Properties

Label 104.1
Level 104
Weight 1
Dimension 2
Nonzero newspaces 1
Newforms 2
Sturm bound 672
Trace bound 0

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Defining parameters

Level: \( N \) = \( 104 = 2^{3} \cdot 13 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newforms: \( 2 \)
Sturm bound: \(672\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(104))\).

Total New Old
Modular forms 78 24 54
Cusp forms 6 2 4
Eisenstein series 72 22 50

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\( 2q - 2q^{3} + 2q^{4} + O(q^{10}) \) \( 2q - 2q^{3} + 2q^{4} - 2q^{10} - 2q^{12} - 2q^{14} + 2q^{16} - 2q^{17} + 2q^{26} + 2q^{27} + 2q^{30} + 2q^{35} - 2q^{40} + 2q^{42} - 2q^{43} - 2q^{48} + 2q^{51} - 2q^{56} + 4q^{62} + 2q^{64} - 2q^{65} - 2q^{68} - 2q^{74} - 2q^{78} - 2q^{81} - 2q^{91} - 2q^{94} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(104))\)

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
104.1.c \(\chi_{104}(103, \cdot)\) None 0 1
104.1.d \(\chi_{104}(79, \cdot)\) None 0 1
104.1.g \(\chi_{104}(27, \cdot)\) None 0 1
104.1.h \(\chi_{104}(51, \cdot)\) 104.1.h.a 1 1
104.1.h.b 1
104.1.j \(\chi_{104}(5, \cdot)\) None 0 2
104.1.l \(\chi_{104}(57, \cdot)\) None 0 2
104.1.n \(\chi_{104}(3, \cdot)\) None 0 2
104.1.p \(\chi_{104}(43, \cdot)\) None 0 2
104.1.q \(\chi_{104}(23, \cdot)\) None 0 2
104.1.t \(\chi_{104}(55, \cdot)\) None 0 2
104.1.v \(\chi_{104}(33, \cdot)\) None 0 4
104.1.x \(\chi_{104}(37, \cdot)\) None 0 4

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(104))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(104)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 2}\)