 q^{49} - 4 q^{55} - 4 q^{63} - 4 q^{73} - 2 q^{79} - 2 q^{81} - 2 q^{87} - 4 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(672))\)

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
672.1.d \(\chi_{672}(449, \cdot)\) None 0 1
672.1.e \(\chi_{672}(335, \cdot)\) None 0 1
672.1.f \(\chi_{672}(97, \cdot)\) None 0 1
672.1.g \(\chi_{672}(463, \cdot)\) None 0 1
672.1.l \(\chi_{672}(433, \cdot)\) None 0 1
672.1.m \(\chi_{672}(127, \cdot)\) None 0 1
672.1.n \(\chi_{672}(113, \cdot)\) None 0 1
672.1.o \(\chi_{672}(671, \cdot)\) None 0 1
672.1.r \(\chi_{672}(265, \cdot)\) None 0 2
672.1.t \(\chi_{672}(281, \cdot)\) None 0 2
672.1.v \(\chi_{672}(167, \cdot)\) None 0 2
672.1.x \(\chi_{672}(295, \cdot)\) None 0 2
672.1.z \(\chi_{672}(383, \cdot)\) None 0 2
672.1.ba \(\chi_{672}(305, \cdot)\) 672.1.ba.a 2 2
672.1.ba.b 2
672.1.be \(\chi_{672}(319, \cdot)\) None 0 2
672.1.bf \(\chi_{672}(145, \cdot)\) None 0 2
672.1.bg \(\chi_{672}(79, \cdot)\) None 0 2
672.1.bh \(\chi_{672}(481, \cdot)\) None 0 2
672.1.bm \(\chi_{672}(47, \cdot)\) None 0 2
672.1.bn \(\chi_{672}(65, \cdot)\) None 0 2
672.1.bp \(\chi_{672}(43, \cdot)\) None 0 4
672.1.br \(\chi_{672}(83, \cdot)\) None 0 4
672.1.bt \(\chi_{672}(13, \cdot)\) None 0 4
672.1.bv \(\chi_{672}(29, \cdot)\) None 0 4
672.1.bx \(\chi_{672}(151, \cdot)\) None 0 4
672.1.bz \(\chi_{672}(215, \cdot)\) None 0 4
672.1.cb \(\chi_{672}(137, \cdot)\) None 0 4
672.1.cd \(\chi_{672}(73, \cdot)\) None 0 4
672.1.ce \(\chi_{672}(53, \cdot)\) None 0 8
672.1.cg \(\chi_{672}(61, \cdot)\) None 0 8
672.1.ci \(\chi_{672}(59, \cdot)\) None 0 8
672.1.ck \(\chi_{672}(67, \cdot)\) None 0 8

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(672))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(672)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(224))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(336))\)\(^{\oplus 2}\)