Properties

Label 300.1
Level 300
Weight 1
Dimension 8
Nonzero newspaces 3
Newforms 4
Sturm bound 4800
Trace bound 9

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Defining parameters

Level: \( N \) = \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 3 \)
Newforms: \( 4 \)
Sturm bound: \(4800\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(300))\).

Total New Old
Modular forms 296 48 248
Cusp forms 16 8 8
Eisenstein series 280 40 240

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

\( 8q - 4q^{6} + O(q^{10}) \) \( 8q - 4q^{6} - 4q^{16} - 4q^{21} - 4q^{31} + 4q^{36} + 8q^{46} - 12q^{61} + 4q^{91} + 4q^{96} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(300))\)

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
300.1.b \(\chi_{300}(149, \cdot)\) 300.1.b.a 2 1
300.1.c \(\chi_{300}(151, \cdot)\) None 0 1
300.1.f \(\chi_{300}(199, \cdot)\) None 0 1
300.1.g \(\chi_{300}(101, \cdot)\) 300.1.g.a 1 1
300.1.g.b 1
300.1.k \(\chi_{300}(157, \cdot)\) None 0 2
300.1.l \(\chi_{300}(107, \cdot)\) 300.1.l.a 4 2
300.1.p \(\chi_{300}(31, \cdot)\) None 0 4
300.1.q \(\chi_{300}(29, \cdot)\) None 0 4
300.1.s \(\chi_{300}(41, \cdot)\) None 0 4
300.1.t \(\chi_{300}(19, \cdot)\) None 0 4
300.1.u \(\chi_{300}(23, \cdot)\) None 0 8
300.1.v \(\chi_{300}(13, \cdot)\) None 0 8

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(300))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(300)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 2}\)