Properties

Label 208.1
Level 208
Weight 1
Dimension 3
Nonzero newspaces 2
Newform subspaces 2
Sturm bound 2688
Trace bound 1

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Defining parameters

Level: \( N \) = \( 208 = 2^{4} \cdot 13 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
Sturm bound: \(2688\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(208))\).

Total New Old
Modular forms 181 53 128
Cusp forms 13 3 10
Eisenstein series 168 50 118

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 3 0 0 0

Trace form

\( 3q + O(q^{10}) \) \( 3q - 3q^{17} - 3q^{25} - 3q^{29} - 3q^{37} + 3q^{41} + 3q^{45} + 3q^{61} + 3q^{65} + 3q^{85} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(208))\)

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
208.1.c \(\chi_{208}(207, \cdot)\) 208.1.c.a 1 1
208.1.d \(\chi_{208}(79, \cdot)\) None 0 1
208.1.g \(\chi_{208}(183, \cdot)\) None 0 1
208.1.h \(\chi_{208}(103, \cdot)\) None 0 1
208.1.j \(\chi_{208}(57, \cdot)\) None 0 2
208.1.m \(\chi_{208}(21, \cdot)\) None 0 2
208.1.o \(\chi_{208}(51, \cdot)\) None 0 2
208.1.q \(\chi_{208}(27, \cdot)\) None 0 2
208.1.r \(\chi_{208}(5, \cdot)\) None 0 2
208.1.t \(\chi_{208}(161, \cdot)\) None 0 2
208.1.v \(\chi_{208}(55, \cdot)\) None 0 2
208.1.x \(\chi_{208}(23, \cdot)\) None 0 2
208.1.y \(\chi_{208}(95, \cdot)\) 208.1.y.a 2 2
208.1.bb \(\chi_{208}(159, \cdot)\) None 0 2
208.1.bd \(\chi_{208}(33, \cdot)\) None 0 4
208.1.be \(\chi_{208}(37, \cdot)\) None 0 4
208.1.bg \(\chi_{208}(3, \cdot)\) None 0 4
208.1.bi \(\chi_{208}(43, \cdot)\) None 0 4
208.1.bl \(\chi_{208}(141, \cdot)\) None 0 4
208.1.bn \(\chi_{208}(41, \cdot)\) None 0 4

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(208))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(208)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 2}\)