Properties

Label 392.1
Level 392
Weight 1
Dimension 11
Nonzero newspaces 3
Newform subspaces 5
Sturm bound 9408
Trace bound 1

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Defining parameters

Level: \( N \) = \( 392 = 2^{3} \cdot 7^{2} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 5 \)
Sturm bound: \(9408\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(392))\).

Total New Old
Modular forms 379 108 271
Cusp forms 19 11 8
Eisenstein series 360 97 263

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 11 0 0 0

Trace form

\( 11q + q^{2} - q^{4} - 5q^{8} + q^{9} + O(q^{10}) \) \( 11q + q^{2} - q^{4} - 5q^{8} + q^{9} - q^{16} - q^{18} - 6q^{22} - 2q^{23} + q^{25} + q^{32} + q^{36} - 6q^{43} + 2q^{46} - q^{50} - 12q^{57} + 11q^{64} - 4q^{71} - q^{72} + 2q^{79} - q^{81} + 4q^{92} + 6q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(392))\)

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
392.1.c \(\chi_{392}(97, \cdot)\) None 0 1
392.1.d \(\chi_{392}(295, \cdot)\) None 0 1
392.1.g \(\chi_{392}(99, \cdot)\) 392.1.g.a 1 1
392.1.g.b 2
392.1.h \(\chi_{392}(293, \cdot)\) None 0 1
392.1.j \(\chi_{392}(117, \cdot)\) 392.1.j.a 2 2
392.1.k \(\chi_{392}(67, \cdot)\) 392.1.k.a 2 2
392.1.k.b 4
392.1.n \(\chi_{392}(79, \cdot)\) None 0 2
392.1.o \(\chi_{392}(129, \cdot)\) None 0 2
392.1.r \(\chi_{392}(13, \cdot)\) None 0 6
392.1.s \(\chi_{392}(43, \cdot)\) None 0 6
392.1.v \(\chi_{392}(15, \cdot)\) None 0 6
392.1.w \(\chi_{392}(41, \cdot)\) None 0 6
392.1.ba \(\chi_{392}(17, \cdot)\) None 0 12
392.1.bb \(\chi_{392}(23, \cdot)\) None 0 12
392.1.be \(\chi_{392}(11, \cdot)\) None 0 12
392.1.bf \(\chi_{392}(5, \cdot)\) None 0 12

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(392))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(392)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 2}\)