Properties

Label 336.1
Level 336
Weight 1
Dimension 8
Nonzero newspaces 3
Newform subspaces 5
Sturm bound 6144
Trace bound 3

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Defining parameters

Level: \( N \) = \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 5 \)
Sturm bound: \(6144\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(336))\).

Total New Old
Modular forms 366 52 314
Cusp forms 30 8 22
Eisenstein series 336 44 292

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 8 0 0 0

Trace form

\( 8q + q^{3} + q^{7} - q^{9} + O(q^{10}) \) \( 8q + q^{3} + q^{7} - q^{9} - 2q^{13} - q^{19} - 4q^{21} - q^{25} - 2q^{27} - q^{31} - 5q^{37} - q^{39} + 2q^{43} - q^{49} - 2q^{57} - 2q^{61} + q^{63} - q^{67} - 5q^{73} + q^{75} - q^{79} - q^{81} - q^{91} + 7q^{93} + 4q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(336))\)

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
336.1.d \(\chi_{336}(113, \cdot)\) None 0 1
336.1.e \(\chi_{336}(167, \cdot)\) None 0 1
336.1.f \(\chi_{336}(97, \cdot)\) None 0 1
336.1.g \(\chi_{336}(295, \cdot)\) None 0 1
336.1.l \(\chi_{336}(265, \cdot)\) None 0 1
336.1.m \(\chi_{336}(127, \cdot)\) None 0 1
336.1.n \(\chi_{336}(281, \cdot)\) None 0 1
336.1.o \(\chi_{336}(335, \cdot)\) 336.1.o.a 1 1
336.1.o.b 1
336.1.r \(\chi_{336}(13, \cdot)\) None 0 2
336.1.t \(\chi_{336}(29, \cdot)\) None 0 2
336.1.v \(\chi_{336}(83, \cdot)\) None 0 2
336.1.x \(\chi_{336}(43, \cdot)\) None 0 2
336.1.z \(\chi_{336}(47, \cdot)\) 336.1.z.a 2 2
336.1.z.b 2
336.1.ba \(\chi_{336}(137, \cdot)\) None 0 2
336.1.be \(\chi_{336}(79, \cdot)\) None 0 2
336.1.bf \(\chi_{336}(73, \cdot)\) None 0 2
336.1.bg \(\chi_{336}(151, \cdot)\) None 0 2
336.1.bh \(\chi_{336}(145, \cdot)\) None 0 2
336.1.bm \(\chi_{336}(215, \cdot)\) None 0 2
336.1.bn \(\chi_{336}(65, \cdot)\) 336.1.bn.a 2 2
336.1.bp \(\chi_{336}(67, \cdot)\) None 0 4
336.1.br \(\chi_{336}(59, \cdot)\) None 0 4
336.1.bt \(\chi_{336}(53, \cdot)\) None 0 4
336.1.bv \(\chi_{336}(61, \cdot)\) None 0 4

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(336))\) into lower level spaces

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