Properties

Label 252.1
Level 252
Weight 1
Dimension 6
Nonzero newspaces 2
Newform subspaces 2
Sturm bound 3456
Trace bound 1

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Defining parameters

Level: \( N \) = \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
Sturm bound: \(3456\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(252))\).

Total New Old
Modular forms 253 50 203
Cusp forms 13 6 7
Eisenstein series 240 44 196

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 6 0 0 0

Trace form

\( 6q + q^{7} + O(q^{10}) \) \( 6q + q^{7} - 4q^{16} - 3q^{19} - 4q^{22} - 5q^{25} + 4q^{28} - 3q^{31} - q^{37} + 2q^{43} + 4q^{46} - 5q^{49} + 4q^{58} + q^{67} + 3q^{73} + q^{79} + 4q^{88} + 3q^{91} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(252))\)

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
252.1.c \(\chi_{252}(197, \cdot)\) None 0 1
252.1.d \(\chi_{252}(181, \cdot)\) None 0 1
252.1.g \(\chi_{252}(127, \cdot)\) None 0 1
252.1.h \(\chi_{252}(251, \cdot)\) 252.1.h.a 4 1
252.1.m \(\chi_{252}(65, \cdot)\) None 0 2
252.1.p \(\chi_{252}(61, \cdot)\) None 0 2
252.1.q \(\chi_{252}(143, \cdot)\) None 0 2
252.1.r \(\chi_{252}(131, \cdot)\) None 0 2
252.1.s \(\chi_{252}(83, \cdot)\) None 0 2
252.1.u \(\chi_{252}(151, \cdot)\) None 0 2
252.1.v \(\chi_{252}(43, \cdot)\) None 0 2
252.1.y \(\chi_{252}(163, \cdot)\) None 0 2
252.1.z \(\chi_{252}(73, \cdot)\) 252.1.z.a 2 2
252.1.bc \(\chi_{252}(13, \cdot)\) None 0 2
252.1.bd \(\chi_{252}(229, \cdot)\) None 0 2
252.1.bg \(\chi_{252}(29, \cdot)\) None 0 2
252.1.bh \(\chi_{252}(137, \cdot)\) None 0 2
252.1.bk \(\chi_{252}(53, \cdot)\) None 0 2
252.1.bl \(\chi_{252}(67, \cdot)\) None 0 2
252.1.bn \(\chi_{252}(47, \cdot)\) None 0 2

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(252))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(252)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 2}\)