Properties

Label 304.1
Level 304
Weight 1
Dimension 1
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 5760
Trace bound 0

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Defining parameters

Level: \( N \) = \( 304 = 2^{4} \cdot 19 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(5760\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(304))\).

Total New Old
Modular forms 276 78 198
Cusp forms 24 1 23
Eisenstein series 252 77 175

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 1 0 0 0

Trace form

\( q - q^{5} + q^{7} + q^{9} + O(q^{10}) \) \( q - q^{5} + q^{7} + q^{9} + q^{11} - q^{17} - q^{19} - 2 q^{23} - q^{35} + q^{43} - q^{45} + q^{47} - q^{55} - q^{61} + q^{63} - q^{73} + q^{77} + q^{81} - 2 q^{83} + q^{85} + q^{95} + q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(304))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
304.1.d \(\chi_{304}(191, \cdot)\) None 0 1
304.1.e \(\chi_{304}(113, \cdot)\) 304.1.e.a 1 1
304.1.f \(\chi_{304}(39, \cdot)\) None 0 1
304.1.g \(\chi_{304}(265, \cdot)\) None 0 1
304.1.j \(\chi_{304}(37, \cdot)\) None 0 2
304.1.l \(\chi_{304}(115, \cdot)\) None 0 2
304.1.o \(\chi_{304}(7, \cdot)\) None 0 2
304.1.p \(\chi_{304}(217, \cdot)\) None 0 2
304.1.q \(\chi_{304}(159, \cdot)\) None 0 2
304.1.r \(\chi_{304}(65, \cdot)\) None 0 2
304.1.w \(\chi_{304}(69, \cdot)\) None 0 4
304.1.y \(\chi_{304}(11, \cdot)\) None 0 4
304.1.z \(\chi_{304}(33, \cdot)\) None 0 6
304.1.ba \(\chi_{304}(41, \cdot)\) None 0 6
304.1.bc \(\chi_{304}(23, \cdot)\) None 0 6
304.1.bf \(\chi_{304}(47, \cdot)\) None 0 6
304.1.bh \(\chi_{304}(35, \cdot)\) None 0 12
304.1.bj \(\chi_{304}(13, \cdot)\) None 0 12

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(304))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(304)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(304))\)\(^{\oplus 1}\)