Properties

Label 297.1
Level 297
Weight 1
Dimension 8
Nonzero newspaces 2
Newform subspaces 2
Sturm bound 6480
Trace bound 1

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Defining parameters

Level: \( N \) = \( 297 = 3^{3} \cdot 11 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
Sturm bound: \(6480\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(297))\).

Total New Old
Modular forms 312 152 160
Cusp forms 12 8 4
Eisenstein series 300 144 156

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

\( 8 q - q^{4} - 4 q^{5} + O(q^{10}) \) \( 8 q - q^{4} - 4 q^{5} + q^{11} - 3 q^{15} - q^{16} + 5 q^{20} + 2 q^{23} - 3 q^{25} - 3 q^{27} - 2 q^{31} - 3 q^{33} + 6 q^{36} - 2 q^{37} - 5 q^{44} - 4 q^{47} - 3 q^{48} - q^{49} + 2 q^{53} - 2 q^{55} - 4 q^{59} - q^{64} + 7 q^{67} + 2 q^{71} + 6 q^{75} + 2 q^{80} - q^{89} + 2 q^{92} + 6 q^{93} + 7 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(297))\)

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
297.1.b \(\chi_{297}(188, \cdot)\) None 0 1
297.1.c \(\chi_{297}(109, \cdot)\) None 0 1
297.1.h \(\chi_{297}(10, \cdot)\) 297.1.h.a 2 2
297.1.i \(\chi_{297}(89, \cdot)\) None 0 2
297.1.l \(\chi_{297}(28, \cdot)\) None 0 4
297.1.m \(\chi_{297}(26, \cdot)\) None 0 4
297.1.p \(\chi_{297}(23, \cdot)\) None 0 6
297.1.q \(\chi_{297}(43, \cdot)\) 297.1.q.a 6 6
297.1.r \(\chi_{297}(71, \cdot)\) None 0 8
297.1.s \(\chi_{297}(19, \cdot)\) None 0 8
297.1.v \(\chi_{297}(5, \cdot)\) None 0 24
297.1.w \(\chi_{297}(7, \cdot)\) None 0 24

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(297))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(297)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 2}\)